365. Water and Jug Problem

365. 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

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public class Solution {
    public boolean canMeasureWater(int x, int y, int z) {
        //limit brought by the statement that water is finallly in one or both buckets
        if(x + y < z) 
            return false;
        //case x or y is zero
        if( x == z || y == z || x + y == z ) 
            return true;
        //get GCD, then we can use the property of Bézout's identity
        return z%GCD(x, y) == 0;
    }

    public int GCD(int a, int b){
        while(b != 0 ){
            int temp = b;
            b = a%b;
            a = temp;
        }
        return a;
    }
}