65 lines
1.8 KiB
Factor
65 lines
1.8 KiB
Factor
! Copyright (c) 2009 Guillaume Nargeot.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays grouping io.encodings.ascii io.files kernel math
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math.parser sequences splitting project-euler.common ;
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IN: project-euler.102
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! http://projecteuler.net/index.php?section=problems&id=102
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! DESCRIPTION
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! -----------
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! Three distinct points are plotted at random on a Cartesian plane, for which
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! -1000 ≤ x, y ≤ 1000, such that a triangle is formed.
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! Consider the following two triangles:
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! A(-340,495), B(-153,-910), C(835,-947)
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! X(-175,41), Y(-421,-714), Z(574,-645)
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! It can be verified that triangle ABC contains the origin, whereas triangle
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! XYZ does not.
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! Using triangles.txt (right click and 'Save Link/Target As...'), a 27K text
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! file containing the co-ordinates of one thousand "random" triangles, find the
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! number of triangles for which the interior contains the origin.
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! NOTE: The first two examples in the file represent the triangles in the
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! example given above.
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! SOLUTION
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! --------
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! A triangle of coordinates (x1, y1) (x2, y2) (x3, y3) contains
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! the origin when (ab * bc > 0) and (bc * ca > 0) where:
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! ab = x1 * (y2 - y1) - y1 * (x2 - x1)
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! bc = x2 * (y3 - y2) - y2 * (x3 - x2)
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! ca = x3 * (y1 - y3) - y3 * (x1 - x3)
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<PRIVATE
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: source-102 ( -- seq )
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"resource:extra/project-euler/102/triangles.txt"
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ascii file-lines [
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"," split [ string>number ] map 2 group
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] map ;
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: det ( coord coord -- n )
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dupd [ [ last ] bi@ - ] [ [ first ] bi@ - ] 2bi 2array
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[ [ first ] bi@ * ] [ [ last ] bi@ * ] 2bi - ;
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: include-origin? ( coord-seq -- ? )
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dup first suffix 2 clump [ [ first ] [ last ] bi det ] map
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2 clump [ product 0 > ] all? ;
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PRIVATE>
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: euler102 ( -- answer )
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source-102 [ include-origin? ] count ;
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! [ euler102 ] 100 ave-time
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! 12 ms ave run time - 0.92 SD (100 trials)
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SOLUTION: euler102
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