[Leetcode in Python] Matrix in Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project: Data Science Interview Questions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# common operations for numpy array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1. how to obtain diagonal of a matrix \n",
    "AAA = np.arange(9).reshape(3,3)\n",
    "AAA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 4, 8])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# diagonal\n",
    "AAA.diagonal()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# diagonal sum \n",
    "AAA.diagonal().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. flatten a matrix \n",
    "AAA.flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3. find determinant\n",
    "np.linalg.det(AAA)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 1: \n",
    "- Given a 4x4 Numpy matrix, reverse the matrix.\n",
    "- https://towardsdatascience.com/python-data-science-interview-questions-d83f396f9954"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  2  3  4]\n",
      " [ 5  6  7  8]\n",
      " [ 9 10 11 12]\n",
      " [13 14 15 16]]\n"
     ]
    }
   ],
   "source": [
    "# step 0: construct a 4*4 Numpy matrix\n",
    "import numpy as np\n",
    "matrix = np.arange(1,17).reshape(4,4)\n",
    "print(matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# step 1: to flatten the numpy array \n",
    "# use np.array.flatten() for numpy arrays\n",
    "# use matrix.ravel() for matrix (list)\n",
    "\n",
    "matrix_flat = matrix.flatten()\n",
    "matrix_flat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([16, 15, 14, 13, 12, 11, 10,  9,  8,  7,  6,  5,  4,  3,  2,  1])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# step 2: read the elements backward into a new matrix\n",
    "matrix_reversed = matrix_flat[::-1]\n",
    "matrix_reversed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[16, 15, 14, 13],\n",
       "       [12, 11, 10,  9],\n",
       "       [ 8,  7,  6,  5],\n",
       "       [ 4,  3,  2,  1]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# step 3: reshape the matrix back into a 4*4 matrix\n",
    "matrix_reversed.reshape(4,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 2: How do you multiply two matrics?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# two solutions\n",
    "1. dot method for numpy array\n",
    "2. nested for loops for non numpy array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "# step 1: numpy array \n",
    "A = np.arange(9).reshape(3,3)\n",
    "B = np.arange(10,19).reshape(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5],\n",
       "       [6, 7, 8]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 11, 12],\n",
       "       [13, 14, 15],\n",
       "       [16, 17, 18]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "# step 2: use dot method\n",
    "result = A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 45  48  51]\n",
      " [162 174 186]\n",
      " [279 300 321]]\n"
     ]
    }
   ],
   "source": [
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solution 2: nested for loop for non-numpy array \n",
    "X = [\n",
    "    [1,2,3],\n",
    "    [2,3,4,],\n",
    "    [4,3,2]\n",
    "]\n",
    "\n",
    "Y = [\n",
    "    [2,3,4],\n",
    "    [3,4,6],\n",
    "    [2,3,5]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# step 1: create a zero matrix to store results\n",
    "Z = [\n",
    "    [0,0,0],\n",
    "    [0,0,0],\n",
    "    [0,0,0]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 0, 0], [0, 0, 0], [0, 0, 0]]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[14, 20, 31], [21, 30, 46], [21, 30, 44]]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# step 2: iterate over rows of X; len(X) returns the number of rows\n",
    "for i in range(len(X)):\n",
    "     \n",
    "    # iterate over columns of Y; len(Y[0]) returns the number of columns of Y\n",
    "    for j in range(len(Y[0])):\n",
    "        \n",
    "        # iterate rows of Y\n",
    "        for k in range(len(Y)):\n",
    "            \n",
    "            Z[i][j] += X[i][k]*Y[k][j]\n",
    "        \n",
    "Z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 3: How to transpose a matrix? \n",
    "Three solutions:\n",
    "1. nested for loop \n",
    "2. using zip\n",
    "3. numpy.transpose"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [\n",
