365. Water and Jug Problem

Question

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


Code

public class Solution {
    public boolean canMeasureWater(int x, int y, int z) {
        if (z == x || z == y) return true;
        if (z > (x + y)) return false;
        int n = get(x, y);
        if (n == 0) return false;
        return z % n == 0;
    }
    
    public int get(int a, int b) {//求最大公约数
        while (b != 0) {
            int temp = a % b;
            a = b;
            b = temp;
        }
        return a;
    }
}

Solution

z不能超过x与y之和。

若z等于x或y则肯定可以完成要求。

若z是x与y的最大公约数的倍数,也可以完成要求。

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