Chapter 7 - Sorting.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:3d328a380e113732103f40f651e6fdc33bb15894701dc5c9c181b4bee2806390"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.1, PAGE 395"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Sequential Search\n",
      "\n",
      "def SeqSearch( a, n, k ):\n",
      "    # Search a[1:n] from left to Right. Return least i such that\n",
      "    # The key of a[i] equals k. If there is no such i, return 0\n",
      "    # NOTE: The indexing is done from 1 ( To comply with the textbook style )\n",
      "    i = 0\n",
      "    while ( i <= n ) and ( a[i] != k ):\n",
      "        i += 1\n",
      "    if ( i > n ):\n",
      "        return 0\n",
      "    else:\n",
      "        return i"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.2, PAGE 397"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Verifying two lists using a sequential search\n",
      "\n",
      "def Verify1( l1, l2, n, m ):\n",
      "    \"\"\"\n",
      "    Compares two unordered lists l1 and l2 of size n and m respectively.\n",
      "    \"\"\"\n",
      "    marked = [False]*(m+1)\n",
      "    for i in range (n+1):\n",
      "        j = SeqSearch(l2, m, l1[i])\n",
      "        if ( j == 0 ):\n",
      "            print l1[i], \" not in l2 \"\n",
      "        else:\n",
      "            if ( l1[i] != l2[j] ):\n",
      "                # Satisfies 3rd condition ( Refer Page 396 )\n",
      "                print \"Discrepancy in \", l1[i]\n",
      "            marked[j] = True\n",
      "            \n",
      "    for i in range(m+1):\n",
      "        if ( not marked[i] ):\n",
      "            print l2[i], \" not in l1. \" # Satsfies 2nd Condition ( Refer Page 396 )\n",
      "    \n",
      "    del marked   "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.4, PAGE 399"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Insertion into a sorted list\n",
      "def Insert(e, a, i):\n",
      "    \"\"\"\n",
      "    Insert e into the ordered sequence a[1:i] such that the \n",
      "    resulting sequence a[1:i+1] is also ordered\n",
      "    The array a must have space allocated for at least i + 2 elements\n",
      "    \"\"\"\n",
      "\n",
      "    a.__setitem__(0, e)\n",
      "    while ( e < a[i] ):\n",
      "        a.__setitem__(i+1, a[i]) # To make an inplace assignments\n",
      "        i -= 1\n",
      "        \n",
      "    a.__setitem__(i+1, e)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.5, PAGE 400"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Insertion Sort\n",
      "\n",
      "def InsertionSort(a, n):\n",
      "    \"\"\"\n",
      "    Sort a[1:n+1] into non decreasing order\n",
      "    \"\"\"\n",
      "    \n",
      "    for j in range(2, n+1):\n",
      "        temp = a[j]\n",
      "        Insert(temp, a, j-1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXAMPLE 7.1, PAGE 400"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 5\n",
      "a = [None, 5, 4, 3, 2, 1] \n",
      "# NOTE: The index-0 element is None to comply with the standards of the Book\n",
      "\n",
      "InsertionSort(a, 5)\n",
      "print a[1:n+1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1, 2, 3, 4, 5]\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXAMPLE 7.2, PAGE 400"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 5\n",
      "a = [None, 2, 3, 4, 5, 1]\n",
      "# NOTE: The index-0 element is None to comply with the standards of the Book\n",
      "\n",
      "InsertionSort(a, 5)\n",
      "print a[1:n+1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1, 2, 3, 4, 5]\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.6, PAGE 402"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Quick Sort\n",
      "def QuickSort(a, left, right, debug=False):\n",
      "    \"\"\"\n",
      "    Sort a[left:right+1] into non decreasing order using quick sort algorithm\n",
      "    \"\"\"\n",
      "    # a[left] is arbitrarily chosen as the pivot.\n",
      "    # Variables i and j are used to partition the subarray so that at any time a[m] <= pivot\n",
      "    # m < i and a[m] >= pivot, m > j. It is assumed that a[left] <= a[right + 1]\n",
      "    \n",
      "    if ( left < right ):\n",
      "        if ( debug ):\n",
      "            print a[1:], \"\\t\", left, \"\\t\", right # To show the working of quick sort step by step\n",
      "        i = left\n",
      "        j = right + 1\n",
      "        pivot = a[left]\n",
      "        \n",
      "        while ( i < j ):\n",
      "            i += 1\n",
      "            while a[i] < pivot:\n",
      "                i += 1\n",
      "            \n",
      "            j -= 1\n",
      "            while a[j] > pivot:\n",
      "                j -= 1\n",
      "                \n",
      "            if i < j:\n",
      "                # Inplace swapping a[i] and a[j]\n",
      "                temp = a[i]\n",
      "                a.__setitem__(i, a[j])\n",
      "                a.__setitem__(j, temp)\n",
      "                \n",
      "        temp = a[j]\n",
      "        a.__setitem__(j, a[left])\n",
      "        a.__setitem__(left, temp)\n",
      "        \n",
      "        QuickSort(a, left, j - 1, debug ) # Recursively call QuickSort for the left subarray\n",
      "        QuickSort(a, j + 1, right, debug ) # Recursively call QuickSort for the right subarray\n",
      "        \n",
      "        # NOTE: debug is just to visualize the working of quick sort and is unnecessary for \n",
      "        # the working of the algorithm."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXAMPLE 7.3, PAGE 402"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 10\n",
      "a = [None, 26, 5, 37, 1, 61, 11, 59, 15, 48, 19]\n",
      "# NOTE: The index-0 element is None to comply with the standards of the Book\n",
      "\n",
      "QuickSort(a, 1 , 10)\n",
      "print a[1:n+1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1, 5, 11, 15, 19, 26, 37, 48, 59, 61]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "FIGURE 7.1, PAGE 403"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 10\n",
      "a = [None, 26, 5, 37, 1, 61, 11, 59, 15, 48, 19]\n",
      "# NOTE: The index-0 element is None to comply with the standards of the Book\n",
      "\n",
      "print \"The working of the quick sort algorithm :\\n\\n\"\n",
      "print \"\\t\\tArray             \\tLeft\\tRight \"\n",
