N queens problem
Solves the N queens problem for any n-by-n board.
bernhardsson(n) bernhardssonA(n) bernhardssonB(n)
n |
Size of the chessboard |
Uses a direct transcript of Bo Bernhardsson's method.
All solutions (up to reflection and translation) for the 8-by-8 case given in the examples.
Robin K. S. Hankin
Bo Bernhardsson 1991. “Explicit solutions to the n-queens problem for all n”. SIGART Bull., 2(2):7
Weisstein, Eric W. “Queens Problem” From MathWorld–A Wolfram Web Resource http://mathworld.wolfram.com/QueensProblem.html
bernhardsson(7)
a <-
matrix(
c(3,6,2,7,1,4,8,5,
2,6,8,3,1,4,7,5,
6,3,7,2,4,8,1,5,
3,6,8,2,4,1,7,5,
4,8,1,3,6,2,7,5,
7,2,6,3,1,4,8,5,
2,6,1,7,4,8,3,5,
1,6,8,3,7,4,2,5,
1,5,8,6,3,7,2,4,
2,4,6,8,3,1,7,5,
6,3,1,8,4,2,7,5,
4,6,8,2,7,1,3,5)
,8,12)
out <- array(0L,c(8,8,12))
for(i in 1:12){
out[cbind(seq_len(8),a[,i],i)] <- 1L
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