PythonTraining.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "daily_balances = [107.92, 108.67, 109.86, 110.15]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "daily_balances.reverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[107.92, 108.67, 109.86, 110.15]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "daily_balances"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_balances(balance):\n",
    "    b_len = len(daily_balances)\n",
    "    \n",
    "    for day in range(b_len-3,b_len-1):\n",
    "        print(\"Slice starting %d days ago: %s\" % (abs(b_len-day), balance[day:day+2]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slice starting 3 days ago: [108.67, 109.86]\n",
      "Slice starting 2 days ago: [109.86, 110.15]\n"
     ]
    }
   ],
   "source": [
    "show_balances(daily_balances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[109.86, 108.67]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "daily_balances[-2:0:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import re\n",
    "\n",
    "# with regex subn function\n",
    "re.subn('[A-Z]', '', string)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "def countCaps(filename):\n",
    "    with open(filename) as fh:\n",
    "        count = 0\n",
    "        for line in fh:\n",
    "            for char in line:\n",
    "                count += 1 if char.isupper() else 0\n",
    "    return count"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "# as a one-liner\n",
    "def countCaps(filename):\n",
    "    with open(filename) as fh:\n",
    "        return sum(char.isupper() for line in fh for char in line)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "countCaps('test.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Pet(object):\n",
    "    num_pets = 0\n",
    "\n",
    "    def __init__(self, name):\n",
    "        self.name = name\n",
    "        Pet.num_pets += 1\n",
    "\n",
    "    def speak(self):\n",
    "        print(\"My name's %s and the number of pets is %d\" % (self.name, self.num_pets))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "rover = Pet(\"rover\")\n",
    "spot = Pet(\"spot\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "My name's rover and the number of pets is 2\n",
      "My name's spot and the number of pets is 2\n"
     ]
    }
   ],
   "source": [
    "rover.speak()\n",
    "spot.speak()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 2, 3], [2, 4, 6], [3, 6, 9]]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iterator = [i for i in range(1, 4)]\n",
    "matrix = [[x * y for y in iterator] for x in iterator]\n",
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement a queue ↴ with 2 stacks. ↴ Your queue should have an enqueue and a dequeue method and it should be \"first in first out\" (FIFO)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import deque"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Queue(object):\n",
    "    def __init__(self):\n",
    "        self.in_stack = deque()\n",
    "        self.out_stack = deque()\n",
    "        \n",
    "    def enqueue(self, item):\n",
    "        self.in_stack.append(item)\n",
    "        \n",
    "    def dequeue(self):\n",
    "        if not self.out_stack:     # if stack is empty\n",
    "            while self.in_stack:   # while stack not empty\n",
    "                self.out_stack.append(self.in_stack.pop())\n",
    "        return self.out_stack.pop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# q = Queue()\n",
    "q.enqueue(1)\n",
    "q.enqueue(2)\n",
    "q.enqueue(3)\n",
    "assert(q.dequeue() == 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "q.enqueue(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q.dequeue()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compute the nth Fibonacci number\n",
    "\n",
    "def fib(n):\n",
    "    if n < 0: raise \"Error\"\n",
    "    if n in [0,1]: return n\n",
    "    \n",
    "    #recursive solution\n",
    "    #elegant but takes O(2^n) time\n",
    "    #return fib(n-1)+fib(n-2)  \n",
    "\n",
    "    #iterative solution runs in O(n) time\n",
    "    prev2 = 0\n",
    "    prev1 = 1\n",
    "    \n",
    "    for _ in range(n-1):\n",
    "        current = prev1+prev2\n",
    "        prev2 = prev1\n",
    "        prev1 = current\n",
    "        \n",
    "    return current\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given an array of integers, return indices of the two numbers such that they add up to a specific target.\n",
    "You may assume that each input would have exactly one solution, and you may not use the same element twice.\n",
    "Example: Given nums = [2, 7, 11, 15], target = 18,\n",
    "nums[1] + nums[2] = 7+ 11= 18, return [1, 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nums.index(11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def myFunc(nums, targ):\n",
    "    n = nums.copy()\n",
    "    for i in nums:\n",
    "        n.remove(i)\n",
    "        for j in n:\n",
    "            if (i+j == targ):\n",
    "                return [nums.index(i),nums.index(j)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  4,  49, 121, 225])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array(nums)\n",
    "y = np.array(nums)\n",
    "x*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2,  7, 11, 15]])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[None,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def myMatrixFunc(nums, targ):\n",
    "    m = np.array(nums)[:,None] + np.array(nums)[None, :]\n",
    "    res = np.where(np.triu(m, k=1) == targ)\n",
    "    return [res[0][0], res[1][0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def myFunc(nums, targ):\n",
    "    for i in nums:\n",
    "        n = nums.copy()\n",
    "        n.remove(i)\n",
    "        for j in n:\n",
    "            if (i+j == targ):\n",
    "                return [nums.index(i),nums.index(j)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "nums = range(100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%time res = myFunc(nums, 17)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 771 ms, sys: 429 ms, total: 1.2 s\n",
      "Wall time: 1.2 s\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[0, 17]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time res = myMatrixFunc(nums, 17)\n",
    "res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FizzBuzz\n",
    "\n",
    "Write a program that prints the numbers from 1 to 100. But for multiples of three print “Fizz” instead of the number and for the multiples of five print “Buzz”. For numbers which are multiples of both three and five print “FizzBuzz”.”"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3 - Fizz\n",
      "4\n",
      "5 - Buzz\n",
      "6 - Fizz\n",
      "7\n",
