chapter6-binary-search.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loading Libraries\n",
    "\n",
    "Let's import all the necessary packages first. You can safely ignore this section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import java.util.Random;\n",
    "import java.lang.*;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%maven org.knowm.xchart:xchart:3.5.2\n",
    "import org.knowm.xchart.*;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Helper Methods\n",
    "\n",
    "Let's code three helper methods:\n",
    "\n",
    "* random array generator\n",
    "* array printer\n",
    "* copyArray\n",
    "\n",
    "It is assumed that you are fully capable of coding two similar methods by yourself. If you are new to Java (but have some experience with a different language), playing with these methods will help you get familiar with Java faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "// random array generator\n",
    "public int[] randomArr(int size) {\n",
    "    Random r = new Random();\n",
    "    int[] arr = new int[size];\n",
    "    \n",
    "    for (int i = 0; i < size; i++) {\n",
    "        arr[i] = r.nextInt(1000) + 1;\n",
    "    }\n",
    "    \n",
    "    return arr;\n",
    "}\n",
    "\n",
    "// array printer\n",
    "public void printArr(int[] arr) {\n",
    "    for (int num : arr) {\n",
    "        System.out.print(num + \" \");\n",
    "    }\n",
    "    System.out.println();\n",
    "}\n",
    "\n",
    "// array deep copy\n",
    "public void copyArray(int[] from, int[] to) {\n",
    "    if (from.length != to.length) {\n",
    "        System.exit(0);\n",
    "    }\n",
    "    \n",
    "    for (int i = 0; i < from.length; i++) {\n",
    "        to[i] = from[i];\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binary Search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Binary search is built upon the assumption that a given array is already sorted. Given a sorted array and a target, binary search compares the target to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half. The process repeats itself until either the target is found or can not be found from the given array.\n",
    "\n",
    "One implementation of binary search is shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15 54 97 126 347 468 471 836 913 929 \n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// implementation\n",
    "public boolean binarySearch(int[] arr, int target) {\n",
    "   boolean found = false;\n",
    "   int s = 0, e = arr.length-1;\n",
    "   int mid;\n",
    "\n",
    "   while (s <= e && !found) {\n",
    "      mid = (s + e) / 2;\n",
    "\n",
    "      if (arr[mid] == target) {\n",
    "          found = true;\n",
    "      } else if (target < arr[mid]) {\n",
    "          e = mid-1;\n",
    "      } else {\n",
    "          s = mid+1;\n",
    "      }\n",
    "\n",
    "   }\n",
    "   return found;\n",
    "}\n",
    "\n",
    "// sanity check\n",
    "int[] arr = randomArr(10);\n",
    "Arrays.sort(arr);\n",
    "printArr(arr);\n",
    "binarySearch(arr, arr[9]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's time binary search by modifying the method. In addition, we also implement a linear search and time its complexity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "// modification of binary search\n",
    "public int binarySearchTrack(int[] arr, int target) {\n",
    "   boolean found = false;\n",
    "   int s = 0, e = arr.length-1;\n",
    "   int mid;\n",
    "   int steps = 4;\n",
    "\n",
    "   while (s <= e && !found) {\n",
    "      mid = (s + e) / 2;\n",
    "      steps += 4;\n",
    "\n",
    "      if (arr[mid] == target) {\n",
    "          found = true;\n",
    "      } else if (target < arr[mid]) {\n",
    "          e = mid-1;\n",
    "          steps += 1;\n",
    "      } else {\n",
    "          s = mid+1;\n",
    "          steps += 1;\n",
    "      }\n",
    "\n",
    "   }\n",
    "   return steps;\n",
    "}\n",
    "\n",
    "// time linear search\n",
    "public int linearSearchTrack(int[] arr, int target) {\n",
    "    boolean found = false;\n",
    "    int steps = 1;\n",
    "    \n",
    "    for (int i = 0; i < arr.length; i++) {\n",
    "        steps += 2;\n",
    "        \n",
    "        if (arr[i] == target) {\n",
    "            steps += 2;\n",
    "            \n",
    "            found = true;\n",
