Talk:Fraction reduction: Difference between revisions
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::: I was originally toying around with the name: ''fallacious fraction reductions'', but I discarded it. Sounded worse than it was. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 11:43, 4 September 2019 (UTC) |
::: I was originally toying around with the name: ''fallacious fraction reductions'', but I discarded it. Sounded worse than it was. -- [[User:Gerard Schildberger|Gerard Schildberger]] ([[User talk:Gerard Schildberger|talk]]) 11:43, 4 September 2019 (UTC) |
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== searching for Optimizations == |
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Like PHIX one can create the list/array of all possible Permutations k out of n very effectivly:<BR> |
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http://rosettacode.org/wiki/Permutations#alternative <BR> |
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Think of cUsedDigits= 5 digits out of cMaxDigits=9 [1..9]<BR> |
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The size of the list is cUsedDigits! * binomial_coefficient(cMaxDigits,cUsedDigits)-> 5!*(9!/(5!*(9-5)!) = 15120 <BR> |
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[12345],[12354] ... [98756],[98765]<BR> |
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To memorize the used digits one can use a bitset 1..9.Logical AND of two bitsets will show, if at least one digit is part of both numbers.<BR> |
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Every section with first digit = 1 or 2... has the size of 15120 DIV cUsedDigits = 1680.<BR> |
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Searching 2* Index (1) = 12345 can start at Index 1680 = 21345<BR> |
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So one can search n DIV 2 .. n div 9 and multiples of those numbers.<Br><Br> |
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I think one good optimization would be going an inverted way.<BR> |
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You know fractions of k digits and extend them by one digit.<BR> to be continued.. |