      "8\n",
      "9 - Fizz\n",
      "10 - Buzz\n",
      "11\n",
      "12 - Fizz\n",
      "13\n",
      "14\n",
      "15 - FizzBuzz\n",
      "16\n",
      "17\n",
      "18 - Fizz\n",
      "19\n",
      "20 - Buzz\n"
     ]
    }
   ],
   "source": [
    "for i in range(1,21):\n",
    "    if i%3==0:\n",
    "        if i%5==0:\n",
    "            print(\"%i - FizzBuzz\" % i)\n",
    "        else:\n",
    "            print(\"%i - Fizz\" % i)\n",
    "    elif i%5==0:\n",
    "        print(\"%i - Buzz\" % i)\n",
    "    else:\n",
    "        print(i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "Fizz\n",
      "4\n",
      "Buzz\n",
      "Fizz\n",
      "7\n",
      "8\n",
      "Fizz\n",
      "Buzz\n",
      "11\n",
      "Fizz\n",
      "13\n",
      "14\n",
      "FizzBuzz\n",
      "16\n",
      "17\n",
      "Fizz\n",
      "19\n",
      "Buzz\n"
     ]
    }
   ],
   "source": [
    "for i in range(1,21):\n",
    "    fizz = 'Fizz' if i%3==0 else ''\n",
    "    buzz = 'Buzz' if i%5==0 else ''\n",
    "    print(f\"{fizz}{buzz}\" or i)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write a function to generate X samples from a normal distribution and plot the histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def histPlot(samps, center=0):\n",
    "    x = np.random.randn(samps) + center\n",
    "    plt.hist(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "histPlot(100,23)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "return the rows where the students favorite color is green or yellow and their grade is above 90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({'age': [24,19,22,21], 'favorite color': ['green', 'blue', 'yellow', 'green'], 'grade': [88,95,92,70]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>favorite color</th>\n",
       "      <th>grade</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>24</td>\n",
       "      <td>green</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>19</td>\n",
       "      <td>blue</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>yellow</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>21</td>\n",
       "      <td>green</td>\n",
       "      <td>70</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age favorite color  grade\n",
       "0   24          green     88\n",
       "1   19           blue     95\n",
       "2   22         yellow     92\n",
       "3   21          green     70"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age</th>\n",
       "      <th>favorite color</th>\n",
       "      <th>grade</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>24</td>\n",
       "      <td>green</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>22</td>\n",
       "      <td>yellow</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age favorite color  grade\n",
       "0   24          green     88\n",
       "2   22         yellow     92"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[(df['favorite color'].isin(['green','yellow'])) & (df['grade'] > 80)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Input: [\"1, 3, 4, 7, 13\", \"1, 2, 4, 13, 15\"]\n",
    "Output: 1,4,13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "strArr = [\"1, 3, 4, 7, 13\", \"1, 2, 4, 13, 15\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 4, 7, 13]"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(map(int, strArr[0].split(', ')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def FindIntersection(strArr):\n",
    "    arr1 = strArr[0].split(\", \").map(int)\n",
    "    arr2 = strArr[1].split(\", \").map(int)\n",
    "\n",
    "    lst = []\n",
    "    for i in arr1:\n",
    "        for j in arr2:\n",
    "            if i < j: pass\n",
    "            if i == j:\n",
    "                lst.append(i)\n",
    "    return \",\".join(lst) if lst else 'False'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def FindIntersection(strArr):\n",
    "    a = map(int, strArr[0].split(\", \"))\n",
    "    b = map(int, strArr[1].split(\", \"))\n",
    "    \n",
    "    return ','.join(map(str, (set(a) & set(b))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1,4,13'"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# keep this function call here \n",
    "FindIntersection(strArr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "arr = [[1,1,1,0,0,0],\n",
    "       [0,1,0,0,0,0],\n",
    "       [1,1,1,0,0,0],\n",
    "       [0,0,2,4,4,0],\n",
    "       [0,0,0,2,0,0],\n",
    "       [0,0,1,2,4,0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 1, 1, 0, 0, 0],\n",
       " [0, 1, 0, 0, 0, 0],\n",
       " [1, 1, 1, 0, 0, 0],\n",
       " [0, 0, 2, 4, 4, 0],\n",
       " [0, 0, 0, 2, 0, 0],\n",
       " [0, 0, 1, 2, 4, 0]]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hourglassSum(arr):\n",
    "    res = []\n",
    "    for row in range(1,5):\n",
    "        for col in range(1,5):\n",
    "            #res.append(arr[row][col])  #centers\n",
    "            res.append(arr[row-1][col-1]+arr[row-1][col]+arr[row-1][col+1]+\n",
    "                       arr[row][col]+\n",
    "                       arr[row+1][col-1]+arr[row+1][col]+arr[row+1][col+1])\n",
    "    return max(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hourglassSum(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 1, 1, 0, 0, 0], [0, 1, 0, 0, 0, 0], [1, 1, 1, 0, 0, 0]]"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arr[0:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 1, 1], [0, 1, 0], [1, 1, 1]]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sl = [arr[i][0:3] for i in range(0,3)]\n",
    "sl"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[7, 4, 2, 0, 4, 8, 10, 8, 3, 6, 7, 6, 3, 9, 19, 14]"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum = []\n",
    "for i in range(len(arr)-2):\n",
    "    for j in range(len(arr)-2):\n",
    "        sum.append(arr[i][j]+arr[i][j+1]+arr[i][j+2]+arr[i+1][j+1]+arr[i+2][j]+arr[i+2][j+1]+arr[i+2][j+2])\n",
    "sum\n",
    "# print(max(sum))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = 'AABCAAADA'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AB\n",
      "CA\n",
      "AD\n"
     ]
    }
   ],
   "source": [
    "idxs = list(range(0,len(s),3))\n",
    "for i in idxs:\n",
    "    t = s[i:i+3]\n",
    "    u = ''\n",
    "    for c in t:\n",
    "        if c not in u: u+=c\n",
    "    print(u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [],
   "source": [
    "import datetime, time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [],
   "source": [
    "def time_delta(t1, t2):\n",
    "    fmt = '%a %d %b %Y %H:%M:%S %z'\n",
    "    t1 = datetime.datetime.strptime(t1, fmt)\n",
    "    t2 = datetime.datetime.strptime(t2, fmt)\n",
