From 6279fa19ac6e2a4087df2e6fe985430ecc2c2d5d Mon Sep 17 00:00:00 2001 From: kinitrupti Date: Fri, 12 May 2017 18:53:46 +0530 Subject: Removed duplicates --- .../screenshots_version_backup/chapter5.ipynb | 312 --------------------- 1 file changed, 312 deletions(-) delete mode 100755 Discrete_Mathematics_and_its_Applications_by_Kenneth_H.Rosen/screenshots/screenshots_version_backup/chapter5.ipynb (limited to 'Discrete_Mathematics_and_its_Applications_by_Kenneth_H.Rosen') 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 deleted file mode 100755 index 14960493..00000000 --- a/Discrete_Mathematics_and_its_Applications_by_Kenneth_H.Rosen/screenshots/screenshots_version_backup/chapter5.ipynb +++ /dev/null @@ -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 -} -- cgit