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POTraversing through all possible moves
 

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    <p>Ok I am sort of stuck with this problem.</p> <p>I have a Puzzle object that has an array for amounts { 1, 2, 3} and an array representing the target {3, 3, 0} and a move function that takes two integers i &amp; j and applies it to the array. </p> <p>Now I am trying to write a solver for this. So the idea is that we apply all possible values for i &amp; j and keep applying it until we get a desired target.</p> <p>I am trying to use a recursive method to handle this but what I am not able to grasp is how to stem my recursion into different ways and find the best "set of moves" that gets me to the target.</p> <p>So the list of possible moves:</p> <p>(0, 1), (0, 2), (1, 0), (1, 2), (2, 1), (2, 0)</p> <p>After each of these move we get a new "amounts array" and we need to apply these moves onto that and check if any of them results in the "target array".</p> <p>So my pseudocode is:</p> <pre><code>solve(puzzle): if puzzle.isSolved: return true; else: solve(puzzle.move(0, 1)); solve(puzzle.move(0, 2)); solve(puzzle.move(1, 0)); solve(puzzle.move(1, 2)); solve(puzzle.move(2, 0)); solve(puzzle.move(2, 1)); </code></pre> <ul> <li>We are assuming that puzzle.move function returns the puzzle with new state.</li> </ul> <p>Now I am sure I am doing something horribly wrong here.. but I can't seem to put my finger on it. So any thoughts / hints / pointers would be appreciated.</p> <p>Thanks.</p> <p><strong>Edit</strong></p> <p>Ok so couple of things to make this more clear for everyone:</p> <p>Since puzzle.move returns the puzzle after applying the move, I am thinking of creating a new puzzle so that the recursion goes through that. Basically, what needs to happen is that after each move we will have a new state of amount array.</p> <p>So after a move (i = 0, j = 1) the puzzle with initial amount of (a, b, c) has an amounts (a-a, b+a, c). We than take this new amount array and apply the next move (i = 0, j = 2) and so one.</p> <p>But that is just one part of the "tree" there is another path that needs to be checked which is when we apply the move (i = 0, j = 2) on the initial amount and then go on from there.</p> <p>Hope this helps :)</p> <p>btw, this is problem is known as Water Jug Problem (http://www.cut-the-knot.org/ctk/Water.shtml)</p>
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