    "    return abs(int((t1-t2).total_seconds()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25200"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "time_delta('Sun 10 May 2015 13:54:36 -0700', 'Sun 10 May 2015 13:54:36 -0000')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "88200"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t1 = \"Sat 02 May 2015 19:54:36 +0530\"\n",
    "t2 = \"Fri 01 May 2015 13:54:36 -0000\"\n",
    "time_delta(t1,t2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [],
   "source": [
    "def game(s):\n",
    "    vowels = 'AEIOU'\n",
    "    v = 0\n",
    "    c = 0\n",
    "    for i in range(len(s)):\n",
    "        if s[i] in vowels:\n",
    "            v += len(s[i:])\n",
    "        else:\n",
    "            c += len(s[i:])\n",
    "    \n",
    "    if v == c: print('Draw'); return\n",
    "    if v > c:\n",
    "        print(f'Kevin {v}')\n",
    "    else:\n",
    "        print(f'Stuart {c}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stuart 12\n"
     ]
    }
   ],
   "source": [
    "s = 'banana'\n",
    "game(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 258,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vowels = 'AEIOU'\n",
    "'B' in vowels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 270,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Draw\n"
     ]
    }
   ],
   "source": [
    "game('BANANANAAAS')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 267,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(4,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def percentIncreasePerYear(start, pct, years):\n",
    "    for i in range(years):\n",
    "        res = start*pct\n",
    "        start+=res\n",
    "    return start"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3582.1568895869996"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "percentIncreasePerYear(3000, .03, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = list(range(2800,3500,100))\n",
    "y = [percentIncreasePerYear(xx, .03, 6) for xx in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(.01,.03,20) #list(range(.02,.03,.001))\n",
    "y = [percentIncreasePerYear(3200, xx, 6) for xx in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc0b5d64990>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, label='6 years')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc0b5f0bc90>]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, [percentIncreasePerYear(3200, xx, 3) for xx in x], label='3 years')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix Multiplication by hand"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = [[1,2,3],[2,3,4]]\n",
    "b = [[2,3],[4,5],[6,7]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def matmul(a,b):\n",
    "    ar,ac = len(a),len(a[0])\n",
    "    br,bc = len(b),len(b[0])\n",
    "    assert(ac == br)\n",
    "    c = [[0]*bc for _ in range(ar)]\n",
    "    \n",
    "    for i in range(ar):\n",
    "        for j in range(ac):\n",
    "            for k in range(bc):\n",
    "                c[i][k] += a[i][j] * b[j][k]\n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[28, 34], [40, 49]]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matmul(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[28, 34],\n",
       "       [40, 49]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.matmul(np.array(a),np.array(b))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.random.random((50,100))\n",
    "b = np.random.random((100,1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "def matmul(a,b):\n",
    "    ar,ac = a.shape\n",
    "    br,bc = b.shape\n",
    "    assert(ac == br)\n",
    "    c = np.zeros((ar,bc))\n",
    "    \n",
    "    for i in range(ar):\n",
    "        #for j in range(ac):   # full 3 loops\n",
    "            for k in range(bc):   # elementwise mult\n",
    "                c[i,k] = (a[i,:] * b[:,k]).sum()   # same as a np.dot(a[i,:], b[:,:])\n",
    "                #c[i] = (np.expand_dims(a[i],1) * b).sum(axis=0)  # broadcasting\n",
    "                \n",
    "    return c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.2 s, sys: 4.42 ms, total: 4.2 s\n",
      "Wall time: 4.2 s\n"
     ]
    }
   ],
   "source": [
    "# full 3 loops\n",
    "%time res = matmul(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 265 ms, sys: 2.56 ms, total: 267 ms\n",
      "Wall time: 266 ms\n"
     ]
    }
   ],
   "source": [
    "# elementwise mult\n",
    "%time res = matmul(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 380 ms, sys: 3.01 ms, total: 383 ms\n",
      "Wall time: 381 ms\n"
     ]
    }
   ],
   "source": [
    "# elementwise mult\n",
    "%time res = matmul(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 8.2 ms, sys: 1.26 ms, total: 9.46 ms\n",
      "Wall time: 8.07 ms\n"
     ]
    }
   ],
   "source": [
    "# broadcasting\n",
    "%time res = matmul(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.61 ms, sys: 1.21 ms, total: 3.82 ms\n",
      "Wall time: 2.24 ms\n"
     ]
    }
   ],
   "source": [
    "# einsum\n",
    "%time res = np.einsum('ij,jk->ik',a,b) #matmul(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.51 ms, sys: 291 µs, total: 1.8 ms\n",
      "Wall time: 409 µs\n"
     ]
    }
   ],
   "source": [
    "%time truth = np.matmul(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "def near(a,b): return np.allclose(a, b, rtol=1e-3, atol=1e-5)\n",
    "assert(near(res,truth))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[19, 10, 62, 86],\n",
       "       [62, 49, 23,  2],\n",
       "       [99, 28, 78, 49]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = np.random.randint(0, 101, (3,4))\n",
    "m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = np.random.randint(0,5, (4,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "assert( np.all( m.dot(n) == np.matmul(m,n) ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[99 49 78 86]\n",
      "[86 62 99]\n"
     ]
    }
   ],
   "source": [
    "print(m.max(axis=0))\n",
    "print(m.max(axis=1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.random.random(50)\n",
    "y_hat = np.random.random(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# mean squared error\n",
    "mse = np.mean(np.square(y - y_hat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True ^ False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "True ^ True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 53\n",
    "b = 7421"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "a ^= b\n",
    "b ^= a\n",
    "a ^= b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7368 7421\n"
     ]
    }
   ],
   "source": [
