365. Water and Jug Problem

• Difficulty: Medium

• Topics: Math

• Similar Questions:

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

Solutions:

class Solution {
public:
    bool canMeasureWater(int x, int y, int z) {
        // ax + by = z
        if (z ==0)  return true;
        if (x + y < z) return false;
        if (x != 0 && y != 0) {
            int divisor = gcd(x, y);
            return z % divisor == 0;
        } else return false;
    }

private:
    int gcd (int x, int y) {
        if (y > x) {
            return gcd(y, x);
        }

        if (y == 0) return x;
        return gcd(y, x % y);
    }

};