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||This finds one solution to the eight queens problem, using a
||different method from that of the previous script, "queens.m".
||To run it, say
|| output
||This time the backtracking is programmed explicitly
output = concat [c:shownum r++" "|(c,r)<-zip2 "rnbqkbnr" soln]
soln = until full extend emptyboard
extend board = until safe alter (addqueen board)
addqueen board = 1:board
emptyboard = []
full board = # board=8
alter (q:board) = q+1:board, if q<8
= alter board, otherwise ||backtrack
safe (q:board) = and [~checks q board i|i<-index board]
checks q board i = q=board!i \/ abs(q-board!i)=i+1
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