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POCreate expression trees from given sets of numbers and operations and find those that evaluate to a target number in Mathematica 8 or above
 

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  1. POCreate expression trees from given sets of numbers and operations and find those that evaluate to a target number in Mathematica 8 or above
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    <p>Given a set of numbers and a set of binary operations, what is the fastest way to create random expression trees or exhaustively check every possible combination in Mathematica?</p> <p>What I am trying to solve is given:</p> <pre><code>numbers={25,50,75,100,3,6} (* each can ONLY be used ONCE *) operators={Plus,Subtract,Times,Divide} (* each can be used repeatedly *) target=99 </code></pre> <p>find expression trees that would evaluate to target.</p> <p>I have two solutions whose performances I give for the case where expression trees contain exactly 4 of the numbers and 3 operators:</p> <ol> <li>random sample &amp; choice: ~25K trees / second</li> <li>exhaustive scan: 806400 trees in ~2.15 seconds</li> </ol> <p>(timed on a laptop with: Intel(R) Core(TM)2 Duo CPU T9300 @ 2.50GHz, 3GB ram, no parallelization used yet but would be most welcome in answers)</p> <p>My notebooks are a bit messy at the moment. So I would first love to pose the question and hope for original ideas and answers while I clean up my code for sharing.</p> <p>Largest possible case is where every expression tree uses up all the (6) numbers and 'Length[numbers]-1' (5) operators.</p> <p>Performance of methods in the largest case is:</p> <ol> <li>random sample &amp; choice: ~21K trees / second</li> <li>exhaustive scan: 23224320 trees in ~100 seconds</li> </ol> <p>Also I am using Mathematica 8.0.1 so I am more than all ears if there are any ways to do it in OpenCL or using compiled functions wiht CompilationTarget->"C", etc.</p>
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    1. COSorry about that I will update the question in the coming minutes.
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    2. COCan you post your solution? I'd like to see how it fares against mine.
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      1. USMike Bailey
 

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