    "    [12,7],\n",
    "    [1,2],\n",
    "    [3,4]\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution 1: nested for loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "# step 1: empty list \n",
    "transpose = [\n",
    "    [0,0,0],\n",
    "    [0,0,0]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "# step 2: nested for loop\n",
    "# iterate through rows \n",
    "for i in range(len(X)):\n",
    "    \n",
    "    # iterate through columns: # len(transpose) = len(X[0])\n",
    "    for j in range(len(transpose)): \n",
    "        \n",
    "        # replace elements \n",
    "        transpose[j][i] = X[i][j]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[12, 1, 3]\n",
      "[7, 2, 4]\n"
     ]
    }
   ],
   "source": [
    "for r in transpose: \n",
    "    print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution 2: using zip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2, 3), (4, 5, 6), (7, 8, 9), (10, 11, 12)]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix = [(1,2,3),(4,5,6),(7,8,9),(10,11,12)]# a list of tuples\n",
    "matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "# unzip the matrix using *\n",
    "# then, zip it back to a matrix\n",
    "matrix_transpose = zip(*matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 4, 7, 10)\n",
      "(2, 5, 8, 11)\n",
      "(3, 6, 9, 12)\n"
     ]
    }
   ],
   "source": [
    "for i in matrix_transpose:\n",
    "    print(i)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution 3: numpy array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [\n",
    "    [12,7],\n",
    "    [1,2],\n",
    "    [3,4]\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[12  1  3]\n",
      " [ 7  2  4]]\n"
     ]
    }
   ],
   "source": [
    "# 3.1 np.transpose()\n",
    "import numpy as np\n",
    "\n",
    "transpose = np.transpose(X)\n",
    "print(transpose)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12,  1,  3],\n",
       "       [ 7,  2,  4]])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3.2 matrix.T for np.array()\n",
    "matrix_array = np.array(X)\n",
    "\n",
    "matrix_array.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(matrix_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 4: how to add two Numpy matrices together?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = [[12,7,3],\n",
    "    [4 ,5,6],\n",
    "    [7 ,8,9]]\n",
    "\n",
    "Y = [[5,8,1],\n",
    "    [6,7,3],\n",
    "    [4,5,9]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[17 15  4]\n",
      " [10 12  9]\n",
      " [11 13 18]]\n"
     ]
    }
   ],
   "source": [
    "# method1： np.array() --> element-wise addition\n",
    "import numpy as np \n",
    "X_np = np.array(X)\n",
    "Y_np = np.array(Y)\n",
    "\n",
    "result = X_np + Y_np\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[17. 15.  4.]\n",
      "[10. 12.  9.]\n",
      "[11. 13. 18.]\n"
     ]
    }
   ],
   "source": [
    "# method2: nested for loops\n",
    "result = np.zeros((3,3))\n",
    "\n",
    "# iterate through rows\n",
    "for i in range(len(X)):\n",
    "\n",
    "    #iterate through columns\n",
    "    for j in range(len(X[0])):\n",
    "        result[i][j] = X[i][j]+Y[i][j]\n",
    "        \n",
    "for r in result: \n",
    "    print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12,  7,  3],\n",
       "       [ 4,  5,  6],\n",
       "       [ 7,  8,  9],\n",
       "       [ 5,  8,  1],\n",
       "       [ 6,  7,  3],\n",
       "       [ 4,  5,  9]])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# related question: how to stack matrices vertically?\n",
    "X = [[12,7,3],\n",
    "    [4 ,5,6],\n",
    "    [7 ,8,9]]\n",
    "\n",
    "Y = [[5,8,1],\n",
    "    [6,7,3],\n",
    "    [4,5,9]]\n",
    "\n",
    "np.vstack((X,Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[12,  7,  3,  5,  8,  1],\n",
       "       [ 4,  5,  6,  6,  7,  3],\n",
       "       [ 7,  8,  9,  4,  5,  9]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# horizontal stacking\n",
    "X = [[12,7,3],\n",
    "    [4 ,5,6],\n",
    "    [7 ,8,9]]\n",
    "\n",
    "Y = [[5,8,1],\n",
    "    [6,7,3],\n",
    "    [4,5,9]]\n",
    "\n",
    "np.hstack((X,Y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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