    "print(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b1000111100101011000000'"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(2345664)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b11'"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b100'"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Magic Square"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[5, 3, 4], [1, 5, 8], [6, 4, 2]]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s = [[5, 3, 4], [1, 5, 8], [6, 4, 2]]\n",
    "# s = np.array(s)\n",
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "flat_s = [item for sublist in s for item in sublist]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5, 3, 4, 1, 5, 8, 6, 4, 2]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flat_s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 12, 14])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.sum(axis=0) #col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([12, 14, 12])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.sum(axis=1) #row"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 5, 2])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.diagonal(axis1=0, axis2=-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[8, 3, 4], [1, 5, 9], [6, 7, 2]]"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol = [[8, 3, 4], [1, 5, 9], [6, 7, 2]]\n",
    "# sol = np.array(sol)\n",
    "sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8, 3, 4, 1, 5, 9, 6, 7, 2])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(sol).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[8, 3, 4, 1, 5, 9, 6, 7, 2]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flat_sol = [item for sublist in sol for item in sublist]\n",
    "flat_sol"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(np.array(flat_s) - np.array(flat_sol)).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum([1,2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# center has to be 5\n",
    "# opposites sum to 10\n",
    "# corners are evens\n",
    "# center edges are odd (w/out 5)\n",
    "# 7,9,8 need to be fully separated\n",
    "\n",
    "def formingMagicSquare(s):\n",
    "    flat_s = [item for sublist in s for item in sublist]\n",
    "    p = permutations(range(1,10))\n",
    "    res = 999\n",
    "    for i in p:\n",
    "        if sum(i[0::3]) == sum(i[1::3]) == sum(i[2::3]) == sum(i[0:3]) == sum(i[3:6]) == sum(i[6:9]):\n",
    "            res = min( res, sum([abs([flat_s[ii] - i[ii]]) for ii in range(0,10)]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from itertools import permutations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "perfects = []\n",
    "for i in p:\n",
    "    if i[]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [],
   "source": [
    "pp = next(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(pp[0::3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def formingMagicSquareHelper(s, res):\n",
    "    if len(set(s.flatten()))==9:\n",
    "        if np.all(s.sum(axis=0)==15):\n",
    "            if np.all(s.sum(axis=1)==15):\n",
    "                return res\n",
    "    else:\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(set(s.flatten()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.all(s.sum(axis=0)==15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[7, 8, 6],\n",
       "       [0, 5, 4],\n",
       "       [7, 8, 6]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.randint(0,10,(3,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 7, 1, 4, 5, 6, 9, 8, 2])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.permutation(range(1,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8494c2ad90>]"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1152x648 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16,9))\n",
    "\n",
    "ax1 = fig.add_subplot(2,2,1)\n",
    "\n",
    "ax2 = fig.add_subplot(2,2,2)\n",
    "ax3 = fig.add_subplot(2,2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f84963de450>]"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax3.plot(np.random.randn(50).cumsum(), 'k--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 3 Axes>"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8496435910>]"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IKHIBkuJs27YN9+/fx+effy5hZNmLEXXq1EmrJUglUVj2N8XLGFfyISEhpFAoaNy4cXodn3tFu3HjRokjM63cr6OaxvBmZmaSs7MzjR07Vqc6Fy1aRABM1i9+9+5dWr16NT/9aiYWLFhAQ4cONUpbuRML6vutQa1Wk4eHB3l4eMh2H27mzJk0c+ZMSeoCd9fkN27cOLKystJrwiO1Wk2tW7em2rVrFzlELzMzkzZu3Khx5Ie5CA0NLbTr6b///qPPP/887w2ekpJS7OPnKSkp+bp6evbsSZ6entIFzJiW1Go1tW3blmrVqqXXUNrcB/jkvJgbNWoUOTg4GPSgZi5O8i+Jj48nBwcH8vX11ev4Q4cOEQBatmyZxv2pqanUv39/AkBff/21IaHKRqVSUfv27alSpUoaH7f+4osvCIBOU6U2bNgw3+RgaWlpFB4eLkm8+kpMTKRffvmFb7qb2L179yS/+V6cEydO0Nq1a3V6cC/X7du3adKkSZKOgHnZ2bNnCQCtXr3a4Lo4yWvQoUMH6tChg97HT5gwIe+hnBdlZGRQp06d8ibKGj58uCFhymb9+vUEgH799VeN+1UqFb377rsEQOspHXx8fMjJyUn2eUN0ER0dTQD0egSdSUOtVlODBg3o3XffNXUoZiW3V6Bp06YGdwkVleRL3Y3XXDt27MDhw4f1Pn7FihXo3Llzge02Njbo1q0btmzZgs8//xxKpdKQMGURHx+PadOmoX379hg1apTGMgqFAhs2bMhbLtHe3r7Yert27YqEhARcunQJy5Ytw5dffill2HqpWbMmOnTogD/++MPUoZRaly9fxq1btzT+vchNpVJhxYoV8PPz0/qY1atX4/z58zJGlU0IgbFjx+Lq1asICAiQr6HCsr8pXsa8kpfC48ePacaMGfTo0SOKiIigc+fOmTokrfj4+JC1tbVW9ySePn1K//zzj1ZXGg8ePCAAtHDhQmrSpAm98cYbUoRrsNWrVxMAs150wpLNnDmTrKysTDKLq1qtJqVSSfXq1dOq2yYqKoqsra1p0qRJRogu+/kTX19fnefBeRm4u6agqKgomjBhAl2+fFnvOq5du0YKhYIGDRpELi4u5ObmVuChidTUVL36BOW0bt062SZba9asGTVq1Ei2SaL08fDhQ1IoFDR79mxTh1LqqNVqcnV1pe7du5sshn379hEA2rBhQ7Flp0yZQlZWViXuHg4neQ3u3r1LAGjNmjUG1ZO7OlL16tULXCkeP36chBB0/Phxg9ooSQ4dOkRjx44lAAZ9gErtjTfeoHfeecfUYZQ6Fy5cIAC0bt06k8WgVqupVatW5OrqWuSTq0+fPiVHR0ejDfN80bNnzwyaUK+oJF9q++Rr1aqFcuXK4fr16wbV880332DcuHE4depUgYeB6tSpAyLCzZs3DWpDKleuXMGPP/6IlJQU2dro1q0bnjx5gqpVq6JZs2aytaMrf39/bN++3dRhlDpNmzbFn3/+iQEDBpgsBiEE5syZg/DwcGzbtq3QcmvXrkVSUpLkDz9pw9HREba2trLUXWqTvEKhgLu7O8LCwgyqp1q1ali1ahXq1atXYF/t2rVhZ2eHGzduGNSGVFasWIGpU6ciMzNT1nYSExPRvXt34z3Rp4WyZcsCgMHnrlar8eDBA6jVainCsni2trbo3bs3XnnlFZPG0bdvX7z//vuoU6dOoWWsrKwwcOBAtG7d2oiRZZP1b6WwS3xTvIx943XYsGFUp04dWdto1qwZ9e7dW9Y2tPH06VMqV65cgfll5HD8+PF8Cxqbi2XLllGNGjV0Hvv8008/0ciRI0mpVJK9vT0BoO+//16mKC3HlStX6H//+5/ZLpt5+/Zt+vzzzzVOulfSgLtrNGvcuDFUKhUyMjJka6Nhw4Zm0V2zdetWpKSk4OOPP5a9rY4dO8LFxUX2dnTVoEEDxMTE4MCBA8WWffE9sXPnThw5cgROTk748MMPMWzYsCKvCFm2zZs3Y+HChVAozCfNPHr0CH379kX37t3h5uaGpUuXIjEx0aK/mYnsDwHzoFQqKSgoyGjtqdVq2d+A/v7+iIqKwoQJE2RtpyhEhObNm8PGxgZBQUFm1Y1iTJmZmahRowY6depU7Ljpzp07w8PDAytXrkRmZiZsbGyMFKVlICK4urrC3d1d44R3prJr1y4MHjwYVapUwbhx4/DRRx+Z5QWJroQQF4hI40M51sYOxpwY4wqjX79+srdRnKdPn6J8+fIYOXJkqU3wQPaDakOHDsUvv/yCZ8+eoUKFChrLBQYG4vjx43n/dpoSfEJCAs6dO4cePXrIGrM21Go1Ro0ahZo1a2LhwoWmDgcAcPHiRURERGD27NmmDiWfQYMGISQkBO7u7qXng7uwfhxTvIzdJ69Wq+ntt982eP3RoqhUKgoPD9e4apKxWeqqVrrIXeCkqCF9vXv3pkqVKtHz588LLTNhwgSytbUtdjUtY1i8eDEBoPLly8s614oupk+fTlZWVhQfH2/qUEoFcJ+8ZkIIBAcH4/jx47K1kZiYCFdXV2zatEm2NoqSlJSE+Ph4ADLfwS8hlEolvvvuO3Tq1Enj/itXrmD//v2YOHFikVM5fPDBB0hPT8eWLVtkilQ7Z86cwcyZM+Hq6goHBwfcuXPHpPHkSktLQ+/evVGpUiVTh1LqleokDwCNGjUyeBhlUSpWrAhnZ2dZhlGq1WocP368yJtGv/76K2rUqIGoqCjJ2y+JhBCYOnUqXF1dNe5fsmQJHBwcMH78+CLrad68OZRKJdauXZv9VKGJpKenQ6lU4uzZs7h37x4aNWpkslhetGzZMuzZs8fUYTBwkkfjxo1x69YtZGVlydZGw4YNJU/yRIQxY8Zg+/bthV6hExF+/vlntGzZErVr15a0/ZLur7/+wr59+wpsX7JkCfz8/ODk5FRsHR999BFCQ0ONMplVYTp27IjAwEBUqlQJQgio1WqTfugAwPPnzwHwN0dzwUm+cWNkZGQgIiJCtjbc3d0lTfJEhMmTJ+OXX37J++MOCQlBXFxcvnIBAQEICwszyrDJkmbBggWYNWtWgYTo7OyMN998U6s6hg4dCnt7exw7dkyOEIv0888/Y+7cuVCpVHnJ9NSpU6hVqxauXLli9HhyUfa9NYwbN85kMbD8Sn2Sb9asGby9vfOuPuTg7u6OuLg4JCQkSFLfF198geXLl2PSpEmYP38+MjIy0LdvX7Rv3x53797NK/fzzz+jQoUKGDJkiCTtWpIRI0bg6tWruHz5MgAgNjYWnTt3RnBwsNZ1lC9fHhEREZg+fbpcYWp0+fJlTJw4EefPn893tezm5obY2FiN31CM5cqVK7h58yY8PT1NFgN7SWF3ZE3xKmlTDRfn7NmzlJycTNevXyc/Pz9KTk42uM4lS5YQAPL19c03WubkyZNUsWJFql69Ol2+fJkSExPJzs6OJkyYYHCblig+Pp5sbGxoypQpREQ0depUUigUdPv2bb3qM9ZCKUlJSdSwYUNycXHRuBzjq6++Skql0iixaPLFF1+QQqEwi9FkpQl4Fkrji4qKIgA0evRoSeu9cOECTZgwQeNSaqGhoVSjRg2qUKECHT9+nG7dukVRUVGStm9J+vXrR9WrV6e4uDhycHDQe+WiadOmGbTKmC5GjRpFCoWCjh07pnH/ggULCEC+tXaNRa1Wk7u7O3Xp0sXobZd2JknyABYDuA7gCoA9ACoWd4ypkvzYsWMln+/6999/JwB0+PBhIsq+0j5//rze9Wk7bW9kZCQ1btyYBgwYoHdbpcXOnTupdu3aNHr0aIOmRv7hhx8IAF25ckXiCPOLjIwkhUJBM2bMKLRMaGioJFNo6+PKlSsEgH788Uejt13amSrJdwdgnfPztwC+Le4YUyb5ChUqSPqw0JgxY8jR0TFv/uoGDRrkW+RaF//88w8JIWjLli1alY+Pjy/yQR6WLSsri5KSkqhSpUrUq1cvveuJi4sjGxsbmjhxooTRaRYeHk5PnjwpdL9arabp06fTmTNnZI/lZQkJCbR27VruqjGBopK8UeauEUIMADCYiN4rqpyx567JtXLlSnz66ae4f/8+qlevLkmdzZo1Q1ZWFkaMGAEfHx989NFHiIyM1GvkQ9u2bfHw4UOEhobmTZnLpJGWloZ169bBy8sLXl5eetczZMgQHD58GDExMbCzs5MwQsaKV9TcNcYaXeMDQOMsRUIIXyFEkBAi6OUhgMbSuHFjADB4AZFcycnJuHv3Ltzc3DB79mwEBgbC3d0dt27d0nm2u9OnT+P06dOYPHkyJ3gZ2NnZYfz48QYleAD48MMP8eTJE+zdu1eiyPL76aef0KdPHyQnJxdblohw8eJFXL16VZZYNAkPD8ePP/6IZ8+eGa1Nph2DkrwQ4rAQIlTDq98LZWYDyAKwVVMdRPQLESmJSFmlShVDwtFbbpKX6slXe3t7PHnyBBs3boSNjQ3OnTsHd3d3pKWl6fzk6dKlS1GxYkWMHj1aktjM0eHDhzFq1Kh8wz9Lmq5du2LRokVo27at5HUTEVauXImHDx8WOdVCrqysLHTt2hWLFy+WPJbCbN26FePHj0dqaqrR2mRaKqwfR4oXgFEATgMop015U/XJq9Vqevfdd+nPP/+UvG6lUkmdO3em48ePEwA6cOCA1sc+f/6cqlatStOnT5c8LnOhVqupWbNmBIAcHBxo165dpg7JYHFxcRQWFiZZfUeOHCEAtHHjRq2Pee+996hSpUpGG9rp4eFBr7/+ulHaYgXBRDdeewK4BqCKtsdYyhBKHx8fWrFiBRERjRs3jhwdHenp06cUGBio8w3RlJQUevr0qRxhmoXcBPbVV19R7969KTQ01NQhGaxXr15UuXJlCg4OlqS+AQMGUKVKlSg1NVXrY7Zv304AKCAgQJIYihIWFkYA8t7zzPiKSvJy9smvAuAI4JAQIlgIsUbGtiSRlJRkcB2pqanYvHkzYmJiAABeXl7IyMjAkydP8Nprr2n1dRvInnhKpVKhbNmyhc57bglCQkJQs2ZNTJ06FX/++SeaNm0KAPD19cXy5cuhUqkkaWfbtm1YtWqVJHUVZ+nSpbCzs0Pnzp1h6ECC6Oho+Pv748MPP9Tphm6PHj1gY2NjlKdfd+zYASEEBg0aJHtbTA+FZX9TvEx5Jb9s2TICQImJiQbVc+zYMQJA+/fvJyKi1NRUysjIICKiAwcO0IYNG7Sq5/vvvydXV9cih8tZirS0tAK/9+rViwBQ+/btKSkpyaD6c8dv6zuEVR937tyhunXrUvny5SkwMFDveh4/fkzz58+niIgInY994403qEWLFnq3ra3333/faA+DMc3AT7wWb8+ePQSAzp07Z1A9X331FQkhNCbn4cOHU61atYqtIzMzk2rXrk0dO3Y0KBZzFxsbW+g+tVpN69evJwC0ZMkSvdtIS0uj5s2bU9WqVTVOAyCnyMhIcnV1pRYtWmh8Qllud+/elWQqDW28/EHNjKuoJF/qJyjLlTsPt6EjbAICAuDh4ZFvqto1a9bAx8cHDRs2RHR0dLHD4Hbv3o2oqCh89tlnBsVizp4+fQo3NzcsWLBA434hBHx8fNCpUycsW7YMmZmZerUzb948XL58GWvXroW1tTV+//13Q8LWSe3atfHff//B399fr6UmDx8+DD8/P727rOrUqYNy5crl2/bs2TOEh4frVZ8mubHZ2tpKVieTFif5HK6urrC2tjZ4rHzNmjXRv3//fNuioqKwefNm1KtXDwBw69atIuv44Ycf4Obmht69exsUizlbv349kpOT0bNnzyLLTZ06FRUqVEB0dLTObQQHB+Pbb7/FBx98gD59+mDr1q147733dJpp0lAuLi6oXbs20tLScOTIEZ2OnTNnDr744guD5mVfv349nJyc0K5dOzg7O6NixYro06cPgOwEHRsbq3fdAPDqq69i1qxZBtXBZFbYJb4pXqYeXdOoUSPq37+/5PXmdgX99ttvBID++OOPQsueOXOGANDq1aslj8NcZGZmUp06dbQacqdWq/WebkKlUtFPP/1Ez549I6Ls/u0yZcrQp59+qld9hpg+fTpZW1vTjRs3tCp/4cIFAkBLly41qN2ff/45r+vvww8/pG+//TZvqHCPHol9n6wAACAASURBVD3otdde07vu3FE1y5cvNyhGZjhwn7x21q5dW2QCLk5h/ZIxMTEEIG/B5fnz5xdaR1ZWFu3evdui557ZtWsXAaDdu3drfUxiYiKFh4frVF6TIUOG0CuvvGL0PuQHDx6Qo6Mj9e3bV6vyPj4+VK5cOUpISJAtppUrVxIAOnXqlF7H595/MsWMlyw/TvJGMnDgQOrUqZPGfTVq1KBhw4ZRTEyMSW7CmZMePXpQ3bp1tX5QR61WU5MmTahr165alT9w4ABVqlSJLl68qHEfAPLz89MpZiksXLiQANCRI0eKLPf48WOys7MjX19fWeN5/vw5vfLKK3rPWNqsWTNq3769xFExfRSV5LlP/gWZmZm4evWqXvNvEBECAgJQq1Ytjft79eoFJycnuLi4aLwJl5GRgQ8++ADffPONzm2XNH5+fti1axesrKy0Ki+EwKhRo3DkyBFcvHixyLJPnjyBj48PqlWrljddxYu6deuGWrVq4ezZs3rFbohJkyahTp06+Oyzz4q8mXr37l3Url0bEyZMkDUee3t7jB07Fnv37i32PtHLrl+/jpCQELzzzjsyRcckU1j2N8XL1Ffy58+f17kbIdeNGzcIAP3yyy9Fljt06BB9/PHH+fqZnzx5Qp07dyYA9O233+rcttxSUlJMHQI9ffqUHB0di1zYIzMzkwYOHEjW1tYar+JzydkFUpw//viDvL29ixw+SkSSTntdlAcPHpCtrS3NnDlTp+NiY2Np/vz5FBMTI1NkTBfg7hrtJCUlEQD65ptvdD523bp1BKDYOUuWL19OAOj+/ftElP3QTKNGjcjGxoY2b96sV9xy2rhxI02aNEmSpBMTE0OtW7fW++GgKVOmkJWVFd29e7fAvrS0NOrbty8BoO+//16r+nLn+jem4m4kX7hwodD7Mffu3aO2bdsadN+osDaNNccNk0dRSZ67a17g4OCAmjVr6jWMMiAgAFWqVIG7u7vG/RkZGWjYsCEuXLgAALh58yYSExPz5oo/dOgQhg8fblD8UktNTcXs2bPzZoc8ceIE5s+fr9V0t5r89NNPuHjxIpydnfU6fuLEiRBCwN/fv8A+GxsbVKxYEatWrdLq+YL58+ejRYsW2Vc6RiSEgBACjx49KjDlQFpaGnr37o2RI0fm254bY7Vq1RAYGIgpU6bo/dyAJq1atYKVlZXW/y8iIyOxe/dupKWlSRYDk1Fh2d8UL1NfyRMRde/enZo2barzcf7+/sUue9a4cWPq0qULAaCff/6ZiLK/ARgyY2FsbCwFBATQ1q1baeHChTRmzBjJRuZ8//33BICOHz9ORESzZ88mAOTi4kLr16/X6epPrVZT7dq16a233jIoppev4qOiovIe+dfl28amTZsIAP33338GxaMvHx8fsrOzo8jIyLxta9asybdkJBHRX3/9RS1btsxbbWn//v15w3GltH37dmrSpIlWXXO5o2q4q8Z8gLtrtLdq1SoCQJcuXZK87lGjRlGVKlUIALVp08bg+i5cuEBCCAKQ93JycqLw8HCKj4+nwYMHU0hIiF51P3v2jCpVqlRg7dtTp07Rq6++SgDI09OToqOjtaov936HLtPlFiUtLS1v4fI2bdro3J30/PlzcnR0lHyhdW1FRkaSnZ0dDRgwgIKCguj27dtUr1498vb2JrVaTY8ePaJhw4YRAGratCldvXqViLI/yDw8PKhp06aSjtI6ceIEAaCffvqp2LI8qsb8cJLXwZMnT+jPP//Uqb/21q1bFBISUmyiWb16NQGgwYMH09ixYw0Nla5du0YffPAB7d+/n65du5ZvIq/Y2FiqWrUqNWrUSK8JvubNm0cANC4+rlarafv27VSmTBmtH9qaMWMGWVtb0+PHj3WO5WXLli0jFxcXqlixIlWvXl3vBbg//PBDsre3N3hSOn3NmTMn78O5Tp06BID8/f2pY8eOVLZsWbKxsaEvv/yS0tPT8x23ZcsWAkAHDx4sto1NmzbRyJEji31vqtVqatOmDTVo0KDIb2jXrl3jaYXNECd5mY0fP57s7e2L/WDIvZrdvn27UeI6cuQIKRQKGj58uM5Xuv/++y/NmDGjyDJxcXFa17dr1y6aPXu2TjEU5vDhwwSA3N3dNd6E1dapU6cIAK1fv16SuHSlVqspMDCQ/P39qXv37uTh4UEqlYoWLlxI48ePL3Ru/czMTDp48GCx/6bXr18nOzs7AqDVwt5+fn4EgPbs2VNomXnz5nFXjRniJK+j58+f0+zZs+mff/7Rqnzz5s2pW7duxZZLT08nX19fOn36tKEh0p07d+jixYvF/qHnXpGvXbvW4DYLY6zhfi+2988//xj8rUCtVtOSJUv0msZXDlJ8y3nRgAEDyMnJiezt7enDDz8stnxmZibVq1eP2rZtW2iZXr168bTCZoiTvI6ysrKoRo0aWt0kTEhIICEEffnll0aI7P9NnjyZypQpU+yqUVlZWdStWzdydXUt8LVfk5iYGJo5c6bW89gPGzaMPvnkkyLLnD9/Pm/IKMsvt/9dHwsXLqR33nmn0P1PnjyhkydP0tSpU7V+f+7fv59OnDhBarWaYmNjC/T7q9VqyT+MmOE4yeth5syZpFAoiv1amjs+/ujRo1rVq1KpKCwszKAx2iqVimrWrKn1PCgPHz7MG51RnDFjxpCNjQ3duXNHq/KjRo2i8uXLF7k0naenp9neqEtPT6cdO3YU+fCUnA4dOkS2trZ08uRJnY/95ptvNA4SiImJyVuoxhDe3t5UrVo1+uSTT+jgwYOS1MnkwUleDzdv3iQAtGjRokLLqNVqatmyJb322mtaj3TYunUrAdD7ZiERUWBgIAHQ+eGpzMxM2rZtW6HdK+Hh4WRtba3TTeGDBw8SANq5c6fG/bdu3SIA9MMPP+gUq7FkZGRQuXLlaMKECSZpv1OnTuTi4qLXhGkJCQnk6OhIQ4cOzduWnp5OLVu2pDfffDNfWZVKpfNEZNu2baPBgwdTuXLl8m4QG7KAC5MPJ3k9tW/fntzd3Yvsc05MTNSpTzf3w8OQPvJJkyaRra1t3hS62tq4cSMBoLFjx9Lff/9d4Gv3iBEjqGzZsjp1rWRlZVG1atUKnaL522+/JQAG3SCVW5cuXah58+ZGb/f06dMGfwBOnTqVFAoF3b59m4j+f8TO3r1785X78ccfCYBeQ2pTUlLI39+fPv74Yzp27JjesTL5cJLX0+bNm+ntt9/WOMQuNjZWqz7ul6nVanJycsp39aUrd3d36tevn87HqVQqGjZsGCkUirwrs3bt2hER0dWrV8nBwYGmTp2qc72TJ08mGxsbjX21Xl5epFQqda7TmObOnUtCCKPPaZPbriFDOGNiYqhMmTL0ySef0Pnz58nKyopGjhxZoNyjR4/IxsaGJk2aZEjIzExxkpeYWq2mjh07Urt27fQaWTJlyhQSQmg1rE2T5ORkioqK0utYouxvH0ePHqUFCxbQ119/TUTZ3RZt2rSh+Ph