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2013-12-26T22:37:37.290
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<h2>Suggested approach</h2> <p>I would recommend you read up on a <a href="http://en.wikipedia.org/wiki/Deterministic_finite_automaton" rel="nofollow">deterministic finite automaton</a>.</p> <p>The way I would attempt to model this kind of problem is to turn the problem into a state machine that is able to recognise strings of the type that you want based on feeding characters in one at a time.</p> <p>Once you have a state machine, you can use dynamic programming to count the number of matching strings that can be generated by starting in a particular state. (The state incorporates knowing how many characters have been generated so far, and the progress in each of your rules.)</p> <p>With the results of this dynamic programming, you can generate the k^th lexicographically ordered example of a matching string in time O(n) where n is the length of the string.</p> <p>However, the cost of solving the dynamic programming will vary a lot depending on the complexity of your rule set.</p> <h2>Example</h2> <p>For your example 3:</p> <pre><code>There must be at least 2 differences from the original string The differences must be in the alphabet set (A,B,C,D,E) Differences must occur within defined index ranges of the string Each range must have 2 differences </code></pre> <p>the state would need to include the following information:</p> <pre><code>Number of differences in first range (0,1,2) Number of differences in second range (0,1,2) </code></pre> <p>so there would be a total of 9 states to model.</p> <p>For a system with R ranges, each requiring D differences, there would be (D+1)^R states required (fewer if the ranges do not overlap).</p>
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1. POGenerating Variants of a String According to Rules
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1. USPeter de Rivaz
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1. COThis looks really promising. I'll do some reading based this info and update with what I find. Thank you!
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  UStorbinsky

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