54 lines
1.1 KiB
Factor
54 lines
1.1 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: arrays assocs combinators kernel math sequences math.ranges locals ;
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IN: project-euler.076
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! http://projecteuler.net/index.php?section=problems&id=76
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! DESCRIPTION
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! -----------
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! How many different ways can one hundred be written as a
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! sum of at least two positive integers?
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! SOLUTION
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! --------
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! This solution uses dynamic programming and the following
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! recurence relation:
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! ways(0,_) = 1
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! ways(_,0) = 0
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! ways(n,i) = ways(n-i,i) + ways(n,i-1)
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<PRIVATE
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: init ( n -- table )
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[1,b] [ 0 2array 0 ] H{ } map>assoc
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1 { 0 0 } pick set-at ;
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: use ( n i -- n i )
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[ - dup ] keep min ; inline
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: ways ( n i table -- )
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over zero? [
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3drop
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] [
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[ [ 1- 2array ] dip at ]
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[ [ use 2array ] dip at + ]
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[ [ 2array ] dip set-at ] 3tri
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] if ;
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:: each-subproblem ( n quot -- )
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n [1,b] [ dup [1,b] quot with each ] each ; inline
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PRIVATE>
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: (euler076) ( n -- m )
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dup init
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[ [ ways ] curry each-subproblem ]
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[ [ dup 2array ] dip at 1- ] 2bi ;
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: euler076 ( -- m )
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100 (euler076) ;
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