[Leetcode] 365. Water and Jug Problem 解题报告

题目：

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 z litres using these two jugs.

If z liters of water is measurable, you must have z liters of water contained within one or both buckets by the end.

Operations allowed:

• Fill any of the jugs completely with water.
• 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: (From the famous "Die Hard" example)

Input: x = 3, y = 5, z = 4Output: True

Example 2:

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

思路：

这是一道数学题目（不过顺便也考查了一下求最大公约数的辗转相除法^_^），具体解释在youtube上面可以看到： "Die Hard" example，我自己也没明白具体原理。不过总体来讲要用x升和y升大小的两个桶精确量出z升水，其充要条件是：1）z必须小于等于（x + y）（否则装不下）；2）z必须可以除尽x和y的最大公约数。其中条件1）显而易见；但是条件2）是为什么呢？求解释。

代码：

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