用于扩展欧几里得算法的Java程序

两个数的 GCD 是除以这两个数的最大数。找到 GCD 的一种简单方法是对两个数字进行因式分解并乘以公因数。

// Java program to demonstrate working of extended
// Euclidean Algorithm
  
import java.util.*;
import java.lang.*;
  
class GFG {
    // extended Euclidean Algorithm
    public static int gcdExtended(int a, int b, int x, int y)
    {
        // Base Case
        if (a == 0) {
            x = 0;
            y = 1;
            return b;
        }
  
        int x1 = 1, y1 = 1; // To store results of recursive call
        int gcd = gcdExtended(b % a, a, x1, y1);
  
        // Update x and y using results of recursive
        // call
        x = y1 - (b / a) * x1;
        y = x1;
  
        return gcd;
    }
  
    // Driver Program
    public static void main(String[] args)
    {
        int x = 1, y = 1;
        int a = 35, b = 15;
        int g = gcdExtended(a, b, x, y);
        System.out.print("gcd(" + a + ", " + b + ") = " + g);
    }
}
// Code Contributed by Mohit Gupta_OMG <(0-o)>

输出：

gcd(35, 15) = 5

有关详细信息，请参阅有关基本和扩展欧几里得算法的完整文章！