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Solution: Water and Jug Problem

Explore how to solve the Water and Jug Problem by applying number theory, specifically using the greatest common divisor. Understand conditions for measuring an exact target amount of water with two jugs, and learn an efficient algorithm with O(log(min(x,y))) time complexity.

Statement

You are given two jugs with capacities of x liters and y liters, respectively, along with an infinite water supply. Determine whether it is possible for the total amount of water in both jugs may reach target liters.

You may perform the following operations any number of times:

  • Fill either jug completely with water.

  • Empty either jug completely.

  • Pour water from one jug into the other until either the receiving jug becomes ...