93 lines
2.3 KiB
Factor
93 lines
2.3 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: accessors kernel locals math project-euler.common ;
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IN: project-euler.215
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! http://projecteuler.net/index.php?section=problems&id=215
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! DESCRIPTION
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! -----------
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! Consider the problem of building a wall out of 2x1 and 3x1 bricks
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! (horizontal x vertical dimensions) such that, for extra strength, the gaps
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! between horizontally-adjacent bricks never line up in consecutive layers,
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! i.e. never form a "running crack".
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! For example, the following 93 wall is not acceptable due to the running crack
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! shown in red:
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! See problem site for image...
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! There are eight ways of forming a crack-free 9x3 wall, written W(9,3) = 8.
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! Calculate W(32,10).
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! SOLUTION
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! --------
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<PRIVATE
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TUPLE: block two three ;
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TUPLE: end { ways integer } ;
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C: <block> block
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C: <end> end
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: <failure> ( -- end ) 0 <end> ; inline
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: <success> ( -- end ) 1 <end> ; inline
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: failure? ( t -- ? ) ways>> 0 = ; inline
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: choice ( t p q -- t t )
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[ [ two>> ] [ three>> ] bi ] 2dip bi* ; inline
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GENERIC: merge ( t t -- t )
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GENERIC# block-merge 1 ( t t -- t )
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GENERIC# end-merge 1 ( t t -- t )
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M: block merge block-merge ;
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M: end merge end-merge ;
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M: block block-merge [ [ two>> ] bi@ merge ]
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[ [ three>> ] bi@ merge ] 2bi <block> ;
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M: end block-merge nip ;
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M: block end-merge drop ;
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M: end end-merge [ ways>> ] bi@ + <end> ;
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GENERIC: h-1 ( t -- t )
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GENERIC: h0 ( t -- t )
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GENERIC: h1 ( t -- t )
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GENERIC: h2 ( t -- t )
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M: block h-1 [ h1 ] [ h2 ] choice merge ;
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M: block h0 drop <failure> ;
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M: block h1 [ [ h1 ] [ h2 ] choice merge ]
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[ [ h0 ] [ h1 ] choice merge ] bi <block> ;
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M: block h2 [ h1 ] [ h2 ] choice merge <failure> swap <block> ;
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M: end h-1 drop <failure> ;
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M: end h0 ;
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M: end h1 drop <failure> ;
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M: end h2 dup failure? [ <failure> <block> ] unless ;
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: next-row ( t -- t ) [ h-1 ] [ h1 ] choice swap <block> ;
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: first-row ( n -- t )
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[ <failure> <success> <failure> ] dip
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1 - [| a b c | b c <block> a b ] times 2drop ;
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GENERIC: total ( t -- n )
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M: block total [ total ] dup choice + ;
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M: end total ways>> ;
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: solve ( width height -- ways )
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[ first-row ] dip 1 - [ next-row ] times total ;
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PRIVATE>
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: euler215 ( -- answer )
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32 10 solve ;
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! [ euler215 ] 100 ave-time
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! 208 ms ave run time - 9.06 SD (100 trials)
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SOLUTION: euler215
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