      "print \"--------------------------------------------------------\"\n",
      "QuickSort(a, 1 , 10, debug=True)\n",
      "print \"\\n\\nThe final sorted array : \"\n",
      "print a[1:n+1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The working of the quick sort algorithm :\n",
        "\n",
        "\n",
        "\t\tArray             \tLeft\tRight \n",
        "--------------------------------------------------------\n",
        "[26, 5, 37, 1, 61, 11, 59, 15, 48, 19] \t1 \t10\n",
        "[11, 5, 19, 1, 15, 26, 59, 61, 48, 37] \t1 \t5\n",
        "[1, 5, 11, 19, 15, 26, 59, 61, 48, 37] \t1 \t2\n",
        "[1, 5, 11, 19, 15, 26, 59, 61, 48, 37] \t4 \t5\n",
        "[1, 5, 11, 15, 19, 26, 59, 61, 48, 37] \t7 \t10\n",
        "[1, 5, 11, 15, 19, 26, 48, 37, 59, 61] \t7 \t8\n",
        "\n",
        "\n",
        "The final sorted array : \n",
        "[1, 5, 11, 15, 19, 26, 37, 48, 59, 61]\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Copy function for Merge operation\n",
      "\n",
      "def copy(list_src, start_pos, end_pos, list_dest, copy_to_pos ):\n",
      "    \"\"\"\n",
      "    Copy list_src[start_pos : end_pos] to list_dest[copy_to_pos:]\n",
      "    \"\"\"\n",
      "    while ( start_pos <= end_pos ):\n",
      "        #print \"in cpy - src:  \", list_src, start_pos, end_pos, \" dest : \", list_dest, copy_to_pos\n",
      "        # In place assignment\n",
      "        list_dest.__setitem__(copy_to_pos, list_src[start_pos])\n",
      "        # Increment copy_to_pos and start_pos\n",
      "        copy_to_pos += 1\n",
      "        start_pos += 1      "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.7, PAGE 408"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Merging two sorted lists\n",
      "def Merge(initList, mergedList, l, m, n):\n",
      "    \"\"\"\n",
      "    Merge the sorted initList[l:m] and initList[m+1:n] into one single sorted list\n",
      "    mergedList[1:n]\n",
      "    \"\"\"\n",
      "    i1 = l; iResult = l; i2 = m+1 # i1, i2 and iResult are list positions\n",
      "    \n",
      "    # while neither input list is exhausted\n",
      "    while ( i1 <= m and i2 <= n ):\n",
      "        if initList[i1] <= initList[i2]:\n",
      "            mergedList.__setitem__(iResult, initList[i1])\n",
      "            i1 += 1\n",
      "        else:\n",
      "            mergedList.__setitem__(iResult, initList[i2])\n",
      "            i2 += 1\n",
      "        iResult += 1\n",
      "        \n",
      "    # Copy remaining records, if any, of first list\n",
      "    copy(initList, i1, m, mergedList, iResult)\n",
      "    copy(initList, i2, n, mergedList, iResult)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.8, PAGE 410"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Merge Pass\n",
      "def MergePass(initList, resultList, n, s):\n",
      "    \"\"\"\n",
      "    Adjacent pairs of sublists of size s are merged from\n",
      "    initList to resultList. n is the number of records in initList\n",
      "    \"\"\"\n",
      "    i = 1 # i is the first position in first of the sublists being merged\n",
      "    \n",
      "    while ( i <= ( n - 2*s + 1 ) ):\n",
      "        Merge(initList, resultList, i, i + s - 1, i + 2 * s - 1)\n",
      "        \n",
      "        # Merge remaining list of size < 2*s\n",
      "        i += 2*s\n",
      "    \n",
      "    if ( i + s - 1 ) < n :\n",
      "        Merge(initList, resultList, i, i+s-1, n)\n",
      "    else:\n",
      "        copy(initList, i, n, resultList, i)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.9, PAGE 410"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Merge Sort\n",
      "def MergeSort(a, n, debug = False):\n",
      "    \"\"\"\n",
      "    Sort a[1:n] into non decreasing order using MergeSort algorithm\n",
      "    \"\"\"\n",
      "    tempList = [None]*(n+1)\n",
      "    \n",
      "    # l is the length of the sublist currently being merged\n",
      "    l = 1\n",
      "    while ( l < n ):\n",
      "        MergePass(a, tempList, n, l)\n",
      "        if ( debug ):\n",
      "            print tempList[1:]\n",
      "        \n",
      "        l *= 2\n",
      "        MergePass(tempList, a, n, l)\n",
      "        # Interchange role of a and empList\n",
      "    \n",
      "        l *= 2\n",
      "        \n",
      "        # debug is used to control printing of the list as it gets modified by the algorithm\n",
      "        # This is to illustrate the working of merge sort algorithm step by step.\n",
      "        if ( debug ):\n",
      "            print a[1:]\n",
      "        \n",
      "    del tempList  "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXAMPLE 7.5, PAGE 409"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 10\n",
      "a = [None, 26, 5, 77, 1, 61, 11, 59, 15, 48, 19]\n",
      "# NOTE: The index-0 element is None to comply with the standards of the Book\n",
      "\n",
      "MergeSort(a, 10)\n",
      "print a[1:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "FIGURE 7.4, PAGE 409"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Working of the MergeSort algorithm\n",
      "n = 10\n",
      "a = [None, 26, 5, 77, 1, 61, 11, 59, 15, 48, 19]\n",
      "# NOTE: The index-0 element is None to comply with the standards of the Book\n",
      "print \"The initial unsorted list is : \"\n",
      "print a[1:], \"\\n\"\n",
      "MergeSort(a, 10, debug=True)\n",
      "print \"\\nThe final sorted list is : \"\n",
      "print a[1:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The initial unsorted list is : \n",
        "[26, 5, 77, 1, 61, 11, 59, 15, 48, 19] \n",
        "\n",
        "[5, 26, 1, 77, 11, 61, 15, 59, 19, 48]\n",
        "[1, 5, 26, 77, 11, 15, 59, 61, 19, 48]\n",
        "[1, 5, 11, 15, 26, 59, 61, 77, 19, 48]\n",
        "[1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n",
        "\n",
        "The final sorted list is : \n",
        "[1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.10, PAGE 412"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Recursive Merge Sort\n",
      "def rMergeSort(a, link, left, right):\n",
      "    \"\"\"\n",
      "    a[left:right] will be sorted in a non decreasing order \n",
      "    using Merge Sort algorithm and recursive function call\n",
      "    \"\"\"\n",
      "    # a[left:right] is to be sorted, link[i] is initially 0 for all i\n",
      "    # rMergeSort returns the index of the first element in the sorted chain\n",
