LeetCode-365-水壶问题 (不定次方程的整数解)

365. Water and Jug Problem

Description

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.

Example

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

Solution

问题转化为: 给定 n 个容器 a1, a2,…,an。 最后需要 m 单位的水。
即求一次不定方程a1*x1 + a2*x2 + ... + an*xn = m的整数解。

原问题中, 只有两个容器 x, y。方程变成: X*x1 + Y*y1 = Z是否有整数解。

Hint