The Three Jugs Problem is a classic puzzle that challenges your ability to measure a specific quantity of water using three jugs of different capacities and a faucet. In this technical blog, we’ll delve into the problem formulation and explore a strategy to solve it.
Problem Formulation
The problem is defined by several key components:
State: We represent the problem state by the amounts of water in each jug. These jugs are named Jug12 (12-gallon capacity), Jug8 (8-gallon capacity), and Jug3 (3-gallon capacity).
Initial State: At the start, all jugs are empty (0 gallons in each).
Actions: We have three types of actions available:
- Fill(X): Fill jug X to its maximum capacity.
- Empty(X): Empty jug X onto the ground.
- Pour(X, Y): Pour the contents of jug X into jug Y until either jug X is empty, jug Y is full, or both.
Goal State: The objective is to measure exactly 1 gallon of water in one of the jugs while the others can have any amount (including empty).
Cost Function: We define the cost as the number of actions required to reach the goal state. Our aim is to minimize this cost.
Solving the Problem
Now, let’s discuss a strategy to solve this problem. It involves a search algorithm, like Breadth-First Search (BFS) or Depth-First Search (DFS), to explore the state space while respecting the problem constraints.