This nqueens solution tries all ^~n possibilities by placing queens rank
by rank, filtering out impossible solutions as it goes, and finally
converting layouts to anagram index. Performance is far superior to
filtering all !n full layouts as it solves n=12 in half minute (on this
computer). I imagine the recursive algorithm tries only !n layouts
filtering each step. The code is longer than others, but it's my entry
and I understand it.
$ ijconsole
identity =: =@:i.
test =: (1 = >./)@:(+/ , +/"1 , +//. , +//.@:|.)
nqueens =: 3 :'A.@:((identity y)&i."2) (#~
test"_1)@:(,/)@:((identity y) ,"1 2/ ])^:y (1 0 0$y)'
nqueens 5
10 13 36 44 50 69 75 83 106 109
#nqueens 8
92
timespacex 'smoutput # nqueens 12'
14200
14200
26.1923 1.14506e9
timespacex '# nqueens 12'
26.1723 1.14506e9
conversions to anagram index with similar performance, shorter than
identity&i:"2 are
to_anagram_index2 =: [:A.2^.#. NB. reversed, which won't matter for
nqueens problem.
to_anagram_index1 =: [:A.i.&1"1
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