      "    \n",
      "    if ( left > right ):\n",
      "        return left\n",
      "    \n",
      "    mid = ( left + right ) / 2\n",
      "    return ListMerge(a, link, \n",
      "                     rMergeSort(a, link, left, mid),\n",
      "                     rMergeSort(a, link, mid+1, right))\n",
      "\n",
      "# The list merge function is defined in PROGRAM 7.11, PAGE 413"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.11, PAGE 413"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Merging sorted chains\n",
      "def ListMerge(a, link, start1, start2):\n",
      "    \"\"\"\n",
      "    Function to merge two chain start1 and  start2 in array a.\n",
      "    Returns the first position of the resulting chain that is linked \n",
      "    in nondecreasing order of key values.\n",
      "    \"\"\"\n",
      "    # The sorted chains beginning at start1 and start2, respectively, are merged.\n",
      "    # link[0] is used as a temporary header. Return start of merged chain\n",
      "    iResult = 0 # Last record of result chain\n",
      "    i1 = start1; i2 = start2\n",
      "    while ( i1 and i2 ):\n",
      "        if a[i1] <= a[i2]:\n",
      "            link.__setitem__(iResult, i1)\n",
      "            iResult = i1; i1 = link[i1]\n",
      "        else:\n",
      "            link[iResult] = i2\n",
      "            iResult = i2\n",
      "            i2 = link[i2]\n",
      "    \n",
      "    # Attach remaining records to result chain\n",
      "    if ( i1 == 0 ):\n",
      "        link.__setitem__(iResult, i2)\n",
      "    else:\n",
      "        link.__setitem__(iResult, i1)\n",
      "        \n",
      "    return link[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "MAX HEAP DATA STRUCTURE"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Max heap Class definition - From Chapter 5 ( Trees )\n",
      "# REFER PROGRAM 5.15, PAGE 282; PROGRAM 5.16, PAGE 285; PROGRAM 5.16, PAGE 286\n",
      "\n",
      "class MaxHeap(object):\n",
      "    def __init__(self, theCapacity = 10):\n",
      "        if theCapacity < 1:\n",
      "            raise Exception(\"Capacity must be >= 1\")\n",
      "\n",
      "        self.capacity = theCapacity\n",
      "        self.heapSize = 0\n",
      "        self.heap = dict()\n",
      "        \n",
      "    def IsEmpty(self):\n",
      "        return ( self.heapSize == 0 ) or ( len(self.heap) == 0 )\n",
      "    \n",
      "    def Push(self, e):\n",
      "        \"\"\" Insert e into max heap \"\"\"\n",
      "    \n",
      "        if self.heapSize == self.capacity:\n",
      "            # Double the capacity\n",
      "            self.capacity *= 2\n",
      "\n",
      "        self.heapSize += 1\n",
      "        currentNode = self.heapSize\n",
      "\n",
      "        while ( currentNode != 1 ) and ( self.heap[currentNode/2] < e) :\n",
      "            # Bubble up\n",
      "            self.heap[currentNode] = self.heap[currentNode / 2] # Move parent down\n",
      "            currentNode /= 2\n",
      "\n",
      "        self.heap[currentNode] = e\n",
      "    \n",
      "    def Pop(self):\n",
      "        \"\"\" Delete max element \"\"\"\n",
      "        \n",
      "        if self.IsEmpty():\n",
      "            raise Exception(\"Heap is empty. Cannot delete\")\n",
      "\n",
      "        # Remove last element from heap\n",
      "        lastE = self.heap[self.heapSize]\n",
      "        self.heapSize -= 1\n",
      "        \n",
      "        popped = self.heap.pop(1) # Store the popped item to return\n",
      "        \n",
      "        if ( self.IsEmpty() ):\n",
      "            return popped\n",
      "        \n",
      "        # Tricle down\n",
      "        currentNode = 1 # Root\n",
      "        \n",
      "        child = 2       # A child of the CurrentNode\n",
      "        while child <= self.heapSize:\n",
      "            # set child to larger child of currentNode\n",
      "            if child < self.heapSize and self.heap[child] < self.heap[child+1]:\n",
      "                child += 1\n",
      "\n",
      "            if lastE >= self.heap[child]:\n",
      "                # If lastE can be put in the currentNode, break out of the loop\n",
      "                break\n",
      "\n",
      "            # If not\n",
      "\n",
      "            self.heap[currentNode] = self.heap[child]\n",
      "            currentNode = child   # move child up\n",
      "            child *= 2  # Move down a level\n",
      "\n",
      "        self.heap[currentNode] = lastE\n",
      "        del self.heap[self.heapSize + 1]\n",
      "        \n",
      "        return popped"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.13, PAGE 415"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Adjusting a Max Heap\n",
      "\n",
      "def Adjust(a, root, n):\n",
      "    \"\"\"\n",
      "    Adjust binary tree with root 'root' to satisfy heap property.\n",
      "    The left and right subtrees of root already satisfy the heap property. No node index is > n\n",
      "    \"\"\"\n",
      "    e = a[root]\n",
      "    # Find a proper place for e\n",
      "    \n",
      "    j = 2*root\n",
      "    \n",
      "    while ( j <= n ):\n",
      "        if ( j < n ) and ( a[j] < a[j+1] ):\n",
      "            j += 1  # j is maxchild of its parent\n",
      "        \n",
      "        if ( e >= a[j] ):\n",
      "            break   # e may be inserted as parent of j\n",
      "            \n",
      "        a.__setitem__(j/2, a[j])  # Move the jth record up the tree\n",
      "        \n",
      "        j *= 2\n",
      "    \n",
      "    a.__setitem__(j/2, e)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.14, PAGE 415"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Heap Sort\n",
      "\n",
      "def HeapSort(a, n):\n",
      "    \"\"\" Sort a[1:n] into non decreasing order using Heap Sort algorithm \"\"\"\n",
      "    \n",
      "    # Heapify\n",
      "    i = n/2\n",
      "    while ( i >= 1 ):\n",
      "        Adjust(a,i,n)\n",
      "        i -= 1\n",
      "    \n",
      "    # Sort\n",
      "    i = n-1\n",
      "    while ( i >= 1 ):\n",
      "        # Swap first and last of current heap\n",
      "        temp = a[1]\n",
      "        a.__setitem__(1, a[i+1])\n",
      "        a.__setitem__(i+1, temp)\n",
      "        \n",
      "        Adjust(a,1,i)  # Heapify\n",