4nesLCQmhr7/+usDN2ocPH5IQghYuXKh3rMZw5MgRAkB//fWXUdsdNGgQNWjQwOB61q1bR6dPn6YmTZpQjRo1Cv2wevvtt6lSpUq8HqsF4iRvoOvXr+dbEHnbtm0EgNasWaNXfYmJieTi4kLDhg2TKkSDqdXqfI/YSyU6Olqn8fSmkJycTNbW1kYfIXXt2rW8KSMMFRERQR4eHnTgwIFCy/z7779GfU6DGQ8neQPkPsCUe5MzKSmJXFxcqFWrVgbN3BcWFqbzaAWVSkXdu3enXbt26d2uXFJTU2nHjh0ldpWgqKgoo4/3l1px70eVSkV16tShIUOGGCkiZixFJXmehbIYrVq1Qr169bBhwwYAwNdff4379+9j1apVWi96oUmjRo1gY2ODZ8+e4fHjx1odc+rUKRw8eBDp6el6tyuX2NhYvP322/jtt98AAI8ePUKfPn2KXeTDXNSqVcugBbN1FRUVhQ0bNmj9b6+N4t6PCoUChw8fxpYtWyRrk5k/2ZO8EOJzIQQJISrL3ZYcFAoFRo8ejaNHjyI8PBwnTpzA6NGj8dprrxlcd3p6Opo3b45JkyZpVX7Hjh2ws7ND7969DW5bavXq1UO7du2wefNmEBH27t2L/fv3G/RBaEzR0dEYOXIkzp07Z5T2jh8/Dh8fH8TFxRmlvVxubm6wtrY2apvMtGRN8kKIWgDeABAlZztyGzVqFIQQ2LJlC06ePImVK1dKUq+trS1GjBiBLVu24MSJE0WWValU2LlzJ9566y04OjpK0r7Uhg8fjrCwMAQHB2PXrl1wdXWFp6enqcPSir29PTZv3oyDBw8apb3Q0FDY2trCzc3NKO29aMuWLfD29i5yCUJmOeS+kl8KYBqyh+uVWHXq1EHnzp1x+/ZtWFlZwcHBQbK6Z82ahXr16mHs2LHIyMgotNypU6cQGxtr1mtqvv3227CxscGqVatw9OhRDBo0yKhdIIZ45ZVX4OHhgYCAAKO0FxISgsaNG5vkqrpcuXI4d+4c/v33X6O3zYxPtiQvhOgLIIaILhdTzlcIESSECDL2V1ddzJs3r9BFug1RtmxZrFixAteuXcOyZcsKLVemTBn07dsXvXr1kjwGqVSqVAlvvvkmfv31V2RlZWHgwIGmDkknr7/+OgIDA5GVlSV7W6GhoWjWrJns7WjSu3dvODs7Y926dSZpnxlZYXdktXkBOAwgVMOrH4CzACrklLsLoHJx9Znj6Bpj6devHw0aNKjEj/B49uwZ+fn5Uc+ePSVd1MIYcofGBgUFydpOQkKCyRdtnzp1KllbW9P+/ftNFgOTDooYXSOy90tLCNEMwBEAKTmbagK4D8CLiB4UdpxSqaSgoCDJ4ykJUlJSULZsWQghMGLECCQnJ8PW1hZlypSBWq3GF198Uej6sUwaMTEx6NatG1auXIlu3brJ2lZcXBwUCgUqVaokazuFefDgAXr27InIyEhERESgYsWKJomDSUMIcYGIlJr2ydIhSEQhAPJWaxZC3AWgJKJ4OdqzBOXKlcv7OSYmBnFxcUhPT0dGRgbS09MRGhqK06dPw87OzoRRWrYaNWogLCzMKG1VqVLFKO0Uplq1ajhz5gyuXr2KihUrgogQHR2N2rVry9quSqXCnj17StT9mpKOx8mboaNHjyIkJAQ3b97E3bt3ERsbi0uXLnGCNxK1Wg05vuHm2rBhA5YuXSpb/dqys7ND69atAQBr1qxB48aNsWHDBtnOnYgwefJkvP322/jzzz9x584dWdph+RklyRNRXb6KZyXBwYMHUblyZdy4cUO2NjZu3Ihdu3bJVr8++vbtC29vb/j4+GDo0KHYvHlzvmcGQkNDcefOHajVar3bWLZsGVauXInPPvsMX3/9NXx8fKQInRWDr+QZe0HdunWRkJAg21BKIkJISAg8PDxkqV9fNWrUwKFDh/DNN99g165dGDlyJH7++WcA2TE3b94crq6umD17tl7179q1C1OmTMGgQYOwePFitG/fHmfOnDHLp7ctDSd5xl7QoEEDODs7y5bkY2NjkZCQYLLhk0WxsrLCrFmzEB8fj1u3buGrr74CkJ3k/fz80KZNG+zdu1fneuPj4zFq1Ci8+uqr2Lx5MxQKBTp06ID09HSU1oEWxsRJnrEXCCHQoUMH2ZJ8SEgIAJjdlfyLKlasCDc3N9SoUQNA9tQegwYNwrvvvovr168jKkq3B9grV66M3bt3Y9++fShbtiwAoH379gCA//77T9rgWQGc5Bl7SYcOHXD37l1ER0dLXveDBw9gZ2dn1km+MD169AAArZ+UjY+Pz5smonv37qhc+f+nr6pSpQoaN25stCeMSzOeqYixl/To0QPTpk2DQiH9NdCoUaMwfPjwEjNx24saN24Mf39/dOzYUavy8+fPxy+//ILo6Oh8CT7XypUrNW5n0pLlYSh9leaHoRizJGq1GjVr1sSrr76K3bt3mzoci1fUw1DcXcOYBmlpaTh//rykdapUKnTp0gU7d+6UtF5jSkhIwKJFi3DlypUiy2kzoR4RYfv27Th+/LjEUbIXcZJnTIOlS5fCy8tL0kU9wsPDcezYMSQlJUlWpynMnj272A8qPz+/Ytc+EEJgxowZWLVqldQhshdwkmdMg86dOwOAXkMGCxMaGgrAvEfWFMfJyQne3t5F3nwlIhw5cgS9evUqdlru3JFM5tRtbGk4yTOmgbe3Nzw8PLBq1SrJElBISAiEEGjSpIkk9ZlKjx49cP78+UK/5QghEBwcrNUV+uuvv45Hjx7h5s2bUofJcnCSZ0wDIQTGjx+P4OBgBAYGSlJnaGgo6tevD3t7e0nqM5UePXqAiHD48OFCy5QpUwbVqlUrtq4OHToAAA+llBEnecYKMXz4cFSoUAF+fn6S1Fe1alV0795dkrpMqU2bNqhWrRoiIyML7FOpVHj99dexfft2repq2LAhnJ2dERwcLHWYLAePk2esEPb29jh37pxk67Bayg1GKysrREVFwcbGpsC+gIAABAQEYPz48VrVJYRAaGgoj5eXEV/JM1aEhg0bQqFQaNUvn5ycjMzMTCNEZXqaEjwA7NixA2XLltVpmcoqVarw3PIy4iTPWDE2btyIZs2aFbnQ+uPHj9G0aVO0a9cOycnJBfZv3boV9evXx7179+QM1WhSU1PRtm3bfOsSq1Qq7Ny5E71799bpvkNCQgLee+89/Pnnn3KEWupxkmesGM7Ozrh69Sr27NmjcT8RwcfHB/fv38eDBw80JvIrV64gJiYGVatWlTtcoyhbtiyePXuGv//+O2/bf//9h0ePHhX5AJQm5cuXx/79+/HXX39JHSYDJ3nGitWzZ0/Ur18fK1eu1Lh/5cqV2LdvHxYvXowbN25oXIs3JCQEjRo1KrSboyTq0aMH/vvvP6SkZC/l7OjoiCFDhuCtt97SqR4rKyu0a9eOZ6SUCSd5xoqhUCgwbtw4nDp1CpcuXcq3LysrC7/++iv69OmDTz/9FGXLloVKpcKUKVPw008/5ZULDQ01yznkDdGzZ0+kp6fjxIkTAAClUok//vgj33rF2urQoQPCwsIQFxcndZilHid5xrTw/vvvo1y5cli9enW+7dbW1jh16hQ2bdqU7+bhjRs3MGHCBBw4cABPnz5FdHR0iX7SVZMOHTrAzs4O//77LyIiIhAeHq53Xa+//joA4OTJk1KFx3JwkmdMC05OTli1ahV8fX0BZPfDr1+/HsnJybC3t4eTk1NeWSsrK2zbtg0eHh545513EBQUhI8//jgvkVmKsmXLYurUqWjTpg2+++47NG/eHGlpaXrVpVQq0apVK6hUKomjZDzVMGN62LBhA3x8fLBixQpMmDBBY5l79+7B29sbVlZWOHv2LKpXr27kKI0jKysLLi4u6NKlC/744w9Th1Mq8VTDjEnk+vXrmDRpEsaPH4/OnTtj7NixhZatWbMm9u/fj5SUFFy+fNmIURrXjh07EBcXp/OoGk1UKhWysrIkiIrl4iTPmA5CQ0OxfPly2NvbY8uWLcWu8NSyZUtERESgZ8+eRorQuIgIw4YNAwC8+eabBtV16dIlvPLKKzhy5IgUobEcPK0BYzro168fxowZg6FDh8LFxUWrYxwdHWWOynSEEPj111/x/PnzvEW69dWgQQOkpKTg2LFjeevJMsPJ2icvhJgAYDyALAB/EdG0ospznzxjpVv79u2Rnp4u+apcls4kffJCiM4A+gHwJKKmAJbI1RZjzDJ069YNFy5cQEJCgqlDsRhy9smPAbCIiNIBgIgeydgWY8wCdO3aFUTE675KSM4k3xBAByHEWSHECSFEG02FhBC+QoggIUQQP+3GWOnm7e2NWbNmoVGjRqYOxWIY1CcvhDgMQNPyL7MBfAPgKICJANoA2A6gPhXRIPfJM8aY7orqkzdodA0RdSui0TEAduck9XNCCDWAygD4cp0xVqj09HQEBgbC09MTlSpVMnU4JZ6c3TV7AXQBACFEQwBlAMTL2B5jzAKEhYWhS5cuPPWwRORM8r8CqC+ECAXwB4BRRXXVMMYYAHh6eqJy5cr8UJREZHsYiogyAAyXq37GmGVSKBTo0qULjhw5AiLipQENxNMaMMbMTteuXRETE4ObN2+aOpQSj5M8Y8zsdO3aFQBw9OhRE0dS8vHcNYwxs1O/fn2cPXsWLVu2NHUoJR5fyTPGzI4QAl5eXkWuiXvnzh3Mmzcvb41ZphknecaYWYqJicHkyZMRGhqqcf+0adPw5Zdf4pNPPsGNGzeMHF3JwUmeMWaWrKyssGzZMo3j5U+cOIFdu3bBx8cHmzdvxrFjx0wQYcnASZ4xZpaqVauGpk2b4vDhw/m2q1QqTJ48GbVq1cLKlStRuXJlnDt3zkRRmj9O8owxs9W1a1ecPHky3wLhmzZtwqVLl/Ddd9+hXLly8Pb2xtmzZ00YpXnjJM8YM1vdunVDWloaTp8+nbetVatW+PTTTzFkyBAAgJeXF8LCwpCYmGiqMM0aJ3nGmNnq2LEjqlevjocPH+Zta9GiBZYvX573JKy3tzcqVKiA8PBwU4Vp1jjJM8bMVvny5RETE4OhQ4fi7t27+OCDD/IlfCD7av/Jkyc8pr4QnOQZY2Yt94p92rRp2LZtGzIzM/Ptt7Ky4vltisBJnjFm1m7evAkhBHbs2IFp06ahZs2aBcqsX78eXbp0AU90WxAnecaYWatTp07ez1OnTtVYJjU1FceOHcO9e/eMFVaJwXPXMMbMmq2tLX7//XfUrl0b9vb2Gst4e3sDAM6ePYtatWoZMzyzx1fyjDGz9+6776Jdu3aF7vf09ESZMmX4oSgNOMkzxko8W1tbtGzZkh+K0oC7axhjFqFfv36IjIw0dRhmh5M8Y8wizJw509QhmCXurmGMWQwiQmpqqqnDMCuc5BljFqNp06aYMGGCqcMwK5zkGWMWo06dOjzC5iWc5BljFsPLywtXr17F8+fPTR2K2ZAtyQshWgghzgghgoUQQUIIL7naYowxIPuhKLVajaCgIFOHYjbkvJL/DsA8ImoBYE7O74wxJhsvr+xrSe6y+X9yJnkCUD7n5woA7svYFmOMoXLlyvjqq6+KfDq2tBFyzdomhGgM4F8AAtkfJm2JqMCTCkIIXwC+AFC7du3W/DADY4zpRghxgYiUmvYZdCUvhDgshAjV8OoHYAyAyURUC8BkAOs11UFEvxCRkoiUVapUMSQcxhhDRkYGzp8/j2fPnpk6FLNgUJInom5E5KHh5Q9gFIDdOUV3AOAbr4wx2V24cAFeXl44evSoqUMxC3L2yd8H0DHn5y4AbsnYFmOMAQBatmwJa2trvvmaQ865az4CsFwIYQ0gDTn97owxJic7Ozs0b96cZ6TMIVuSJ6KTAFrLVT9jjBXG29sbv/32G1QqFaysrEwdjknxE6+MMYvj5eWF58+f48aNG6YOxeQ4yTPGLM6bb76Jo0ePol69eqYOxeR4PnnGmMVxdnaGs7OzqcMwC3wlzxizSIGBgVi7dq2pwzA5TvKMMYu0c+dOTJw4EVlZWaYOxaQ4yTPGLJJSqURqaiquXbtm6lBMipM8Y8wiKZXZU7mU9mmHOckzxiySm5sbypcvz0ne1AEwxpgcFAoFWrdujZCQEFOHYlI8hJIxZrH8/Pzg5ORk6jBMipM8Y8xiVa5c2dQhmBx31zDGLFZKSgo++eQT7N2719ShmAwnecaYxSpbtix27NiBv//+29ShmAwnecaYxRJCQKlUluoRNpzkGWMWTalUIiQkBGlpaUZp79q1a0ZrSxuc5BljFk2pVCIrKwtXrlyRtZ20tDT873//Q4sWLbB48WJZ29IFj65hjFk0pVKJunXr4smTJ7K1cfz4cfj6+uLWrVsYOXIkxowZI1tbuuIrecaYRatVqxYiIiLQs2dPWepfvHgxOnfuDJVKhUOHDmHTpk2IiopC//798fTpU1na1AUnecYYM0CPHj0wY8YMhISEoFu3bgAAlUoFf39/+Pn5mTg6TvKMsVJg27ZtqFu3LpKTkyWp7/Lly5g8eTIyMzPh6emJhQsXoly5cnn7lUolmjZtig0bNkjSniE4yTPGLJ6DgwMiIyMRHBxscF0PHz5E3759sWPHjkL7+YUQGD16NM6cOYPr168b3KYhOMkzxiyeVNMOp6enY+DAgYiLi8O+fftQtWrVQsu+9957sLKywqZNmwxq01A8uoYxZvGqV6+OGjVqGJTkiQi+vr4IDAzEjh070KpVq2Lb/OSTT1CnTh2925QCJ3nGWKlg6JOvt27dws6dOzFv3jwMHjxYq2NWrVqld3tSMai7RgjxthDiqhBCLYRQvrRvphDithDihhCih2FhMsaYYQYMGIDu3buDiPQ6vmHDhrhy5Qr+97//6XRcWloaAgMD9WpTCob2yYcCGAjgvxc3CiGaABgKoCmAngB+FEJYGdgWY4zpbdSoUVi+fDmEEDodFxISgrVr1wIAXF1ddT5+1qxZ6NKlCxISEnQ6TioGJXkiCiOiGxp29QPwBxGlE1EEgNsAvAxpizHGDJWVlaXTk6+5I2nmzp2LZ8+e6dXme++9h/T0dGzfvl2v4w0l1+iaGgCiX/j9Xs62AoQQvkKIICFEUFxcnEzhMMYY4OHhgbFjx2pVNjU1Ff3798fDhw+xb98+VKhQQa82W7VqBQ8PD2zcuFGv4w1VbJIXQhwWQoRqePUr6jAN2zR2hBHRL0SkJCJllSpVtI2bMcZ05uHhodXNV7Vajffffx9nzpzBli1b8oZg6kMIgffffx9nz55FWFhYvn3nz5+Hr68vVCqV3vUXp9gkT0TdiMhDw8u/iMPuAaj1wu81Adw3NFjGGDOEUqlEeHh4sf3jAQEB2L59O7799lsMHDjQ4HZzx8z7+2enzbCwMAwaNAheXl7Ys2cPbt26ZXAbhZGru2YfgKFCCFshRD0ADQCck6ktxhjTStu2bQEAvXr1KnLq4Y4dO+Ls2bOYBjbgwgAABSVJREFUOnWqJO1WrVoVV69exZgxY+Dj4wMPDw8cOnQI8+bNw507d9CoUSNJ2tHE0CGUA4QQ9wC8BuAvIcS/AEBEVwH4AbgG4ACAcUQk3/cRxhjTwuuvv461a9ciOjoa1tbZjwmp1eq8/SdPnsSJEycAAF5eXjqPpCmKu7s77O3tcfHiRUyaNAl37tzBnDlz4OjoKFkbmgh9x4zKQalUUmleposxZhxZWVl5SX7YsGFwcHDAyJEj0b9/f7i4uODSpUuwspJn1PeLbUtFCHGBiDTeOOC5axhjpc6LV/FVq1bFxo0b0aFDBxARdu/eLVuCf7FtY+EkzxgrtRQKBZYuXYrr169j4sSJ+Pvvv+Hm5mbqsCTF3TWMMVbCcXcNY4yVUpzkGWPMgnGSZ4wxC8ZJnjHGLBgnecYYs2Cc5BljzIJxkmeMMQvGSZ4xxiyYWT0MJYSIAxCp5+GVAcRLGE5JUlrPnc+7dOHzLlwdItK4IIdZJXlDCCGCCnviy9KV1nPn8y5d+Lz1w901jDFmwTjJM8aYBbOkJP+LqQMwodJ67nzepQuftx4spk+eMcZYQZZ0Jc8YY+wlnOQZY8yCWUSSF0L0FELcEELcFkLMMHU8chFC/CqEeCSECH1h2ytCiENCiFs5/3UyZYxyEELUEkIcE0KECSGuCiEm5my36HMXQtgJIc4JIS7nnPe8nO31hBBnc857uxCijKljlYMQwkoIcUkIsT/nd4s/byHEXSFEiBAiWAgRlLPNoPd5iU/yQggrAKsBvAmgCYB3hRBNTBuVbDYC6PnSthkAjhBRAwBHcn63NFkAphBRYwCvAhiX829s6eeeDqALETUH0AJATyHEqwC+BbA057wTAHxgwhjlNBFA2Au/l5bz7kxELV4YG2/Q+7zEJ3kAXgBuE9EdIsoA8AeAfiaOSRZE9B+AJy9t7gdgU87PmwD0N2pQRkBEsUR0MefnJGT/4deAhZ87ZXue86tNzosAdAGwM2e7xZ03AAghagLoBWBdzu8CpeC8C2HQ+9wSknwNANEv/H4vZ1tpUZWIYoHsZAjA2cTxyEoIURdASwBnUQrOPafLIhjAIwCHAIQDeEpEWTlFLPX9vgzANADqnN8roXScNwE4KIS4IITwzdlm0PvcWuIATUFo2MbjQi2QEMIBwC4Ak4goMfvizrIRkQpACyFERQB7ADTWVMy4UclLCNEbwCMiuiCE6JS7WUNRizrvHO2I6L4QwhnAISHEdUMrtIQr+XsAar3we00A900Uiyk8FEJUB4Cc/z4ycTyyEELYIDvBbyWi3TmbS8W5AwARPQVwHNn3JCoKIXIv0Czx/d4OQF8hxF1kd792QfaVvaWfN4jofs5/HyH7Q90LBr7PLSHJnwfQIOfOexkAQwHsM3FMxrQPwKicn0cB8DdhLLLI6Y9dDyCMiH54YZdFn7sQokrOFTyEEGUBdEP2/YhjAAbnFLO48yaimURUk4jqIvvv+SgRvQcLP28hhL0QwjH3ZwDdAYTCwPe5RTzxKoR4C9mf9FYAfiWib0wckiyEENsAdEL21KMPAcwFsBeAH4DaAKIAvE1EL9+cLdGEEO0BBAAIwf/30c5Cdr+8xZ67EMIT2TfarJB9QeZHRF8JIeoj+wr3FQCXAAwnonTTRSqfnO6az4mot6Wfd8757cn51RrA70T0jRCiEgx4n1tEkmeMMaaZJXTXMMYYKwQnecYYs2Cc5BljzIJxkmeMMQvGSZ4xxiwYJ3nGGLNgnOQZY8yC/R/RiZTrwiKKLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.random.randn(50).cumsum(), 'k--')\n",
    "plt.plot(np.random.randn(50).cumsum(), 'k--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "_ = ax1.hist(np.random.randn(100), bins=20, color='k', alpha=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 3 Axes>"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f84973add10>"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ax2.scatter(np.arange(20), np.arange(20)+3*np.random.randn(20), color='green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x648 with 3 Axes>"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2,2,sharex=True,sharey=True)\n",
    "for i in range(2):\n",
    "    for j in range(2):\n",
    "        axes[i,j].hist(np.random.randn(500), bins=50, color='k', alpha=0.5)\n",
    "plt.subplots_adjust(wspace=0, hspace=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x4YQSkfKXaIkkJSTx525/5o7Od2gdnQpKyzCIxLlt+7ex+9BumqU0Y2L/iSr7Ck6lLxLHvtr1Fb2f742ZseK6FSQmJAYdSSJMpS8Sp1bnrKb3873ZfWg3c4bNUeHHCe2lEYlD89bN49yJ55JXkMfCkQvp0rRL0JGknGhLXyTOuDt/ee8vNKnZhFeHv0rjmvpGfDxR6YvEibyCPA4cPkCNKjWYNXQWVRKrUKNKjaBjSTlT6YvEgd2HdjNs5jBy83OZ96t51K1WN+hIEhDN6YtUcBt3bqTjpI68+fmbDGo9SDts45y29EUqsEWbFjFg+gAO5h3k9V++Tq/mvYKOJAFT6YtUUHkFeYzIGEH1ytVZcMUCTks9LehIEgVU+iIVjLtT4AVUSqjEK8NeoV71eprDl++o9EUqkEN5h7j6n1dTu2pt/nHhP2id2jroSBJltCNXpILI2ZdDjyk9eH7F89SrXo/CtQ9Fvk9b+iIVwOqc1Vw09SKy92bz4qAXGXL6kKAjSZRS6YvEuAOHD9BjSg/cnYUjF9KhYYegI0kUU+mLxLjkpGQmD5hM69TWWlJBjktz+iIxKDc/lzGvjWHi0okA9DmljwpfiqXUpW9mrcxseZGf3WZ2i5n9ycy+LjLetywDi8S7Tbs30eWZLjye9Tif7/g86DgSY0o9vePunwLtAMwsEfgayKDwnLgPuvv9ZZJQRL6zYMMChs4cyoG8A8wYPINBrQcFHUliTFnN6fcAPnf3jTrVmkhkfL79c3o914sWdVqQMTSDU+ueGnQkiUFlNac/DJhW5PqNZrbCzCaZWcrRHmBmo80sy8yycnJyyiiGSMVT4AUANK/dnOcveZ5/X/1vFb6UWtilb2aVgf7AjNDQE0BzCqd+soG/H+1x7j7e3dPdPT01NTXcGCIV0uqc1bR9si3/+vJfAAxrM0xr4EtYymJL/0JgqbtvAXD3Le6e7+4FwNOADhoWKYWXVr1Eh6c7sHXf1u+29kXCVRalfxlFpnbMrEGR2y4GVpbBa4jEjcP5hxk7byxDZw7ljPpnsHT0Ujo36Rx0LKkgwtqRa2bVgF7AtUWG/9fM2gEOfPGD20TkOJ5b8RwPfPQAN3W4ifsvuJ/KiZWDjiQVSFil7+77gTo/GBsRViKROLX/8H6qJVVjZLuRNK7ZmJ5pPYOOJBWQvpErEjB355FFj9DikRZ8tesrEixBhS8Ro9IXCdC+3H38KuNX/PqNX3NWg7N0ZI5EnBZcEwnIZ9s+Y9BLg1i5dSV/7vZnbu98Owmm7TCJLJW+SEDuee8eNu/ZzBu/eoMLml8QdByJExYNZ9dJT0/3rKysoGOIRNz2A9vZfWg3TWs1ZefBnezL3UfDExsGHUtilJktcff0kjxG/5cUKSfvfPEObZ9sy7CZw3B3alWtpcKXcqfSF4mww/mHuf3t2+n+bHeqJVXjsb6PoYUJJSia0xeJoM17NjNw+kAWb17M1WdezUN9HqJ65epBx5I4ptIXiaCUqikkJyUzc/BMLm19adBxRDS9I1LWdh7cyS1v3MLuQ7tJTkrmnSveUeFL1FDpi5Sh9za+R9sn2/LY4sd4d+O7AJq/l6ii0hcpA4fzD3NX5l10fbYrSQlJ/GvUv7io5UVBxxL5Ec3pi5SBsW+O5ZF/P8LIdiN5uM/DWk5BopZKX6SU3J1D+YeoWqkqvz3vt3Rq3Ikhpw8JOpbIT1Lpi5TCN3u/4ca5N7L/8H5eG/4ajWs2pnHNxkHHEjkuzemLlIC78+zyZ2n9WGte/exVzm9yvk5lKDFFW/oixZS9J5srZ1/JvM/n0bFRRyb0n8CpdU8NOpZIiYRd+mb2BbAHyAfy3D3dzGoDLwJNKTxl4hB33xHua4kEKTkpmQ07N/DIhY9ww3/doGWQJSaV1ae2m7u3K7La2zhgvru3AOaHrovEnM+2fcbof47mcP5halWtxaobVnFjhxtV+BKzIvXJHQA8G7r8LDAwQq8jEhF5BXn87f2/ccYTZzBj9QxW56wGoFKCZkQltpVF6TvwppktMbPRobH67p4NEPpd74cPMrPRZpZlZlk5OTllEEOkbHz8zcecPeFsxs0fR7+W/VgzZg1tf9Y26FgiZaIsNls6uvtmM6sHvGVmnxTnQe4+HhgPhSdRKYMcImFzd0bNGcXXu7/WImlSIYVd+u6+OfR7q5llAB2ALWbWwN2zzawBsDXc1xGJpEWbFnFq3VOpWbUmUy+ZSmr1VGon1w46lkiZC2t6x8yqm1mNI5eBC4CVwBzgitDdrgBmh/M6IpGyL3cft75xK+dOPJd73rsHgFZ1W6nwpcIKd0u/PpARWkWwEjDV3d8ws8XAS2Z2FfAlMDjM1xEpc2+se4Mxc8ewfsd6bki/gd+f//ugI4lEXFil7+7rgR/t4XL3bUCPcJ5bJJLuff9ebp9/Oy3rtGThyIWc3+T8oCOJlAsdfyZxY2/uXvYc2kODGg0YcvoQEi2Rm8+5mcqJlYOOJlJu9A0TqfDcnRdWvECrR1tx9T+vBiAtJY3bOt6mwpe4o9KXCm1p9lI6T+7MrzJ+RYMTGvD7zpq3l/im6R2psGaunsmQGUOoW60uE34xgSvPvFLLJ0jcU+lLhZJXkEf2nmwa1WxEr7RejOs0jv/X8f9Rq2qtoKOJRAVt9kiFsWDDAs586kz6Tu1LXkEeNavW5J4e96jwRYpQ6UvM27hzI0NmDKH7lO7szd3L3d3uJtESg44lEpU0vSMxbfHXi+nyTBcA7u52N2PPHUtyUnLAqUSil0pfYs6hvEN8uu1Tzqh/Bmc2OJMx/zWGm86+SeeoFSkGTe9IzMgryGPyssm0erQVvZ7rxf7D+6mUUIn7LrhPhS9STCp9iXoFXsCLK1+kzeNtGDVnFKnVU3nu4udIrqRpHJGS0vSORL0PvvqAYS8P4/TU08kYmsGAVgMILfInIiWk0peotGDDAj759hOu/6/r6dS4E2/88g16pvUkMUFH5YiEQ9M7ElUWbVpEzyk96T6lOw989ACH8w8D0PuU3ip8kTKg0peosHbbWgZMH8A5E89hxZYVPNj7Qf5z/X9ISkwKOppIhaLpHQlUgReQYAnkFeTx/pfv8+duf+bmc27mhMonBB1NpEJS6UsglmUv4+8f/p28gjymD5rOaamnsenWTfpilUiElXp6x8wamdkCM1tjZqvM7ObQ+J/M7GszWx766Vt2cSWWuTvz1s2j55SetB/fntmfzubkE0+mwAsAVPgi5SCcLf08YKy7Lw2dHH2Jmb0Vuu1Bd78//HhSkTy86GFumXcLDU5owL097uXa9Gu1GJpIOSt16bt7NpAdurzHzNYADcsqmMS+XQd38fTSpzmj/hlc0PwChrUZRs2qNRn+8+E6Y5VIQMrk6B0zawqcCSwKDd1oZivMbJKZpRzjMaPNLMvMsnJycsoihkSJTbs3cdubt9HowUbc9tZtvL72dQDqn1Cfke1GqvBFAmTuHt4TmJ0ALAT+4u6zzKw+8C3gwN1AA3cf9VPPkZ6e7llZWWHlkOhwx/w7uO+D+yjwAoacPoSx544l/aT0oGOJVEhmtsTdS/QXLKyjd8wsCXgZeMHdZwG4+5