# LeetCode Water and Jug Problem

LeetCode Water and Jug Problem

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 = 4
Output: True

Example 2:

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

1. 盛满5L水罐；
2. 将5L水罐中的水导入3L水罐，此时5L水罐中还剩2L水；
3. 将3L水罐中的水清空；
4. 将5L水罐中的2L水倒入3L水罐中；
5. 盛满5L水罐；
6. 将5L水罐中的水倒入3L水罐中，此时5L水罐中剩余4L水，3L水罐中是满的；
7. 将3L水罐中的水清空，此时只剩5L水罐中的4L水。

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