      "        i -= 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXAMPLE 7.7, PAGE 415"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 10\n",
      "list_a = [None, 26, 5, 77, 1, 61, 11, 59, 15, 48, 19]\n",
      "dict_a = dict(zip(range(1,n+1), [26, 5, 77, 1, 61, 11, 59, 15, 48, 19]))\n",
      "dict_a_cpy = dict_a.copy()\n",
      "# NOTE: The index-0 element is None to comply with the standards of the Book\n",
      "\n",
      "print \"The input list ( unsorted ) : \"\n",
      "print list_a\n",
      "print \"\\nThe input list ( represented as a dictionary ) : \"\n",
      "print dict_a\n",
      "print \"\\nThe sorted dictionary using HeapSort Function : \"\n",
      "HeapSort(dict_a, 10)\n",
      "print dict_a\n",
      "print \"\\nThe list representation of the sorted dictionary : \"\n",
      "print list(dict_a.itervalues())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The input list ( unsorted ) : \n",
        "[None, 26, 5, 77, 1, 61, 11, 59, 15, 48, 19]\n",
        "\n",
        "The input list ( represented as a dictionary ) : \n",
        "{1: 26, 2: 5, 3: 77, 4: 1, 5: 61, 6: 11, 7: 59, 8: 15, 9: 48, 10: 19}\n",
        "\n",
        "The sorted dictionary using HeapSort Function : \n",
        "{1: 1, 2: 5, 3: 11, 4: 15, 5: 19, 6: 26, 7: 48, 8: 59, 9: 61, 10: 77}\n",
        "\n",
        "The list representation of the sorted dictionary : \n",
        "[1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "FIGURE 7.7, PAGE 416"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Array interpreted as binary tree\n",
      "\n",
      "# Imports to graphically visualize the Heap\n",
      "# Requires graphviz and pydot2 libraries to be pre-installed\n",
      "import networkx as nx\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import collections # For using OrderedDict with nx.Graph objects\n",
      "%matplotlib inline\n",
      "plt.axis('off')\n",
      "\n",
      "# NOT IN TEXTBOOK\n",
      "# Function to convert the array representation of tree to networkx edges\n",
      "def to_edge_pairs(tree_array):\n",
      "    \"\"\" Convert array representation of tree to edge pair tuples to add to networkx graph \"\"\"\n",
      "    edges = []\n",
      "    size = len(tree_array)\n",
      "    # NOTE: index starts from 1 for the tree_array.\n",
      "    for i in range(1,size+1):\n",
      "        if ( 2*i <= size ): # If Left child exists\n",
      "            edges.append((tree_array[i], tree_array[2*i]))\n",
      "        if ( 2*i + 1 ) <= size : # If Right child exists\n",
      "            edges.append((tree_array[i], tree_array[2*i + 1]))\n",
      "    return edges\n",
      "\n",
      "\n",
      "print \"The input array ( Represented as dictionary ) : \"\n",
      "print dict_a_cpy\n",
      "\n",
      "G = nx.DiGraph()\n",
      "G.node = collections.OrderedDict() \n",
      "# To preserve the order of edges ( Right / Left subtree will be displayed in the correct order )\n",
      "G.add_edges_from(to_edge_pairs(dict_a_cpy))\n",
      "nx.draw(G, nx.graphviz_layout(G,prog='dot'), arrows=False, with_labels=True)\n",
      "plt.title(\"Input array\")\n",
      "plt.show()\n",
      "\n",
      "print \"Heap representation using the MaxHeap data structure ( Chapter 5 ): \"\n",
      "heap_a = MaxHeap()\n",
      "sorted_arr = list()\n",
      "[ heap_a.Push(list_a[i]) for i in range(1, n+1) ]\n",
      "print heap_a.heap\n",
      "\n",
      "G.clear()\n",
      "G.add_edges_from(to_edge_pairs(heap_a.heap))\n",
      "nx.draw(G, nx.graphviz_layout(G,prog='dot'), arrows=False, with_labels=True, node_color='b')\n",
      "plt.title(\"Initial Heap\")\n",
      "plt.show()\n",
      "\n",
      "sorted_arr.append(heap_a.Pop())\n",
      "\n",
      "while ( not heap_a.IsEmpty()):\n",
      "    G.clear()\n",
      "    G.add_nodes_from( list(heap_a.heap.itervalues()) )\n",
      "    G.add_edges_from(to_edge_pairs(heap_a.heap))\n",
      "    nx.draw(G, nx.graphviz_layout(G,prog='dot'), arrows=False, with_labels=True, node_color='b')\n",
      "    plt.title(\"Heap Size = \" + str(heap_a.heapSize))\n",
      "    plt.show()\n",
      "    print \"Sorted : \", sorted_arr\n",
      "    sorted_arr.append(heap_a.Pop())\n",
      "    \n",
      "print \"The final sorted array is : \", sorted_arr"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The input array ( Represented as dictionary ) : \n",
        "{1: 26, 2: 5, 3: 77, 4: 1, 5: 61, 6: 11, 7: 59, 8: 15, 9: 48, 10: 19}\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEKCAYAAAD+XoUoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6e42fe310>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Heap representation using the MaxHeap data structure ( Chapter 5 ): \n",
        "{1: 77, 2: 61, 3: 59, 4: 48, 5: 19, 6: 11, 7: 26, 8: 1, 9: 15, 10: 5}\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAd4AAAFLCAYAAAB4Ne0zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6c30298d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAd4AAAFLCAYAAAB4Ne0zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n2EjBKyIiYiMFr4iIiI3+P8DiqeMmlj6eAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6c7916a10>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAd4AAAFLCAYAAAB4Ne0zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyOCVJClCBq8kSRH6/9egP2F9c8TCAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6c30bc210>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77, 61]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdwAAAFLCAYAAAB8wD0OAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6e42fe310>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77, 61, 59]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdwAAAFLCAYAAAB8wD0OAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsYH/D5n4hMN8PioaAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6cea0e850>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77, 61, 59, 48]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdwAAAFLCAYAAAB8wD0OAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxA1UuCIiIm6gwhUREXEDFa6IiIgb/P8HnzG2P95tjwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6e42fe310>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77, 61, 59, 48, 26]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdMAAAFLCAYAAACNy2aDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6c30bccd0>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77, 61, 59, 48, 26, 19]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAdMAAAFLCAYAAACNy2aDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6c1ee5c90>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77, 