为什么我的程序在某些情况下输出不正确？

Question

I have made an implementation of the Euclidean Algorithm in Java to find the Greatest Common Divisor (GCD) of two given numbers.

For the most part, my program works fine, I have tested it with a few random sets of numbers, although, I have found in one case (that I know of) that it's giving an incorrect output, which is for the following combination of numbers:

Enter integer a: 8965 Enter integer b: 55

The output of the program should be 55, although this is not the case. The out given is as follows:

gcd = 1 Execution time: 0.005747ms.

I'm not sure why this particular combination of numbers is causing a problem, as it works fine for other numbers, for example, here is the results for a different set of numbers:

Enter integer a: 15000

Enter integer b: 5325

gcd = 75

Execution time: 0.007389ms.

import java.util.Scanner;
public class EuclideanAlgorithm {
    public static void main (String [] args) {
        int a, b;
        try(Scanner sc = new Scanner(System.in);) {
            System.out.print("Enter integer a: ");
            a = sc.nextInt();
            System.out.print("Enter integer b: ");
            b = sc.nextInt();
        }
        long start = System.nanoTime();
        int answer = EuclideanAlgorithm(a, b);
        long stop = System.nanoTime();
        System.out.println("gcd = " + answer);
        System.out.println("Execution time: " + ((stop - start) / 1e+6) + "ms.");

    }

    public EuclideanAlgorithm() {}; //Suppress default constructor

    private static int EuclideanAlgorithm(int a, int b) {
        if ( (a == 0) || (b == 0)) {
            return 0;
        }
        if (b > a) {
            int temp = a;
            a = b;
            b = temp;
        }
        int gcd = 1;
        while(gcd != 0) {
            if( (a % b) == 0) {
                break;
            }
            gcd = a % b;
            a  = b;
            b = gcd;
        }
        return gcd;
    }
}

Answer 1

Whenever one of your numbers a , b is a multiple of the other, then your if condition will cause a break and 1 will be returned, which is incorrect. But the rest of the algorithm is incorrect also.

According to the pseudocode for the Euclidean Algorithm :

function gcd(a, b)
while b ≠ 0
   t := b
   b := a mod b
   a := t
return a

You need to check if b is not 0 , not the gcd. You'll need to modify your code to match this algorithm; your code is not currently matching this algorithm.

Answer 2

Because of the if condition inside this while loop

int gcd = 1;
while(gcd != 0) {
    if( (a % b) == 0) {
        break;
    }
    gcd = a % b;
    a  = b;
    b = gcd;
}

So, in case a % b = 0 at the beginning -> result is always equaled to 1.

You need to handle that case separately.

int gcd = b;
while(a % b != 0){
   gcd = a % b;
   a = b;
   b = gcd;
}

Answer 3

It's easy 55 divides 8965 that means you programm breaks in the first line and returns your initial value which is 1.

Instead something like this could help.

int gcd = 1;
if( (a % b) == 0) {
   return b;
}
while(gcd != 0) {
    if( (a % b) == 0) {
        break;
    }
    gcd = a % b;
    a  = b;
    b = gcd;
}