Author: Vincent Diepeveen
Date: 14:24:50 09/10/02
Go up one level in this thread
On September 10, 2002 at 16:53:36, Heiner Marxen wrote:
>On September 10, 2002 at 15:09:10, Vincent Diepeveen wrote:
>
>>On September 10, 2002 at 14:28:51, Guido wrote:
>[snip]
>>>It is not necessary to have a table for 1891 positions and one for 1128
>>>position.
>>>The 62*61/2 table can be used for all the case N*(N-1)/2 with N <= 62.
>>>All these tables are contained inside the biggest. So 62*61/2 is the
>>>biggest table because kings are already positioned.
>>
>>I do get the idea i could reuse it somehow but i don't understand it
>>completely.
>>
>>suppose i have a chess board sized table [5][5]
>>for a board of 5x5 to place 2
>>pieces. lefttop = 0 of course. and entry 0 is illegal
>>because 2 pieces cannot be on the same square and
>>also second piece is at a higher square than the first:
>>
>
>>Now suppose i use this table to index it for 2 similar pieces
>>after 1 piece has been put already on the board.
>>
>>then i do not see how i index into this table
>>anymore.
>
>Try this one (or a transposition of it):
>table[5][5] = {
> {-1, 0, 1, 3, 6},
> {-1,-1, 2, 4, 7},
> {-1,-1,-1, 5, 8},
> {-1,-1,-1,-1, 9},
> {-1,-1,-1,-1,-1} }
I see, that solves the problem completely indeed.
>It also can be computed efficiently on-the-fly with a small table of
>binomial coefficients.
I am very interested in formula's doing that, because
of 5 of the same men i won't put in a table.
Already some mathematical stuff (with correction even!!) from Simon Finn
gave me some great insights here that it should be possible.
>Cheers,
>Heiner
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