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diff --git a/Discrete_Mathematics_and_its_Applications_by_Kenneth_H.Rosen/screenshots/screenshots_version_backup/chapter5.ipynb b/Discrete_Mathematics_and_its_Applications_by_Kenneth_H.Rosen/screenshots/screenshots_version_backup/chapter5.ipynb
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@@ -1,312 +0,0 @@
-{

- "cells": [

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "# 05:INDUCTION AND RECURSION"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "## Example 01: Page 346"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 1,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "The value of f( 1 ) is 9\n",

-      "The value of f( 2 ) is 21\n",

-      "The value of f( 3 ) is 45\n",

-      "The value of f( 4 ) is 93\n"

-     ]

-    }

-   ],

-   "source": [

-    "#to compute the recursive functions\n",

-    "def f(n):\n",

-    "\n",

-    "    if n==0:\n",

-    "        return 3\n",

-    "    else:\n",

-    "        n=n-1\n",

-    "        result=2*f(n)+3 #recursive call\n",

-    "        return result\n",

-    "for num in range(1,5):\n",

-    "    r=f(num)\n",

-    "    print \"The value of f(\",num,\") is\",r #Prints the result for individual instance\n"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "# 05:INDUCTION AND RECURSION"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "## Example 01: Page 361"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 2,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "Enter a number whose factorial is to be found4\n",

-      "The factorial of 4 is 24\n"

-     ]

-    }

-   ],

-   "source": [

-    "#To compute the factorial of a given number using recursion\n",

-    "def factorial(n):\n",

-    "    if n==0:\n",

-    "        return 1\n",

-    "    else:\n",

-    "        return n*factorial(n-1) #recursive function call\n",

-    "num=input(\"Enter a number whose factorial is to be found\");\n",

-    "print \"The factorial of\",num,\"is\",factorial(num);\n"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "# 05:INDUCTION AND RECURSION"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "## Example 02: Page 361"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 3,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "Enter the number5\n",

-      "Enter the power4\n",

-      "The value of 5 to the power 4 is 625\n"

-     ]

-    }

-   ],

-   "source": [

-    "#To compute power using recursive algorithm\n",

-    "def power(a,n):\n",

-    "    if n==0:\n",

-    "        return 1\n",

-    "    else:\n",

-    "        return a*power(a,n-1) #recursive call algorithm\n",

-    "num=input(\"Enter the number\");\n",

-    "p=input(\"Enter the power\");\n",

-    "print \"The value of\",num,\"to the power\",p,\"is\",power(num,p);\n"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "# 05:INDUCTION AND RECURSION"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "## Example 03: Page 362"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 5,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "Enter the first number5\n",

-      "Enter the second number8\n",

-      "The gcd of 5 , 8 is 1\n"

-     ]

-    }

-   ],

-   "source": [

-    "#To compute gcd using modular recursion\n",

-    "def gcd(a,b):\n",

-    "    if a==0:\n",

-    "        return b\n",

-    "    else:\n",

-    "        return gcd(b%a,a) #recursive call\n",

-    "\n",

-    "num1=input(\"Enter the first number\")\n",

-    "num2=input(\"Enter the second number\")\n",

-    "print \"The gcd of\",num1,\",\",num2,\"is\",gcd(num1,num2)\n"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "# 05:INDUCTION AND RECURSION"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "## Example 04: Page 362"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 4,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "Enter the number2\n",

-      "Enter the power5\n",

-      "Enter the modulo number3\n",

-      "The answer of mpower( 2 , 5 , 3 ) is 2\n"

-     ]

-    }

-   ],

-   "source": [

-    "#To compute mpower function using recursion\n",

-    "def mpower(b,n,m):\n",

-    "    if n==0:\n",

-    "        return 1\n",

-    "    else:\n",

-    "        if n%2==0:\n",

-    "            return ((mpower(b,n/2,m))**2) % m #recursive call\n",

-    "        else:\n",

-    "            return ((mpower(b,n/2,m)**2)%m*(b%m))%m #recursive call\n",

-    "number=input(\"Enter the number\")\n",

-    "power=input(\"Enter the power\")\n",

-    "modulo=input(\"Enter the modulo number\");\n",

-    "print \"The answer of mpower(\",number,\",\",power,\",\",modulo,\") is\",mpower(number,power,modulo)\n"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "# 05:INDUCTION AND RECURSION"

-   ]

-  },

-  {

-   "cell_type": "markdown",

-   "metadata": {},

-   "source": [

-    "## Example 09: Page 367"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": 5,

-   "metadata": {

-    "collapsed": false

-   },

-   "outputs": [

-    {

-     "name": "stdout",

-     "output_type": "stream",

-     "text": [

-      "enter the numbers to be merge sorted8,2,4,6,9,7,10,1,5,3\n",

-      "Ther Merge sort is ['1', '10', '2', '3', '4', '5', '6', '7', '8', '9']\n"

-     ]

-    }

-   ],

-   "source": [

-    "def msort2(x): #function for merge sort\n",

-    "    if len(x) < 2:\n",

-    "        return x\n",

-    "    result = []          \n",

-    "    mid = int(len(x)/2) #divides the elements into halves\n",

-    "    y = msort2(x[:mid])\n",

-    "    z = msort2(x[mid:])\n",

-    "    while (len(y) > 0) and (len(z) > 0):\n",

-    "            if y[0] > z[0]:\n",

-    "                result.append(z[0]) #merges to append the elements\n",

-    "                z.pop(0)\n",

-    "            else:\n",

-    "                result.append(y[0])\n",

-    "                y.pop(0)\n",

-    "    result += y\n",

-    "    result += z\n",

-    "    return result\n",

-    "l=[]\n",

-    "r=[]\n",

-    "l=raw_input(\"enter the numbers to be merge sorted\").split(\",\")\n",

-    "r=msort2(l)\n",

-    "print \"Ther Merge sort is\", r\n"

-   ]

-  },

-  {

-   "cell_type": "code",

-   "execution_count": null,

-   "metadata": {

-    "collapsed": true

-   },

-   "outputs": [],

-   "source": []

-  }

- ],

- "metadata": {

-  "kernelspec": {

-   "display_name": "Python 2",

-   "language": "python",

-   "name": "python2"

-  },

-  "language_info": {

-   "codemirror_mode": {

-    "name": "ipython",

-    "version": 2

-   },

-   "file_extension": ".py",

-   "mimetype": "text/x-python",

-   "name": "python",

-   "nbconvert_exporter": "python",

-   "pygments_lexer": "ipython2",

-   "version": "2.7.9"

-  }

- },

- "nbformat": 4,

- "nbformat_minor": 0

-}