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

Bézout's identity

int gcd(int a, int b) {
    while (b) {
        int tmp = b;
        b = a % b;
        a = tmp;
    }
    return a;
}
bool 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;
}