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    <p>If you think of this as a path finding problem you could try an A* algorithm. </p> <p>(A heuristic based search of the answer space.)</p> <p>Also, do you just want to find a solution or the best solution? </p> <p><strong>EDIT</strong></p> <p><em>I don't feel like changing this, but I see that my example is bad since a single step solves it. Ignore that issue when looking at the example.</em></p> <p>Quick overview of how A* works (and slightly applied to this problem)</p> <p>To use A* you need a function that evaluates a given state (of completion). You want a higher value for states which are closer to the goal.</p> <p>For this problem two example functions</p> <ul> <li>(every letter that is correct * 1) - (number of letters different from goal * 10)</li> <li>(every letter that is correct * 100) - (number of letters different from goal)</li> </ul> <p>As you can see the first favors word size being close over correct letters The 2nd favors letters correct.</p> <p>Not sure which is better -- tho you could do a balanced formula too.</p> <p>Lets say we are trying to get from bot -> boat</p> <p>You would then evaluate all possible changes of boy, lets use the first function so two examples you would evaluate would be boot and bat (and others.) boot has a value of 3 and bat has a value of -7. Boot is better (according to this function) so then we would evaluate all possible changes of Boot (before any of the others) and find the solution. </p> <p>Clear as mud? Maybe Wikipedia explains it better.</p> <p><a href="http://en.wikipedia.org/wiki/A" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/A</a>*_search_algorithm</p> <p>Side Notes: </p> <ul> <li><p>A* will find the best solution if the function is designed right, if such a function exists for a give problem. This is the neat feature of A*.</p></li> <li><p>An A* enhancement is to short circuit looking at states (for example in the case above -- positive 3 is a very good score (4 is the max score) so your algorithm could stop looking at other states and move on to the one that is very close.</p></li> <li><p>The two hard parts of A* are 1) finding the right function and 2) being able to enumerate all the possible states. I think 2 is not so hard to do with a good dictionary file and some fast hashing/searching functions. </p></li> </ul>
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    1. POWhat is the best algorithm to find a doublet / word ladder?
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    1. COyeah, but to find the path, I need to build the graph first, right? or am I wrong? First step is to build the graph (lets say I have a 10000 word list). Second step would be to find the shortest path. There are algorithms for the second step, but how do I do the first step?
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      1. USuser251502
    2. CO@unknown: It is usual to build the graph as you go. Any tutorial on A* search should explain things further.
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    3. COA* is an ok way to go here as long as you can find a good heuristic for it. Finding a heuristic for this problem which is <i>always</i> good is going to take some research.
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      1. USNick Larsen
 

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