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<P>Reinhard Scharnagl wrote:</P> <BLOCKQUOTE> it seems as if you would use a very complex method to detect invalid starting positions. I will add a more simple method in short to the reference code I have posted here yesterday. Thus one will be able to see, that generating valid CRC positions only is neither a run time problem nor too complex to be programmed. </BLOCKQUOTE> <P>No, my method is not so complex, and once I fixed the infinite loop bug, there were no run time problems. I have since modified it to your exact specifications, but here is how the method you're commenting on worked.</P> <OL> <LI> Clear the first rank.</LI> <LI> Select a random setup per your instructions.</LI> <LI> Check whether each Pawn is defended, and if any is undefended, start over.</LI> <LI> Generate a string of the setup and calculate its Levenshtein Distance from the setup for Gothic Chess. If the Levenshtein Distance is too small, start over. </OL> <P>The Levenshtein Distance is the minimal number of operations it takes to change one string into another, counting insertions, deletions, and substitutions as operations. Your instructions use the Hamming Distance, which is the number of substitutions it takes to change one string into another string of the same length. Although calculation of the Levenshtein Distance is more complicated than calculation of the Hamming Distance, I don't have to worry about that, because it is handled by a PHP function. Since almost all setups will pass, using the Levenshtein Distance doesn't cause any appreciable increase in time.</P> <P>Using the Hamming Distance, as your instructions use, has the advantage of being easier for humans to calculate, but as long as computers do the calculations, the more sophisticated Levenshtein Distance might be preferable. Whenever they are unequal, the Levenshtein Distance will be smaller than the Hamming Distance. This would be useful if you want to avoid setups that differ from Gothic Chess not only by a couple substitutions but also by moving one piece in a way that shifts much of the lineup one space left or right but keeps most of the order intact. For example, 'BRNBQCKANR' has all Pawns defended, and its Hamming Distance from Gothic Chess is 8, but its Levenshtein Distance is 2, because I got it by simply deleting a Bishop and inserting it on the left side.</P> <P>Your reference code has answered one question I had. I wasn't sure whether you meant to exclude setups whose Hamming Distance from Gothic Chess was less than three or less than or equal to three. From your code, it looks like less than three. So you're excluding any setup with a Hamming Distance of two or less. Given the same pieces, you will never have a Hamming Distance of only 1. So what you are excluding is limited to only setups that differ by switching the places of two pieces.</P> <P>The preset I made currently uses the Hamming Distance and follows your instructions to the letter for generating a random position and excluding invalid setups. If you ever decide that you would rather use the Levenshtein Distance, all I will have to do is replace the hamming operator with the levenshtein operator in my code.</P>