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C++ Program to Implement Extended Euclidean Algorithm
The Extended Euclidean Algorithm is just a another way of calculating GCD of two numbers. It has extra variables to compute ax + by = gcd(a, b). It's more efficient to use in a computer program
Algorithm
Begin Declare variable a, b, x and y gcdExtended(int a, int b, int *x, int *y) if (a == 0) *x = 0; *y = 1; return b; Take two variables to store the result Update x and y using results of recursive call End
Example Code
#include <bits/stdc++.h> using namespace std; int gcdExtended(int a, int b, int *x, int *y) { if (a == 0) { *x = 0; *y = 1; return b; } int x1, y1; int gcd = gcdExtended(b%a, a, &x1, &y1); *x = y1 - (b/a) * x1; *y = x1; return gcd; } int main() { int x, y; int a = 35, b = 15; cout<<"gcd "<<gcdExtended(a, b, &x, &y); return 0; }
Output
gcd 5
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