【leetcode】365. Water and Jug Problem

题目描述：

You are given two jugs with capacities x and y litres. There is an infinite amount of water supply available. You need to determine whether it is possible to measure exactly zlitres using these two jugs.

Operations allowed:

• Fill any of the jugs completely.
• Empty any of the jugs.
• Pour water from one jug into another till the other jug is completely full or the first jug itself is empty.

解题分析：

这是我本科时算法课上到一道经典题。两个瓶子可能量出的水是两个瓶子容量最大公约数的倍数。所以只要判断z是否可以被x，y的最大公约数整除即可。

具体代码：

public class Solution {
      public static boolean canMeasureWater(int x, int y, int z) {
        int n=Math.max(x, y);
        int m=Math.min(x, y);
        x=n;
        y=m;
        if(z>x)
            return false;
        if(z==x||z==y)
            return true;
        n=fun(x,y);
        return z%n==0;
    }
    //求x，y的最大公约数
    public static int fun(int x,int y){
        if(x%y==0)
            return y;
        while(x%y!=0){
            int m=Math.max(x-y, y);
            int n=Math.min(x-y, y);
            x=m;
            y=n;
        }
        return y;
    }
}