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

Credits:
Special thanks to @vinod23 for adding this problem and creating all test cases.

Analysis:

It is a number theory problem.

https://discuss.leetcode.com/topic/49238/math-solution-java-solution/2

Solution:

public class Solution {
    public boolean canMeasureWater(int x, int y, int z) {
        if (x+y < z) return false;
        
        if (x==z || y==z || x+y==z) return true;
        
        return z%GCD(x,y)==0;
        
    }
    
    public int GCD(int x, int y){
        while (x%y!=0){
            int temp = x;
            x = y;
            y = temp%y;
        }
        return y;
    }
}