61, 59, 48, 26, 19, 15]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAeQAAAFYCAYAAACCpo/3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6ec421b10>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77, 61, 59, 48, 26, 19, 15, 11]\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAfQAAAFYCAYAAAClCA4fAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAADf5JREFUeJzt3GuM1fWdx/HPOVyEkWFEoV4oCEg6WRoTiV1XtPjEB5pd\nW6zWC2maVLKhtak2JKZKTNOkBrykDQV3ceuuyja0aUNtxeASTAjLI62dmjYhliKtiuvEuE7BEbk6\nnH3Q7pTBAbRFBr/zeiX/cIb/5Xw5CfPO79warVarFQDgI6051AMAAH87QQeAAgQdAAoQdAAoQNAB\noABBB4ACBB0YVHt7e15++eWhHgN4nwQdTqJp06Zl48aNA/5u1apVmTt37kmfZdeuXVmwYEHOPffc\njB8/Pp2dnbn//vv797/99tuZNm3aSZ/rSAcPHsznP//5TJ8+Pc1mM5s3bx7qkeCUJOhwEjUajTQa\njaEeI0myaNGi7NmzJ1u3bk1vb2+efPLJzJw5c6jHGtQVV1yR1atX55xzzjllHj841Qg6DLEjA9Xd\n3Z3rr78+H/vYxzJjxow8+OCD/fuee+65zJkzJxMmTMh5552X2267LQcPHuzf32w28+CDD+aCCy7I\npEmT8o1vfCNH+zLIrq6uzJ8/Px0dHUmSzs7OXH/99QOu9Yc//CHd3d1pb2/v39ra2tJs/uVXx6OP\nPppZs2blzDPPzNVXX50dO3ackMfl/40aNSq33357Lr/88owYMeKEXhsqEXQ4yY4M7OE/Hzp0KJ/5\nzGcye/bsdHd3Z+PGjfne976Xp59+OkkycuTILF++PD09PXnmmWeycePGrFy5csD1nnjiifzqV7/K\n888/n7Vr1+bRRx8ddI5LL700d999d1atWpUXX3zxqPOed955efvtt/u36667LvPnz0+SrF27Nvfe\ne29+/vOf580338zcuXP79w3mjDPOyIQJEwbdHnjggWM/cMCxtYCT5vzzz2+NGzeudcYZZ/RvbW1t\nrblz57ZarVbr2WefbU2dOnXAOUuXLm3dcsstg15v2bJlrc997nP9PzcajdaGDRv6f165cmXryiuv\nHPTcvXv3tpYuXdq6+OKLW6NGjWrNnDmztX79+gHX+v3vfz/gnPvuu6/1qU99qrVv375Wq9VqXX31\n1a1HHnmkf39fX1+rra2ttWPHjvfzcHxgH//4x1ubN2/+UK4NH3VW6HASNRqNrF27Njt37uzfVq5c\n2b9Kf+WVV9Ld3T1g5XrvvffmjTfeSJJs27Yt11xzTc4999x0dHTk7rvvTk9Pz4D7mDJlSv/tqVOn\npru7e9BZxowZk8WLF6erqys9PT258cYbc8MNN2TXrl2DHr9+/fqsWLEiTzzxRE477bT+eb/+9a/3\nz3rWWWclSV577bW/7YECPjBBhyHWOuwp9ylTpmT69OkDgt/b25t169YlSW699dbMmjUr27dvz1tv\nvZUlS5bk0KFDA653+GvYO3bsyOTJk487Q3t7exYvXpx33nknL7300nv2/+53v8uXvvSlrFmzZsD1\npk6dmocffnjAvO+8804uvfTSQe9n3LhxA16PP3y77777jjsncHSCDqeQSy65JO3t7XnggQeyd+/e\n9PX1ZcuWLenq6kqS7N69u/+NaVu3bs1DDz30nmt85zvfya5du/Lqq69mxYoVuemmmwa9r3vuuSdd\nXV05cOBA9u3bl+XLl2fChAnp7OwccFxvb2/mzZuXJUuW5LLLLhuw7ytf+UqWLl2aF154IUny1ltv\nZc2aNUf99+3evXvA6/GHb3fddddRz9u/f3/27dv3ntvAXwg6DLHDP8o2YsSIrFu3Lr/+9a8zY8aM\nTJo0KQsXLkxvb2+SP8X6Rz/6UcaPH5+FCxfm5ptvfs+75OfNm5eLL744s2fPzjXXXJMFCxYMer/N\nZjO33HJLJk2alMmTJ2fjxo156qmn0tbW1j9Xkjz//PPZtm1bFi1a1L+aHj9+fJLk2muvzZ133pmb\nb745HR0dufDCC7Nhw4YT/hh1dnamra0t3d3dueqqq3L66aef8HfTw0ddo9U6ymdagI+cZrOZ7du3\nZ8aMGUM9CnCSWaEDQAGCDoX4FjUYvjzlDgAFWKEDQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAU\nIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICg\nA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4A\nBQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg\n6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKAD\nQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAF\nCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDo\nAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANA\nAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUI\nOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgA\nUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFDByqAcAht7u3bvz7LPP5o9//GOazWYmTpyY\nOXPm5LTTThvq0YD3SdBhGNu6dWuWLVuZ1at/mJEjZyU5O0kryWtptV7KwoUL8rWvfTnTpk0b2kGB\n42q0Wq3WUA8BnFx9fX259dZFWb16TQ4e/Oe8++7CJFOOOGpbRo/+tzSbP8gdd9yeb3/7m2k0GkMx\nLvA+CDoMM319fZk3b342bdqZPXt+mqTjOGe8nra2f8oXvnB5vv/95aIOpyhvioNhZtGixdm06X+z\nZ8+6HD/mSXJO9uzZlB/+cHO++93lH/Z4wF/JCh2Gkddffz3Tpv1d9u/fnuSsw/b8S5JVSbYkmZ/k\nsUHO3p5x4+bkjTd2ZOzYsR/+sMAHYoUOw8jDDz+SRuOGDIx5kkxO8s0kC45x9swk/5Cf/OQnH9Z4\nwN/ACh2Gib6+vpx99vT09DyZ5KKjHPXNJP+TwVfoSfJf6ez8VrZu/eWHMiPw17NCh2Hi1Vdfzd69\nrRw95smfPrJ2LFflxRd/k/3795/AyYATQdBhmNi5c2dGjjzyqfYjHe8d7CMyenRHdu3adaLGAk4Q\nQYdhYvTo0Wm1DhznqOO/Anfo0IGMHj36xAwFnDCCDsPE2WefnQMHupMc6+ny463Q30yrdTAdHe/n\n427AySToMExMnDgxF13090l+OsjeviT7krz759v7//znQM3mY7n22hvTbPrVAaca/ythGLnzzq9m\n3LiVg+y5J0lbkvuTrE4yNsmSI445lDFjHsodd3z1Q54S+Gv42BoMI++++27OOWdGenr+PclVH+jc\nRuOxfOIT/5rf/vaXvv4VTkFW6DCMjBw5Mj/72eqMHfvFJF0f4Mync/rpd+Xxx/9TzOEUJegwzFxx\nxRX58Y//I21t/5jkB0kOHuPovWk0VqS9/YtZv/7xfPKTnzxJUwIflKDDMPTZz342mzaty+zZj2Ts\n2PMzYsS3kryQpCfJm0l+k1Gj7siYMVNy+eXr84tf/Hc+/elPD+3QwDF5DR2GuS1btmTZsofy1FMb\n0tvbk0ajmY6Oibnxxnm57bYv54ILLhjqEYH3QdABoABPuQNAAYIOAAUIOgAUIOgAUICgA0ABgg4A\nBQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg\n6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKAD\nQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAF\nCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDo\nAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANA\nAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUI\nOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgA\nUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0AB\ngg4ABQg6ABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6\nABQg6ABQgKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQ\ngKADQAGCDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGC\nDgAFCDoAFCDoAFCAoANAAYIOAAUIOgAUIOgAUICgA0ABgg4ABQg6ABQg6ABQgKADQAGCDgAFCDoA\nFCDoAFDA/wEJLhhyYdrv8QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7fd6c1ee5050>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Sorted :  [77, 61, 59, 48, 26, 19, 15, 11, 5]\n",
        "The final sorted array is :  [77, 61, 59, 48, 26, 19, 15, 11, 5, 1]\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.15, PAGE 420"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# LSD Radix Sort\n",
      "\n",
      "# Use debug to understand the working of Radix sort step by step.\n",
      "def RadixSort(a, link, d, r, n, debug=False):\n",
      "    \"\"\"\n",
      "    Sort a[1:n] ( both 1 and n inclusive ) using a d-digit radix-r sort. digit(a[i], j, r) returns the jth radix-r\n",
      "    digit ( from the left ) of a[i]'s key. Each digit is in the range is [0,r)\n",
      "    Sorting within a digit is done using bin sort.\n",
      "    \"\"\"\n",
      "    # NOTE: a[n] is the last element and a[1] is the first element. Pythonically speaking a[1:n+1] is being sorted\n",
      "    \n",
      "    # Queue front and end pointers\n",
      "    e = [0]*r\n",
      "    f = [0]*r\n",
      "    \n",
      "    # Create initial chain of records starting at first\n",
      "    first = 1\n",
      "    for i in range(1, n):\n",
      "        link.__setitem__(i, i+1)\n",
      "        \n",
      "    link.__setitem__(n, 0) # Terminating the chain of records\n",
      "\n",
      "    for i in range(d-1, -1, -1):\n",
      "        # Sort on digit i\n",
      "        f = [0]*r # Initial bins to empty spaces\n",
