58 lines
1.3 KiB
Factor
58 lines
1.3 KiB
Factor
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! Copyright (c) 2009 Guillaume Nargeot.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays kernel math math.ranges project-euler.common sequences ;
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IN: project-euler.085
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! http://projecteuler.net/index.php?section=problems&id=85
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! DESCRIPTION
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! -----------
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! By counting carefully it can be seen that a rectangular grid measuring
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! 3 by 2 contains eighteen rectangles.
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! Although there exists no rectangular grid that contains exactly two million
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! rectangles, find the area of the grid with the nearest solution.
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! SOLUTION
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! --------
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! A grid measuring x by y contains x * (x + 1) * y * (x + 1) rectangles.
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<PRIVATE
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: distance ( m -- n )
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2000000 - abs ;
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: rectangles-count ( a b -- n )
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2dup [ 1 + ] bi@ * * * 4 / ;
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: unique-products ( a b -- seq )
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tuck [a,b] [
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over dupd [a,b] [ 2array ] with map
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] map concat nip ;
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: max-by-last ( seq seq -- seq )
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[ [ last ] bi@ < ] most ;
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: array2 ( seq -- a b )
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[ first ] [ last ] bi ;
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: convert ( seq -- seq )
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array2 [ * ] [ rectangles-count distance ] 2bi 2array ;
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: area-of-nearest ( -- n )
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1 2000 unique-products
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[ convert ] [ max-by-last ] map-reduce first ;
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PRIVATE>
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: euler085 ( -- answer )
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area-of-nearest ;
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! [ euler085 ] 100 ave-time
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! 2285 ms ave run time - 4.8 SD (100 trials)
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SOLUTION: euler085
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