README.md

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

Constraints:

• 0 <= x <= 10^6
• 0 <= y <= 10^6
• 0 <= z <= 10^6

Solutions (Ruby)

1. Mathematical

# @param {Integer} x
# @param {Integer} y
# @param {Integer} z
# @return {Boolean}
def can_measure_water(x, y, z)
  x + y >= z && (x + y == 0 || z % x.gcd(y) == 0)
end