      "        e = [0]*r\n",
      "        \n",
      "        current = first\n",
      "        \n",
      "        while current != 0:\n",
      "            # Put the record into queues\n",
      "            k = digit(a[current], i, r, d)\n",
      "            \n",
      "            if f[k] == 0:\n",
      "                f[k] = current\n",
      "            else:\n",
      "                link.__setitem__(e[k], current)\n",
      "                \n",
      "            e[k] = current\n",
      "            \n",
      "            current = link[current]\n",
      "        \n",
      "        if debug:\n",
      "            print \"PASS \", (d-1) - i, \" The f[ ] list is   : \", f\n",
      "            print \"         The e[ ] list is   : \", e\n",
      "\n",
      "        # Finding the first non-empty bin\n",
      "        \n",
      "        j = 0\n",
      "        \n",
      "        while f[j] == 0:\n",
      "            j += 1\n",
      "\n",
      "        # The folowing code contatenates the rest of the queue.\n",
      "        print \"         First non empty chain is at :\", j\n",
      "        first = f[j]\n",
      "        last = e[j]\n",
      "\n",
      "        for k in range(j+1, r):\n",
      "            if f[k] != 0:\n",
      "                link.__setitem__(last, f[k])\n",
      "                last = e[k]\n",
      "            \n",
      "        link.__setitem__(last, 0)\n",
      "        \n",
      "        if debug:\n",
      "            print \"         The links are      : \", link\n",
      "            current_copy = first\n",
      "            print \"         First is at :\", current_copy\n",
      "            print \"         Resulting Chain is :\",\n",
      "            while current_copy != 0:\n",
      "                print a[current_copy], \n",
      "                current_copy = link[current_copy]\n",
      "            print \"\\n\"\n",
      "            \n",
      "        \n",
      "    return first\n",
      "\n",
      "def digit(number, i, radix, number_of_digits):\n",
      "    \"\"\"\n",
      "    Returns the ith digit ( from the right of the number having a length of number_of_digits ).\n",
      "    \"\"\"\n",
      "    numerals = \"0123456789abcdefghijklmnopqrstuvwxyz\"\n",
      "    number_base_radix = _toBaseRadix(number, radix)\n",
      "    \n",
      "    if i > len(number_base_radix):\n",
      "        return numerals.find(number_base_radix[-1])\n",
      "    \n",
      "    try:\n",
      "        digit_value = numerals.find(number_base_radix[ i - number_of_digits ])\n",
      "    except:\n",
      "        digit_value = -1            \n",
      "    \n",
      "    if digit_value < 0:\n",
      "        return 0\n",
      "    else:\n",
      "        return digit_value\n",
      "\n",
      "\n",
      "def _toBaseRadix(number, radix):\n",
      "    \"\"\"\n",
      "    Convert decimal number to string of the number in base radix representation.\n",
      "    \"\"\"\n",
      "    \n",
      "    if number < 0:\n",
      "        return \"-\" + _toBaseRadix(-number, radix)\n",
      "    \n",
      "    number_radix = \"\"\n",
      "    numerals = \"0123456789abcdefghijklmnopqrstuvwxyz\"\n",
      "    \n",
      "    while number > 0:\n",
      "        number_radix = numerals[(number % radix)] + number_radix\n",
      "        number /= radix\n",
      "        \n",
      "    return number_radix"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXAMPLE 7.8, PAGE 419"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = [None, 179, 208, 306, 93, 859, 984, 55, 9, 271, 33]\n",
      "n = len(a)\n",
      "indices = [0]*n\n",
      "current = RadixSort(a, indices, 3, 10, 10, debug=True)\n",
      "print \"The first element\", a[current], \"is at\", current\n",
      "print \"The sorted list is :\", \n",
      "while current != 0:\n",
      "    print a[current],\n",
      "    current = indices[current]\n",
      "print \"\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "PASS  0  The f[ ] list is   :  [0, 9, 0, 4, 6, 7, 3, 0, 2, 1]\n",
        "         The e[ ] list is   :  [0, 9, 0, 10, 6, 7, 3, 0, 2, 8]\n",
        "         First non empty chain is at : 1\n",
        "         The links are      :  [0, 5, 1, 2, 10, 8, 7, 3, 0, 4, 6]\n",
        "         First is at : 9\n",
        "         Resulting Chain is : 271 93 33 984 55 306 208 179 859 9 \n",
        "\n",
        "PASS  1  The f[ ] list is   :  [3, 0, 0, 10, 0, 7, 0, 9, 6, 4]\n",
        "         The e[ ] list is   :  [8, 0, 0, 10, 0, 5, 0, 1, 6, 4]\n",
        "         First non empty chain is at : 0\n",
        "         The links are      :  [0, 6, 8, 2, 0, 9, 4, 5, 10, 1, 7]\n",
        "         First is at : 3\n",
        "         Resulting Chain is : 306 208 9 33 55 859 271 179 984 93 \n",
        "\n",
        "PASS  2  The f[ ] list is   :  [8, 1, 2, 3, 0, 0, 0, 0, 5, 6]\n",
        "         The e[ ] list is   :  [4, 1, 9, 3, 0, 0, 0, 0, 5, 6]\n",
        "         First non empty chain is at : 0\n",
        "         The links are      :  [0, 2, 9, 5, 1, 6, 0, 4, 10, 3, 7]\n",
        "         First is at : 8\n",
        "         Resulting Chain is : 9 33 55 93 179 208 271 306 859 984 \n",
        "\n",
        "The first element 9 is at 8\n",
        "The sorted list is : 9 33 55 93 179 208 271 306 859 984 \n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.16, PAGE 424"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Rearranging records using a doubly linked list\n",
      "\n",
      "def List1(a, linka, n, first):\n",
      "    \"\"\"\n",
      "    Rearranges the sorted chain beginning at first so that the records a[1:n] ( both inclusive )\n",
      "    are in sorted order.\n",
      "    Note that actual sorting does not take place. The input is assumed to be sorted already. The sorted \n",
      "    order is specified by linka.\n",
      "    \"\"\"\n",
      "    \n",
      "    linkb = [0]*(n+1) # Array to use as backward links \n",
      "    # NOTE: There will be n + 1 elements in linkb. The first element will remain unused.\n",
      "    # This is in accordance with the approach followed in the text book.\n",
      "    \n",
      "    prev = 0\n",
      "    current = first\n",
      "    while current != 0:\n",
      "        # Converting the singly linked list chain to a dll form\n",
      "        linkb[current] = prev\n",
      "        prev = current\n",
      "        current = linka[current]\n",
