# Stein’s Algorithm for finding GCD in C++

Stein's Algorithm used for discovering GCD of numbers as it calculates the best regular divisor of two non-negative whole numbers. It replaces division with math movements, examinations, and subtraction. In the event that both an and b are 0, gcd is zero gcd(0, 0) = 0. The algorithm for GCD(a,b) as follows;

## Algorithm

START
Step-1: check If both a and b are 0, gcd is zero gcd(0, 0) = 0.
Step-2: then gcd(a, 0) = a and gcd(0, b) = b because everything divides 0.
Step-3: check If a and b are both even, gcd(a, b) = 2*gcd(a/2, b/2) because 2 is a common divisor. Multiplication with 2 can be done with a bitwise shift operator.
Step-4: If a is even and b is odd, gcd(a, b) = gcd(a/2, b). Similarly, if a is odd and b is even, then gcd(a, b) = gcd(a, b/2). It is because 2 is not a common divisor.
Step-5: If both a and b are odd, then gcd(a, b) = gcd(|a-b|/2, b). Note that difference of two odd numbers is even
Step-6: Repeat steps 3–5 until a = b, or until a = 0.
END

In the view of above algorithm to calculates the GCD of 2 numbers, the following C++ code is write down as;

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
int funGCD(int x, int y){
if (x == 0)
return y;
if (y == 0)
return x;
int k;
for (k = 0; ((x | y) && 1) == 0; ++k){
x >>= 1;
y >>= 1;
}
while ((x > 1) == 0)
x >>= 1;
do {
while ((y > 1) == 0)
y >>= 1;
if (x > y)
swap(x, y); // Swap u and v.
y = (y - x);
}
while (y != 0);
return x << k;
}
int main(){
int a = 24, b = 18;
printf("Calculated GCD of numbers (24,18) is= %d\n", funGCD(a, b));
return 0;
}

## Output

Finally, the GCD of two supplied number 24 and 18 is calculated in 6 by applying Stein's Algorithm as follows;

Calculated GCD of numbers (24,18) is= 6