Yitz8NvBrOa0h0c3cyN2RyXqPzSE5KJi0ljRvSb+DWc2+laa2mQccTkR8odelb4eInE4E17v5AkfEGofl+gIuBleFFlGi059AeXlz1Io8vfpxl3yxjYv+JjDpzFFe3vzroaCLyE8LZ0u8IjAD+Y2bLQ2N3AJeZWTsKp3e+AK4NK6FElUN5hxgzdwzTV05n3+F9nJ56OhN+MYHhPx8edDQRKYZwjt55HzjaUodzSx9HotG3+79lyeYl9D6lN1UqVWHd9nUMazOMq9tfzdkNz9aKlyIxRN/IlaMq8AIyN2QyYekEMj7JINES2fLbLdSoUoMFVyxQ0YvEKJW+/Mjb69/mmn9ewxc7v6B2cm2uT7+eq868ihpVagCo8EVimEpfOJx/mNfWvkbjmo1p36A9J9U4ibSUNP7a468MPHUgVStVDTqiiJQRlX6ccndWbFnBtJXTeGb5M2zZt4XR7Ufz1C+eonVqa+ZfPj/oiCISASr9ONXzuZ5kbsgk0RK5qOVFXN3+avqc0ifoWCISYSr9Cq7AC/jwqw+ZuXom73/1Ph9d9RGJCYlc1uYyhp0+jIGnDiS1emrQMUWknKj0K6g1OWt49N+PkvFJBtl7s6mcWJnezXuz7cA26lWvpy9RicQplX4FkZufy4INC0hLSaNFnRZs3rOZycsn07dFXy497VL6tezHiVVODDqmiARMpR/D9ubuJXNDJi+veZk5n85h58Gd/K7j77i35710bdqVnNtyqF65etAxRSSKqPRjSG5+Lpt2byItJQ13J+0faeTsz6FW1Vr0b9WfQacNolfzXgAkJiSq8EXkR1T6USy/IJ9l3ywjc0Mm8zfM5/0v36dJzSasHrMaM+P+C+6nwQkN6NK0i9aoF5FiUelHEXfns22f0bJOS8yMa1+9lonLJgLQOrU1V515FT3TeuLumBmXt7084MQiEmtU+gFyd77c9SWZGzLJ/CKTzA2ZbN6zmbU3reWU2qcwst1IujfrTrem3WhQo0HQcUWkAlDplxN3Z+OujSzNXkq7n7UjLSWNVz97lf7T+wNQr3o9ujfrTvem3amTXAeATo07BRlZRCoglX4EbT+wnXvfv5el2UtZmr2UHQd3APBg7we55Zxb6NCwAw/3eZiuTbvSpl4bLWQmIhEX9jlyy0IsnyM3ryCPT7795LtiX5q9lF5pvbiry13sP7yf1PtSaZ3amvY/a0/7BoU/beq1ITkpOejoIhLjyv0cufFi18FdbNi5gQ07NrB+x3pOrHIi15x1DQCnPHwKG3dtBKBaUjXa/awddarV+e76rnG7qJSgt1lEokPE2sjM+gD/ABKBCe5+b6ReK1y5+bls3LmR9TvWs2HnBnLzc/n12b8GoMeUHmRuyPze/Ts17vRd6f/2vN+SUjWF9g3a07JOSxITEr93XxW+iESTiEzvmFki8BnQC9gELAYuc/fVR7t/WU3vHMw7yI4DO9h5cCen1j0VM+PDrz4ka3MWOw/uZMfBHew4uIODeQeZduk0AK5/9XqeWvIUzv+9DyfVOImvf/M1ABOWTmDHgR00S2lGs1rNSEtJIyU5JeysIiLhiqbpnQ7AOndfD2Bm04EBwFFLPxwPfvgg//vB/7LjwA4O5R/6bnzfHfuollSNl1a9xEOLHgKgelJ1UpJTSKmaQoEXkGAJnNfoPOqfUJ+0lDSa1WpGs5RmnFTjpO+eRwuTiUhFEqnSbwh8VeT6JuDsoncws9HAaIDGjRuX+oWa127OL1r+gpSqKdSqWouU5MLfiVY4zXJXl7u4o/Md1Kpai6TEpB89fkTbEaV+bRGRWBOp0j/asYffm0dy9/HAeCic3intC/Vv1Z/+rfof8/baybVL+9QiIhVOQoSedxPQqMj1k4HNEXotEREppkiV/mKghZk1M7PKwDBgToReS0REiiki0zvunmdmNwLzKDxkc5K7r4rEa4mISPFF7CByd58LzI3U84uISMlFanpHRESikEpfRCSOqPRFROKISl9EJI5ExdLKZpYDbAzjKeoC35ZRnHij9y48ev/Co/cvPK3cvUZJHhAVS0C6e2o4jzezrJIuOiSF9N6FR+9fePT+hcfMSrxSpaZ3RETiiEpfRCSOVJTSHx90gBim9y48ev/Co/cvPCV+/6JiR66IiJSPirKlLyIixaDSFxGJIzFd+mbWx8w+NbN1ZjYu6Dyxxsy+MLP/mNny0hz6FW/MbJKZbTWzlUXGapvZW2a2NvRbJ1A+hmO8f38ys69Dn8HlZtY3yIzRzMwamdkCM1tjZqvM7ObQeIk+gzFb+qGTrz8GXAi0Bi4zs9bBpopJ3dy9nY6VLpZngD4/GBsHzHf3FsD80HU5umf48fsH8GDoM9gutDqvHF0eMNbdTwPOAcaEOq9En8GYLX2KnHzd3XOBIydfF4kId38X2P6D4QHAs6HLzwIDyzVUDDnG+yfF5O7Z7r40dHkPsIbC85GX6DMYy6V/tJOvNwwoS6xy4E0zWxI6Ub2UXH13z4bCv5RAvYDzxKIbzWxFaPpH02PFYGZNgTOBRetaXm0AAAE+SURBVJTwMxjLpX/ck6/LcXV09/YUTpGNMbPzgw4kcecJoDnQDsgG/h5snOhnZicALwO3uPvukj4+lktfJ18Pk7tvDv3eCmRQOGUmJbPFzBoAhH5vDThPTHH3Le6e7+4FwNPoM/iTzCyJwsJ/wd1nhYZL9BmM5dLXydfDYGbVzazGkcvABcDKn36UHMUc4IrQ5SuA2QFmiTlHyirkYvQZPCYzM2AisMbdHyhyU4k+gzH9jdzQ4V0P8X8nX/9LwJFihpmlUbh1D4WrrU7V+/fTzGwa0JXC5YC3AH8EXgFeAhoDXwKD3V07K4/iGO9fVwqndhz4Arj2yPy0fJ+ZdQLeA/4DFISG76BwXr/Yn8GYLn0RESmZWJ7eERGRElLpi4jEEZW+iEgcUemLiMQRlb6ISBxR6YuIxBGVvohIHPn/aUBFyXZGADQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(np.arange(20).cumsum(), 'g--')\n",
    "plt.xticks(range(0,21,5)); None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f8499d82e10>]"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0,10)\n",
    "y = np.sin(x)\n",
    "plt.plot(x,y,'yo--')\n",
    "plt.plot(x,np.cos(x),'o-')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f849afb0fd0>"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = np.random.randn(30).cumsum()\n",
    "plt.plot(data, label='default')\n",
    "#plt.plot(data, 'k-', drawstyle='steps-post', label='steps post')\n",
    "plt.plot(data, 'g-', drawstyle='steps-mid', label='steps-mid')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(np.random.randn(10,4).cumsum(0), columns=list('ABCD'), index=np.arange(0,100,10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>A</th>\n",
       "      <th>B</th>\n",
       "      <th>C</th>\n",
       "      <th>D</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.560411</td>\n",
       "      <td>1.219710</td>\n",
       "      <td>-0.310610</td>\n",
       "      <td>1.129443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.404623</td>\n",
       "      <td>-1.457838</td>\n",
       "      <td>0.880357</td>\n",
       "      <td>1.854186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-0.977427</td>\n",
       "      <td>0.006501</td>\n",
       "      <td>0.567706</td>\n",
       "      <td>1.756284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>-0.809158</td>\n",
       "      <td>0.768668</td>\n",
       "      <td>-1.376248</td>\n",
       "      <td>1.644238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>-1.117318</td>\n",
       "      <td>0.697280</td>\n",
       "      <td>-0.696351</td>\n",
       "      <td>1.202871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>-1.956402</td>\n",
       "      <td>0.987120</td>\n",
       "      <td>-2.066287</td>\n",
       "      <td>1.252815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>-2.587444</td>\n",
       "      <td>0.832578</td>\n",
       "      <td>-1.371479</td>\n",
       "      <td>-0.329028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>-2.291952</td>\n",
       "      <td>0.537737</td>\n",
       "      <td>-1.088626</td>\n",
       "      <td>-0.307515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>-3.305039</td>\n",
       "      <td>-0.149081</td>\n",
       "      <td>-0.228166</td>\n",
       "      <td>0.194461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>-1.424626</td>\n",
       "      <td>0.853369</td>\n",
       "      <td>0.013621</td>\n",
       "      <td>1.413565</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           A         B         C         D\n",
       "0   0.560411  1.219710 -0.310610  1.129443\n",
       "10 -0.404623 -1.457838  0.880357  1.854186\n",
       "20 -0.977427  0.006501  0.567706  1.756284\n",
       "30 -0.809158  0.768668 -1.376248  1.644238\n",
       "40 -1.117318  0.697280 -0.696351  1.202871\n",
       "50 -1.956402  0.987120 -2.066287  1.252815\n",
       "60 -2.587444  0.832578 -1.371479 -0.329028\n",
       "70 -2.291952  0.537737 -1.088626 -0.307515\n",
       "80 -3.305039 -0.149081 -0.228166  0.194461\n",
       "90 -1.424626  0.853369  0.013621  1.413565"
      ]
     },
     "execution_count": 225,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f847d1b2110>"
      ]
     },
     "execution_count": 228,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f847cb28850>"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot(kind='density')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f847d25dc10>"
      ]
     },
     "execution_count": 229,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.bar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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