      "    \n",
      "    # Positioning a[first] to i while maintiaining the list\n",
      "    for i in range(1, n):\n",
      "        \n",
      "        if first != i:\n",
      "            if linka[i] != 0:\n",
      "                linkb[linka[i]] = first\n",
      "            linka.__setitem__(linkb[i], first) # Inplace modification of the list linka\n",
      "            \n",
      "            # Swapping a[first] and a[i]\n",
      "            temp = a[i]\n",
      "            a.__setitem__(i, a[first])\n",
      "            a.__setitem__(first, temp)\n",
      "            \n",
      "            # Swapping linka[first] and linka[i]\n",
      "            temp = linka[i]\n",
      "            linka.__setitem__(i, linka[first])\n",
      "            linka.__setitem__(first, temp)\n",
      "            \n",
      "            # Swapping linkb[first] and linkb[i]\n",
      "            linkb[first], linkb[i] = linkb[i], linkb[first]\n",
      "        \n",
      "        first = linka[i]\n",
      "        \n",
      "        print \"PASS\", i\n",
      "        print \"       key   : \", a\n",
      "        print \"       linka : \", linka\n",
      "        print \"       linkb : \", linkb\n",
      "        print \"       first : \", first\n",
      "        print \"\"\n",
      "            \n",
      "        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXAMPLE 7.9, PAGE 424"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "array = [None, 26, 5, 77, 1, 61, 11, 59, 15, 48, 19]\n",
      "n = len(array)\n",
      "order = [ 0, 9, 6, 0, 2, 3, 8, 5, 10, 7, 1 ]\n",
      "print \"The linking order is :\", order\n",
      "print \"The input array is :\", array\n",
      "print \"\"\n",
      "\n",
      "List1(array, order, n-1, 4)\n",
      "\n",
      "print \"After rearranging the order is :\", order\n",
      "print \"After rearranging the array is :\", array\n",
      "print array"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The linking order is : [0, 9, 6, 0, 2, 3, 8, 5, 10, 7, 1]\n",
        "The input array is : [None, 26, 5, 77, 1, 61, 11, 59, 15, 48, 19]\n",
        "\n",
        "PASS 1\n",
        "       key   :  [None, 1, 5, 77, 26, 61, 11, 59, 15, 48, 19]\n",
        "       linka :  [0, 2, 6, 0, 9, 3, 8, 5, 10, 7, 4]\n",
        "       linkb :  [0, 0, 4, 5, 10, 7, 2, 9, 6, 4, 8]\n",
        "       first :  2\n",
        "\n",
        "PASS 2\n",
        "       key   :  [None, 1, 5, 77, 26, 61, 11, 59, 15, 48, 19]\n",
        "       linka :  [0, 2, 6, 0, 9, 3, 8, 5, 10, 7, 4]\n",
        "       linkb :  [0, 0, 4, 5, 10, 7, 2, 9, 6, 4, 8]\n",
        "       first :  6\n",
        "\n",
        "PASS 3\n",
        "       key   :  [None, 1, 5, 11, 26, 61, 77, 59, 15, 48, 19]\n",
        "       linka :  [0, 2, 6, 8, 9, 6, 0, 5, 10, 7, 4]\n",
        "       linkb :  [0, 0, 4, 2, 10, 7, 5, 9, 6, 4, 8]\n",
        "       first :  8\n",
        "\n",
        "PASS 4\n",
        "       key   :  [None, 1, 5, 11, 15, 61, 77, 59, 26, 48, 19]\n",
        "       linka :  [0, 2, 6, 8, 10, 6, 0, 5, 9, 7, 8]\n",
        "       linkb :  [0, 0, 4, 2, 6, 7, 5, 9, 10, 8, 8]\n",
        "       first :  10\n",
        "\n",
        "PASS 5\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 77, 59, 26, 48, 61]\n",
        "       linka :  [0, 2, 6, 8, 10, 8, 0, 10, 9, 7, 6]\n",
        "       linkb :  [0, 0, 4, 2, 6, 8, 10, 9, 10, 8, 7]\n",
        "       first :  8\n",
        "\n",
        "PASS 6\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 26, 59, 77, 48, 61]\n",
        "       linka :  [0, 2, 6, 8, 10, 8, 9, 10, 0, 7, 8]\n",
        "       linkb :  [0, 0, 4, 2, 6, 8, 10, 9, 10, 8, 7]\n",
        "       first :  9\n",
        "\n",
        "PASS 7\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 26, 48, 77, 59, 61]\n",
        "       linka :  [0, 2, 6, 8, 10, 8, 9, 9, 0, 10, 8]\n",
        "       linkb :  [0, 0, 4, 2, 6, 8, 10, 8, 10, 9, 9]\n",
        "       first :  9\n",
        "\n",
        "PASS 8\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 26, 48, 59, 77, 61]\n",
        "       linka :  [0, 2, 6, 8, 10, 8, 9, 9, 10, 0, 9]\n",
        "       linkb :  [0, 0, 4, 2, 6, 8, 10, 8, 9, 10, 9]\n",
        "       first :  10\n",
        "\n",
        "PASS 9\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n",
        "       linka :  [0, 2, 6, 8, 10, 8, 9, 9, 10, 10, 0]\n",
        "       linkb :  [0, 0, 4, 2, 6, 8, 10, 8, 9, 9, 10]\n",
        "       first :  10\n",
        "\n",
        "After rearranging the order is : [0, 2, 6, 8, 10, 8, 9, 9, 10, 10, 0]\n",
        "After rearranging the array is : [None, 1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n",
        "[None, 1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.17, PAGE 427"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Rearranging records using only one link field\n",
      "def List2(a, link, n, first):\n",
      "    \"\"\"\n",
      "    Rearranges a of n elements, using the order given in list link.\n",
      "    \"\"\"\n",
      "    # Does not use backward linking list linkb as used in List1\n",
      "    for i in range(1, n):\n",
      "        # Position ith record aptly.\n",
      "        # Note that its index will be greater than i, since records till i have\n",
      "        # already been positioned\n",
      "        \n",
      "        while first < i:\n",
      "            first = link[first]\n",
      "                \n",
      "        q = link[first] # a[q] is next record in sorted order.\n",
      "        if first != i:\n",
      "            # a[first] has the ith smallest key. Move record to ith position\n",
      "            # Also set link from old position of a[i] to new one\n",
      "            \n",
      "            # swap a[i] and a[first]\n",
      "            temp = a[i]\n",
      "            a.__setitem__(i, a[first])\n",
      "            a.__setitem__(first, temp)\n",
      "            \n",
      "            link.__setitem__(first, link[i])\n",
      "            link.__setitem__(i, first)\n",
      "            \n",
      "        first = q\n",
      "        \n",
      "        print \"PASS\", i\n",
      "        print \"       key   : \", a\n",
      "        print \"       link : \", link\n",
      "        print \"       first : \", first\n",
      "        print \"\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "array = [None, 26, 5, 77, 1, 61, 11, 59, 15, 48, 19]\n",
      "n = len(array)\n",
