【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;
     }
 }