# 365. Water and Jug Problem

## Description

You are given two jugs with capacities jug1Capacity and jug2Capacity liters. There is an infinite amount of water supply available. Determine whether it is possible to measure exactly targetCapacity liters using these two jugs.

If targetCapacity liters of water are measurable, you must have targetCapacity liters of water contained within one or both buckets by the end.

Operations allowed:

• Fill any of the jugs 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:

Input: jug1Capacity = 3, jug2Capacity = 5, targetCapacity = 4
Output: true
Explanation: The famous Die Hard example


Example 2:

Input: jug1Capacity = 2, jug2Capacity = 6, targetCapacity = 5
Output: false


Example 3:

Input: jug1Capacity = 1, jug2Capacity = 2, targetCapacity = 3
Output: true


Constraints:

• 1 <= jug1Capacity, jug2Capacity, targetCapacity <= 106

## Solutions

• class Solution {
public boolean canMeasureWater(int jug1Capacity, int jug2Capacity, int targetCapacity) {
if (jug1Capacity + jug2Capacity < targetCapacity) {
return false;
}
if (jug1Capacity == 0 || jug2Capacity == 0) {
return targetCapacity == 0 || jug1Capacity + jug2Capacity == targetCapacity;
}
return targetCapacity % gcd(jug1Capacity, jug2Capacity) == 0;
}

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

• class Solution {
public:
bool canMeasureWater(int jug1Capacity, int jug2Capacity, int targetCapacity) {
if (jug1Capacity + jug2Capacity < targetCapacity) return false;
if (jug1Capacity == 0 || jug2Capacity == 0)
return targetCapacity == 0 || jug1Capacity + jug2Capacity == targetCapacity;
return targetCapacity % gcd(jug1Capacity, jug2Capacity) == 0;
}

int gcd(int a, int b) {
return b == 0 ? a : gcd(b, a % b);
}
};

• class Solution:
def canMeasureWater(
self, jug1Capacity: int, jug2Capacity: int, targetCapacity: int
) -> bool:
if jug1Capacity + jug2Capacity < targetCapacity:
return False
if jug1Capacity == 0 or jug2Capacity == 0:
return targetCapacity == 0 or jug1Capacity + jug2Capacity == targetCapacity
return targetCapacity % gcd(jug1Capacity, jug2Capacity) == 0


• func canMeasureWater(jug1Capacity int, jug2Capacity int, targetCapacity int) bool {
if jug1Capacity+jug2Capacity < targetCapacity {
return false
}
if jug1Capacity == 0 || jug2Capacity == 0 {
return targetCapacity == 0 || jug1Capacity+jug2Capacity == targetCapacity
}

var gcd func(a, b int) int
gcd = func(a, b int) int {
if b == 0 {
return a
}
return gcd(b, a%b)
}
return targetCapacity%gcd(jug1Capacity, jug2Capacity) == 0
}

• using System;

public class Solution {
public bool CanMeasureWater(int x, int y, int z) {
if (x == 0 || y == 0) return z == x || z == y;
var gcd = GetGcd(x, y);
return z >= 0 && z <= x + y && z % gcd == 0;
}

private int GetGcd(int x, int y)
{
while (x > 0)
{
var quotient = x / y;
var reminder = x % y;
if (reminder == 0)
{
return y;
}
x = y;
y = reminder;
}
throw new Exception("Invalid x or y");
}
}