56 lines
1.6 KiB
Factor
56 lines
1.6 KiB
Factor
! Copyright (c) 2008 Eric Mertens
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.ranges sequences sequences.lib ;
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IN: project-euler.116
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! http://projecteuler.net/index.php?section=problems&id=116
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! DESCRIPTION
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! -----------
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! A row of five black square tiles is to have a number of its tiles replaced
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! with coloured oblong tiles chosen from red (length two), green (length
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! three), or blue (length four).
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! If red tiles are chosen there are exactly seven ways this can be done.
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! If green tiles are chosen there are three ways.
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! And if blue tiles are chosen there are two ways.
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! Assuming that colours cannot be mixed there are 7 + 3 + 2 = 12 ways of
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! replacing the black tiles in a row measuring five units in length.
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! How many different ways can the black tiles in a row measuring fifty units in
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! length be replaced if colours cannot be mixed and at least one coloured tile
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! must be used?
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! SOLUTION
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! --------
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! This solution uses a simple dynamic programming approach using the
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! following recurence relation
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! ways(n,_) = 0 | n < 0
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! ways(0,_) = 1
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! ways(n,i) = ways(n-i,i) + ways(n-1,i)
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! solution(n) = ways(n,1) - 1 + ways(n,2) - 1 + ways(n,3) - 1
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<PRIVATE
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: nth* ( n seq -- elt/0 )
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[ length swap - 1- ] keep ?nth 0 or ;
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: next ( colortile seq -- )
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[ nth* ] [ peek + ] [ push ] tri ;
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: ways ( length colortile -- permutations )
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V{ 1 } clone [ [ next ] 2curry times ] keep peek 1- ;
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PRIVATE>
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: (euler116) ( length -- permutations )
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3 [1,b] [ ways ] with sigma ;
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: euler116 ( -- permutations )
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50 (euler116) ;
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