Solving the Three Jugs Problem: A Precise Formulation and Algorithmic Approach
<p>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.</p>
<p><em>Problem Formulation</em></p>
<p>The problem is defined by several key components:</p>
<p>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).</p>
<p>Initial State: At the start, all jugs are empty (0 gallons in each).</p>
<p>Actions: We have three types of actions available:</p>
<ol>
<li>Fill(X): Fill jug X to its maximum capacity.</li>
<li>Empty(X): Empty jug X onto the ground.</li>
<li>Pour(X, Y): Pour the contents of jug X into jug Y until either jug X is empty, jug Y is full, or both.</li>
</ol>
<p>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).</p>
<p>Cost Function: We define the cost as the number of actions required to reach the goal state. Our aim is to minimize this cost.</p>
<p><em>Solving the Problem</em></p>
<p>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.</p>
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