2008-02-06 00:53:18 -05:00
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! Copyright (c) 2008 Aaron Schaefer.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.functions math.ranges project-euler.common sequences ;
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IN: project-euler.044
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! http://projecteuler.net/index.php?section=problems&id=44
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! DESCRIPTION
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! -----------
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! Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten
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! pentagonal numbers are:
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! 1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
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! It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference,
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! 70 − 22 = 48, is not pentagonal.
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! Find the pair of pentagonal numbers, Pj and Pk, for which their sum and
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! difference is pentagonal and D = |Pk − Pj| is minimised; what is the value of D?
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! SOLUTION
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! --------
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! Brute force using a cartesian product and an arbitrarily chosen limit.
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<PRIVATE
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: nth-pentagonal ( n -- seq )
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dup 3 * 1- * 2 / ;
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: sum-and-diff? ( m n -- ? )
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2008-03-29 21:36:58 -04:00
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2dup + -rot - [ pentagonal? ] bi@ and ;
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2008-02-06 00:53:18 -05:00
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PRIVATE>
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: euler044 ( -- answer )
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2500 [1,b] [ nth-pentagonal ] map dup cartesian-product
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2008-04-26 00:17:08 -04:00
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[ first2 sum-and-diff? ] filter [ first2 - abs ] map infimum ;
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2008-02-06 00:53:18 -05:00
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! [ euler044 ] 10 ave-time
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! 8924 ms run / 2872 ms GC ave time - 10 trials
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! TODO: this solution is ugly and not very efficient...find a better algorithm
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MAIN: euler044
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