    "            break;\n",
    "        }\n",
    "    }\n",
    "    \n",
    "    return steps;\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the time complexity of binarySearch and compare it to a function that grows by O(n). As you can see from the plot, binary search grows by log function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "BufferedImage@73e5f74b: type = 1 DirectColorModel: rmask=ff0000 gmask=ff00 bmask=ff amask=0 IntegerInterleavedRaster: width = 600 height = 400 #Bands = 3 xOff = 0 yOff = 0 dataOffset[0] 0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "// predetermined size\n",
    "int size = 80;\n",
    "\n",
    "// storage of steps\n",
    "int[] binarySearchArr = new int[size];\n",
    "int[] linearSearchArr = new int[size];\n",
    "\n",
    "// populate storage\n",
    "for (int i = 1; i < size; i++) {\n",
    "    // prepare one sorted array\n",
    "    int[] temp = randomArr(i);\n",
    "    Arrays.sort(temp);\n",
    "    \n",
    "    binarySearchArr[i] = binarySearchTrack(temp, 1001);\n",
    "    linearSearchArr[i] = linearSearchTrack(temp, 1001);\n",
    "}\n",
    "\n",
    "// size of input - convert int to double for plotting\n",
    "double[] xData = new double[size];\n",
    "for (int i = 1; i < xData.length; i++) {\n",
    "    xData[i] = i;\n",
    "}\n",
    "\n",
    "// binarySearchTrack\n",
    "double[] yDataB = new double[size];\n",
    "for (int i = 0; i < yDataB.length; i++) {\n",
    "    yDataB[i] = binarySearchArr[i];\n",
    "}\n",
    "\n",
    "// linear func\n",
    "double[] yDataN = new double[size];\n",
    "for (int i = 0; i < yDataN.length; i++) {\n",
    "    yDataN[i] = linearSearchArr[i];\n",
    "}\n",
    "\n",
    "// plot it\n",
    "XYChart chart = new XYChartBuilder().width(600).height(400).title(\"Binary Search\").xAxisTitle(\"Input Size n\").yAxisTitle(\"Running Time T(n)\").build();\n",
    "chart.addSeries(\"Binary Search\", xData, yDataB);\n",
    "chart.addSeries(\"A linear function\", xData, yDataN);\n",
    "BitmapEncoder.getBufferedImage(chart);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Do It Yourself"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Practice - binary search on a 2D array\n",
    "\n",
    "Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:\n",
    "\n",
    "* Integers in each row are sorted from left to right.\n",
    "* The first integer of each row is greater than the last integer of the previous row.\n",
    "\n",
    "For example, consider the following matrix:\n",
    "\n",
    "```\n",
    "[[1,   3,  5,  7],\n",
    " [10, 11, 16, 20],\n",
    " [23, 30, 34, 50]]\n",
    " \n",
    "Given target = 3, return true.\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "// you have to use the provided method name and parameters\n",
    "public boolean searchMatrix(int[][] matrix, int target) {\n",
    "    // your code goes here\n",
    "    // remove this line\n",
    "    return true;\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**<span style=\"color:red\">Can you also test your solution?</span>**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Practice - Implement sqrt\n",
    "\n",
    "Implement int sqrt(int x) that computes and returns the square root of x. x is guaranteed to be a non-negative integer.\n",
    "\n",
    "Example 1:\n",
    "```\n",
    "Input: 4\n",
    "Output: 2\n",
    "```\n",
    "\n",
    "Example 2:\n",
    "```\n",
    "Input: 8\n",
    "Output: 2\n",
    "```\n",
    "Explanation: The square root of 8 is 2.82842..., and since we want to return an integer, the decimal part will be truncated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "// you have to use the provided method name and parameters\n",
    "public int mySqrt(int x) {\n",
    "    // your code goes here\n",
    "    // remove this line\n",
    "    return 0;\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**<span style=\"color:red\">Can you also test your solution?</span>**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**When you finish (or not) playing your exploration of the whole interactive notebook and DIY assignment, you should download a html file and upload it to the assignment box on Canvas:**\n",
    "\n",
    "* File --> Download as --> HTML (.html)\n",
    "\n",
    "![download](images/html.png)"
   ]
  }
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