leetcode.365. Water and Jug Problem

happyxuma1991

于 2016-06-24 16:30:51 发布

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探讨使用两个容量分别为x和y升的水壶如何精确测量出z升水的方法。文章提供了一种数学解决方案，利用最大公约数的概念来判断是否能实现目标水量。

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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.

Example 1:

Input: x = 2, y = 6, z = 4
Output: True

Example 2:

Input: x = 2, y = 6, z = 5
Output: False

class Solution {
public:
     int gcd(int x, int y)  
    {  
        return y==0?x:gcd(y, x%y);  
    }  
    bool canMeasureWater(int x, int y, int z) {
        if(z <= max(x, y)&&(z%gcd(x, y) == 0))
            return true;  
        return false; 
    }
};