Question

C++ PROGRAM ONLY!

For this lab you need to write a program that will read in two values from a user and output the greatest common divisor (using a recursive implementation of the Euclidean algorithm) to a file. In Lab #3, you implemented this program using an iterative method. Greatest Common Divisor In mathematics, the greatest common divisor (GCD) of two or more integers (when at least one of of them is zero then the larger value is the GCD. Euclidean Algorithm The Euclidean algorithm works by performing successive long divisions of two numbers that are unequal. Based on the result of the division of the larger number divided by the smaller number, the algorithm will either terminate and return the GCD, or will perform another long division using the smallest of the two original values as the numerator, and the remainder of the calculated long division as the divisor. The algorithm continues dividing and updating the numerator and divisor until the remainder of the division is 0. Recursion The Euclidean algorithm can be solved using iteration (as in Lab#3: Intro to Functions - GCD) or by recursion. Recursion is defined as a function repeatedly calling itself. Recursion is similar to looping in that the parameters serve as loop control variables, the parameters are initialized outside of the function by the initial function call, the same body of code is executed repeatedly, each call/iteration advances the solution toward completion and changes the parameter(s) for each subsequent call. However, the control flow between looping and recursion differ. When looping, the control flow of the loop structure does not leave the procedure/method it is currently executing in; whereas with recursion, looping is performed by successive (recursive) function calls where each recursive call invokes a new instance of the procedure on the call stack, and hence loops through the same body of code. A recursive function is usually defined as having one or multiple base-case(s), which terminates the recursion, and one or more inductive or recursive case(s). As a general rule, it is important to test base cases before making recursive calls to avoid infinite recursion. A summary of a recursive Euclidian algorithm & example follow: Base case: If n divides m with no remainder, return n For m2 n>0, gcd(m,n) = – Recursive Case: Otherwise, return gedín, remainder of m/n)

Answer 1

The C++ code implementing gcd is as follows:-

The output is stored in a file with name "results.txt"

 #include<iostream> #include<algorithm> #include<iomanip> #include<fstream> #include<vector> #include<utility> #include<conio.h> using namespace std; int gcd(int a,int b){ if(b==0) return a; return gcd(b,a%b); } void readValues(int &a,int &b){ cout<<"\nEnter first integer: "; cin>>a; cout<<"Enter the second integer:"; cin>>b; } void outputToFile(ofstream &File,int gcdValue){ File<<gcdValue<<endl; } int main(){ ofstream File; File.open("results.txt",ios::out|ios::trunc); for(int i=1;i<=4;i++){ int a,b; readValues(a,b);// Function to read inputs int gcdValue=gcd(a,b);// Function to implement gcd outputToFile(File,gcdValue);// Function to output value } File.close(); }

The screen input/output-

Enter first integer: 72 Enter the second integer:32 Enter first integer: 99 Enter the second integer:30 Enter first integer: 48 Enter the second integer:18 Enter first integer: 12 Enter the second integer:0

The output file:-

results.txt como

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