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.

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.

Constraints

• 0 <= x <= 10^6

• 0 <= y <= 10^6

• 0 <= z <= 10^6

Approach

Links

• GeeksforGeeks

• Leetcode

• ProgramCreek

• YouTube

Examples

Example 1

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

Output: True

Example 2

Solutions

Solution 1

/**
 * Time complexity : 
 * Space complexity : 
 */

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;
    }
    
    private int gcd(int a, int b) {
        if(b == 0) {
            return a;
        }
        return gcd(b, a%b);
    }
}

Follow up