From 4a9cfb56048e10e688745605289cbe76de84a0bf Mon Sep 17 00:00:00 2001
From: Tony <tonychen950529@gmail.com>
Date: Fri, 6 Dec 2024 17:43:53 +0800
Subject: [PATCH] =?UTF-8?q?=E7=8E=B0=E6=9C=89=E8=A7=A3=E6=B3=95python?=
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---
 ...7.\350\247\243\346\225\260\347\213\254.md" | 84 +++++++++++--------
 1 file changed, 50 insertions(+), 34 deletions(-)

diff --git "a/problems/0037.\350\247\243\346\225\260\347\213\254.md" "b/problems/0037.\350\247\243\346\225\260\347\213\254.md"
index 6a9f69bd07..5f3f881cf1 100644
--- "a/problems/0037.\350\247\243\346\225\260\347\213\254.md"
+++ "b/problems/0037.\350\247\243\346\225\260\347\213\254.md"
@@ -366,40 +366,56 @@ class Solution:
         """
         Do not return anything, modify board in-place instead.
         """
-        self.backtracking(board)
-
-    def backtracking(self, board: List[List[str]]) -> bool:
-        # 若有解，返回True；若无解，返回False
-        for i in range(len(board)): # 遍历行
-            for j in range(len(board[0])):  # 遍历列
-                # 若空格内已有数字，跳过
-                if board[i][j] != '.': continue
-                for k in range(1, 10):
-                    if self.is_valid(i, j, k, board):
-                        board[i][j] = str(k)
-                        if self.backtracking(board): return True
-                        board[i][j] = '.'
-                # 若数字1-9都不能成功填入空格，返回False无解
-                return False
-        return True # 有解
-
-    def is_valid(self, row: int, col: int, val: int, board: List[List[str]]) -> bool:
-        # 判断同一行是否冲突
-        for i in range(9):
-            if board[row][i] == str(val):
-                return False
-        # 判断同一列是否冲突
-        for j in range(9):
-            if board[j][col] == str(val):
-                return False
-        # 判断同一九宫格是否有冲突
-        start_row = (row // 3) * 3
-        start_col = (col // 3) * 3
-        for i in range(start_row, start_row + 3):
-            for j in range(start_col, start_col + 3):
-                if board[i][j] == str(val):
-                    return False
-        return True
+        row_used = [set() for _ in range(9)]
+        col_used = [set() for _ in range(9)]
+        box_used = [set() for _ in range(9)]
+        for row in range(9):
+            for col in range(9):
+                num = board[row][col]
+                if num == ".":
+                    continue
+                row_used[row].add(num)
+                col_used[col].add(num)
+                box_used[(row // 3) * 3 + col // 3].add(num)
+        self.backtracking(0, 0, board, row_used, col_used, box_used)
+
+    def backtracking(
+        self,
+        row: int,
+        col: int,
+        board: List[List[str]],
+        row_used: List[List[int]],
+        col_used: List[List[int]],
+        box_used: List[List[int]],
+    ) -> bool:
+        if row == 9:
+            return True
+
+        next_row, next_col = (row, col + 1) if col < 8 else (row + 1, 0)
+        if board[row][col] != ".":
+            return self.backtracking(
+                next_row, next_col, board, row_used, col_used, box_used
+            )
+
+        for num in map(str, range(1, 10)):
+            if (
+                num not in row_used[row]
+                and num not in col_used[col]
+                and num not in box_used[(row // 3) * 3 + col // 3]
+            ):
+                board[row][col] = num
+                row_used[row].add(num)
+                col_used[col].add(num)
+                box_used[(row // 3) * 3 + col // 3].add(num)
+                if self.backtracking(
+                    next_row, next_col, board, row_used, col_used, box_used
+                ):
+                    return True
+                board[row][col] = "."
+                row_used[row].remove(num)
+                col_used[col].remove(num)
+                box_used[(row // 3) * 3 + col // 3].remove(num)
+        return False
 ```
 
 ### Go