      "link = [ 0, 9, 6, 0, 2, 3, 8, 5, 10, 7, 1 ]\n",
      "print \"The linking order is :\", link\n",
      "print \"The input array is :\", array\n",
      "print \"\"\n",
      "\n",
      "List2(array, link, n-1, 4)\n",
      "\n",
      "print \"After rearranging the link is :\", link\n",
      "print \"After rearranging the array is :\", array"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "The linking order is : [0, 9, 6, 0, 2, 3, 8, 5, 10, 7, 1]\n",
        "The input array is : [None, 26, 5, 77, 1, 61, 11, 59, 15, 48, 19]\n",
        "\n",
        "PASS 1\n",
        "       key   :  [None, 1, 5, 77, 26, 61, 11, 59, 15, 48, 19]\n",
        "       link :  [0, 4, 6, 0, 9, 3, 8, 5, 10, 7, 1]\n",
        "       first :  2\n",
        "\n",
        "PASS 2\n",
        "       key   :  [None, 1, 5, 77, 26, 61, 11, 59, 15, 48, 19]\n",
        "       link :  [0, 4, 6, 0, 9, 3, 8, 5, 10, 7, 1]\n",
        "       first :  6\n",
        "\n",
        "PASS 3\n",
        "       key   :  [None, 1, 5, 11, 26, 61, 77, 59, 15, 48, 19]\n",
        "       link :  [0, 4, 6, 6, 9, 3, 0, 5, 10, 7, 1]\n",
        "       first :  8\n",
        "\n",
        "PASS 4\n",
        "       key   :  [None, 1, 5, 11, 15, 61, 77, 59, 26, 48, 19]\n",
        "       link :  [0, 4, 6, 6, 8, 3, 0, 5, 9, 7, 1]\n",
        "       first :  10\n",
        "\n",
        "PASS 5\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 77, 59, 26, 48, 61]\n",
        "       link :  [0, 4, 6, 6, 8, 10, 0, 5, 9, 7, 3]\n",
        "       first :  1\n",
        "\n",
        "PASS 6\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 26, 59, 77, 48, 61]\n",
        "       link :  [0, 4, 6, 6, 8, 10, 8, 5, 0, 7, 3]\n",
        "       first :  9\n",
        "\n",
        "PASS 7\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 26, 48, 77, 59, 61]\n",
        "       link :  [0, 4, 6, 6, 8, 10, 8, 9, 0, 5, 3]\n",
        "       first :  7\n",
        "\n",
        "PASS 8\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 26, 48, 59, 77, 61]\n",
        "       link :  [0, 4, 6, 6, 8, 10, 8, 9, 9, 0, 3]\n",
        "       first :  5\n",
        "\n",
        "PASS 9\n",
        "       key   :  [None, 1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n",
        "       link :  [0, 4, 6, 6, 8, 10, 8, 9, 9, 10, 0]\n",
        "       first :  3\n",
        "\n",
        "After rearranging the link is : [0, 4, 6, 6, 8, 10, 8, 9, 9, 10, 0]\n",
        "After rearranging the array is : [None, 1, 5, 11, 15, 19, 26, 48, 59, 61, 77]\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.18, PAGE 429"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Table Sort\n",
      "def Table(a, n, t, debug = False):\n",
      "    \"\"\"\n",
      "    Rearrange a[1:n] ( both inclusive ) corresponding to the sequence a[t[1]], ...., a[t[n]]]; n >= 1\n",
      "    \"\"\"\n",
      "    cycle = 0\n",
      "    t_copy = t[:]\n",
      "    key_copy = key[:]\n",
      "    \n",
      "    for i in range(1, n):\n",
      "        if t[i] != 1:\n",
      "            # There is a non-trivial cycle starting at i\n",
      "            p = a[i]\n",
      "            j = i\n",
      "            \n",
      "            while True:\n",
      "                k = t[j]\n",
      "                a.__setitem__(j, a[k])\n",
      "                t.__setitem__(j, j)\n",
      "                j = k\n",
      "                if t[j] == i:\n",
      "                    break\n",
      "            \n",
      "            a.__setitem__(j, p) # j is the position for record p\n",
      "            t.__setitem__(j, j)\n",
      "            \n",
      "            if ( t_copy != t ) or ( key_copy != key ):\n",
      "                t_copy = t[:]\n",
      "                key_copy = key[:]\n",
      "                cycle += 1\n",
      "                \n",
      "                if debug:\n",
      "                    print \"\\nAfter cycle\", cycle, \":\"\n",
      "                    print \"Key :\", key\n",
      "                    print \"t   :\", t, \"\\n\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "EXAMPLE 7.11, PAGE 430"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Table Sort Example\n",
      "key = [None, 35, 14, 12, 42, 26, 50, 31, 18]\n",
      "t = [0, 3, 2, 8, 5, 7, 1, 4, 6]\n",
      "n = len(key) - 1\n",
      "\n",
      "\n",
      "print \"\\nInitial configuration : \"\n",
      "print \"key: \", key\n",
      "print \"t  : \", t, \"\\n\"\n",
      "\n",
      "Table(key, n, t, debug=True)\n",
      "\n",
      "print \"\\nFinal configuration : \"\n",
      "print \"Key : \", key\n",
      "print \"t   : \", t, \"\\n\""
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Initial configuration : \n",
        "key:  [None, 35, 14, 12, 42, 26, 50, 31, 18]\n",
        "t  :  [0, 3, 2, 8, 5, 7, 1, 4, 6] \n",
        "\n",
        "\n",
        "After cycle 1 :\n",
        "Key : [None, 12, 14, 18, 42, 26, 35, 31, 50]\n",
        "t   : [0, 1, 2, 3, 5, 7, 6, 4, 8] \n",
        "\n",
        "\n",
        "After cycle 2 :\n",
        "Key : [None, 12, 14, 18, 26, 31, 35, 42, 50]\n",
        "t   : [0, 1, 2, 3, 4, 5, 6, 7, 8] \n",
        "\n",
        "\n",
        "Final configuration : \n",
        "Key :  [None, 12, 14, 18, 26, 31, 35, 42, 50]\n",
        "t   :  [0, 1, 2, 3, 4, 5, 6, 7, 8] \n",
        "\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.20, PAGE 436"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from random import randint\n",
      "\n",
      "def Permute(a, n):\n",
      "    \"\"\"Random permutations generator\"\"\"\n",
      "    for i in range(n-1, -1, -1):\n",
      "        j = randint(0, i)\n",
      "        \n",
      "        # Swapping a[j] and a[i]\n",
      "        temp = a[i]\n",
      "        a.__setitem__(i, a[j])\n",
      "        a.__setitem__(j, temp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Sample example of random permutation generator\n",
      "\n",
      "a = [1,2,3,4,5]\n",
      "Permute(a, len(a))\n",
      "print a"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[5, 4, 1, 2, 3]\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "PROGRAM 7.22, PAGE 452"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Run generation using Loser Tree\n",
      "\n",
      "# This method of Run generation using Loser Tree was devised by Walters, Painter and Zalk.\n",
      "\n",
      "\n",
      "\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}