package euclidean_algorithm;

import java.util.Scanner;

/**
 * @author ALazy_cat
 * 歐幾里得演算法的自然語言描述：
 *    計算兩個非負整數x和y的最大公約數: 若y = 0，則最大公約數為x; 否則將remainder = x % y，x和y的
 * 最大公約數即為y和remainder的最大公約數 
 */
public class EuclideanAlgorithm {
    public static void main(String[] args) {
        Scanner in = new
 
 Scanner(System.in);
        System.out.print("請輸入兩個整數: ");
        int x = 0, y = 0;
        x = in.nextInt();
        y = in.nextInt();
        System.out.println("x, y的最大公約數是: " + euclideanAlgorithm_01(x, y, 1));
        System.out.println("---------------------");
        System.out.println("x, y的最大公約數是: "
 
 + euclideanAlgorithm_02(x, y, 1));
    }

    //歐幾里得演算法的遞迴實現
    public static int euclideanAlgorithm_01(int x, int y, int count) {
        //當y = 0時，遞迴結束
        int remainder = 0;
        System.out.println("第" + count++ + "次遞迴: " + "x = " + x + " , " + "y = " + y);
        if (y == 0)
            return x;
        remainder = x % y;
        return
 
 euclideanAlgorithm_01(y, remainder, count);
    }

    //歐幾里得演算法的迴圈實現
    public static int euclideanAlgorithm_02(int x, int y, int count) {
        int remainder = 0;
        while (y != 0) {
            System.out.println("第" + count++ + "次迴圈: " + "x = " + x + " , " + "y = " + y);
            remainder = x % y;
            x = y;
            y = remainder;
        }
        System.out.println("第" + count++ + "次迴圈: " + "x = " + x + " , " + "y = " + y);
        return x;
    }
}