factor/extra/project-euler/102/102.factor

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1.8 KiB
Factor

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