{
 "cells": [
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   "cell_type": "markdown",
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   "source": [
    "# 03:ALGORITHMS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 03: Page 195"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Found number 19 at the position 12\n"
     ]
    }
   ],
   "source": [
    "def binarysearch(a,num): #function definition with its parameters 'a' is the inputlist\n",
    "                         #and 'num' number to be found\n",
    "\n",
    "    first=0 #initially the first position is zero\n",
    "    last=len(a)-1 #initially the last position is the total length of the inputlist-1\n",
    "    found=False #boolean value to indicate if the number to be searched is found or not.\n",
    "\n",
    "    while first<=last and not found:\n",
    "        midpoint=(first+last)//2 #dividing the inputlist into two halves and comparing the number to be found with the midpoint.\n",
    "\n",
    "        if a[midpoint]==num: #If the number to be found is equal to the midpoint returns the position.\n",
    "           found=True\n",
    "        else:\n",
    "            if num<a[midpoint]: #if the number to be found is less than the midpoint\n",
    "                                #then the first half of the divided input list is taken for further computation.\n",
    "\n",
    "                last=midpoint-1 #by assigning the last number of the first half(number before the midpoint) to the variable last.\n",
    "\n",
    "\n",
    "            else:\n",
    "                first=midpoint+1 #if the number to be found is greater than the midpoint\n",
    "                                 #then the second half of the divided input list is taken for further computation.\n",
    "                                #by assigning the first number of the second half(number following the midpoint) to the variable first.\n",
    "\n",
    "    return midpoint #returns the position of the number found in the list. \n",
    "\n",
    "\n",
    "\n",
    "numlist=[1, 23, 5, 6, 7, 8, 10, 12, 13, 15, 16, 18, 19, 20, 22] #List of inputs\n",
    "print \"Found number 19 at the position\",(binarysearch(numlist, 19)) #Printing the position of the number to be found by a function call.\n",
    "                                                                    #The function binarysearch is called along with its parameters, inputlist\n",
    "                                                                    #and the number to be found.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 03:ALGORITHMS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Example 05: Page 198"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 4, 1, 5]\n",
      "[1, 2, 3, 4, 5]\n",
      "[1, 2, 3, 4, 5]\n"
     ]
    }
   ],
   "source": [
    "#To perform insertionsort\n",
    "def sort_insertion(inputlist):\n",
    "\n",
    "    for i in range(1,len(inputlist)):\n",
    "\n",
    "        val_current = inputlist[i]\n",
    "        pos = i \n",
    "         \n",
    "        # check backwards through sorted list for proper pos of val_current\n",
    "        while((pos > 0) and (inputlist[pos-1] > val_current)):\n",
    "            inputlist[pos] = inputlist[pos-1]\n",
    "            pos = pos-1\n",
    "             \n",
    "        if pos != i:\n",
    "            inputlist[pos] = val_current \n",
    "            print(inputlist)\n",
    "    return inputlist\n",
    "inputlist = [3,2,4,1,5]\n",
    "print sort_insertion(inputlist)\n"
   ]
  }
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