Water Jug Problem in AI

The Water Jug Problem is a classic problem in artificial intelligence and computer science that involves finding a series of steps to measure a specific volume of water using jugs of known capacities. The problem typically goes like this:

You are given two jugs, one with a capacity of a liters and the other with a capacity of b liters, where a and b are positive integers. The objective is to measure exactly c liters of water, where c is a positive integer, using only these two jugs and an infinite supply of water.

The operations allowed are:

  1. Filling a jug completely from the tap.

  2. Emptying a jug completely onto the ground.

  3. Pouring water from one jug into another until either the pouring jug is empty or the receiving jug is full.

The task is to determine whether it is possible to measure exactly c liters of water and, if so, to find a sequence of operations to achieve this goal.

This problem can be solved using various search algorithms such as depth-first search (DFS), breadth-first search (BFS), or even using mathematical methods such as the greatest common divisor (GCD) algorithm to check if c is a multiple of the greatest common divisor of a and b.

Here's a high-level approach to solving the Water Jug Problem using a search algorithm like BFS:

  1. Define a state space representation where each state represents the water levels in the two jugs.

  2. Start with an initial state where both jugs are empty.

  3. Generate successor states by applying all possible operations (filling, emptying, pouring) to the current state.

  4. Add the successor states to a queue (or stack for DFS) and continue the process until a goal state (where one of the jugs contains c liters of water) is reached or all states have been explored.

  5. If a goal state is found, backtrack to reconstruct the sequence of operations that led to that state.

The solution to the Water Jug Problem lies in finding a sequence of valid operations that transforms the initial state into a goal state, where one of the jugs contains exactly c liters of water. The search algorithm explores the state space to find this sequence efficiently.

Implementing this solution involves designing appropriate data structures, defining state transition rules, and implementing the search algorithm to traverse the state space. For more check out the free online Artificial tutorial by AlmaBetter!