miridian-2 wrote:
>
> bill lam wrote:
>
>> mar, 15 Dec 2009, miridian skribis:
>>> Maybe someone can suggest how to re-implement in J.
>>
>> What is your J solution?
>
> Here the J code.
>
> To have the "real" solution of the problem W must be 9.
>
> I have check Python and J with
> W = 2 answer = 153
> W = 3 answer = 58234
> W = 4 answer = 1895145
> W = 5 answer = 198253934 (from here J is slow)
> W = 6 answer = 27438555522 (here J is very slow)
> W = 7 answer = 1949314526229 (from here only Python solutions)
> W = 8 answer = 193553900967497
> W = 9 answer = 20574308184277971 (This is the answer to euler
> 161; Python takes about 4.5 seconds)
>
> ---- J code ----
>
> W =: 2 NB. 9
> H =: 12
> C =: 2 ^ 2 * W
>
> Mem =: ( C, W , H ) $ _1x
>
> Size =: 6 2 $ 3 1 1 3 2 2 2 2 2 1 2 2
> Piece =: 6 2 $ (2^W), (2^( 2 * W )), (2^1), (2^2), (2^1), (2^W), (2^1),
> (2^( W + 1 )), (2^W), (2^( W - 1 )), (2^W), (2^( W + 1 ))
>
> PlacePiece =: monad define
> 'c w h i' =. y
> if. ( h > H - ( < i, 0 ) { Size ) +. ( w > W - ( < i, 1 ) { Size )
> do.
> 0, c, w, h return.
> end.
> if. ( i = 4 ) *. ( w = 0 ) do.
> 0, c, w, h return.
> end.
> f0 =. +./ *./ #: c, ( < i, 0 ) { Piece
> f1 =. +./ *./ #: c, ( < i, 1 ) { Piece
> if. ( f0 +. f1 ) do.
> 0, c, w, h return.
> end.
> c =. c + ( ( < i, 0 ) { Piece ) + ( ( < i, 1 ) { Piece )
> c =. <. c % 2
> w =. w + 1
> while. 1 = 2 | c do.
> c =. <. c % 2
> w =. w + 1
> end.
> while. w >: W do.
> w =. w - W
> h =. h + 1
> end.
> 1, c, w, h return.
> )
>
> p161 =: monad define
> 'c w h' =. y
> if. ( w = 0 ) *. ( h = H ) *. ( c = 0 ) do.
> 1 return.
> end.
> if. _1x ~: ret =. ( < c, w, h ) { Mem do.
> ret return.
> end.
> ret =. 0x
> for_i. i. 6 do.
> 'f ct wt ht' =. PlacePiece c, w, h, i
> if. f do.
> ret =. ret + p161 ct, wt, ht
> end.
> end.
> Mem =: ret ( < c, w, h ) } Mem
> ret return.
> )
>
> NB. answer =: p161 0 0 0
>
>
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
>
You could also try 64-bit machine and use ordinary integers
instead of extended ones. From my laptop:
$ ~/j64-602/bin/jconsole
W=:9
load 'pieces.ijs'
time =: 6!:2
time 'Ans9=:p161 0 0 0'
188.896
Ans9
20574308184277971
which agrees with the expected answer.
File pieces.ijs is your code without the first line and
with all three occurrences of extended precision integers
replaced by ordinary integers (just remove x).
Granted, the code is not very fast but it is also very long.
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