50 lines
1.8 KiB
Racket
50 lines
1.8 KiB
Racket
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(define (enumerate-interval low high)
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(if (> low high)
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'()
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(cons low (enumerate-interval (+ low 1) high))))
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(define (list-ref l n)
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(if (= n 0) (car l)
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(list-ref (cdr l) (- n 1))))
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;; Not sure how to get a procedure to create (amb 1 ... n) for
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;; arbitrary n without doing quasiquote, unsplice, etc, so fix for
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;; n=8.
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(define (queens)
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(define (position row col) (cons row col))
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(define (row position) (car position))
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(define (col position) (cdr position))
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(define (positive-intercept position)
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(- (row position) (col position)))
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(define (negative-intercept position)
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(+ (row position) (col position)))
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(define (safe? k positions)
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(if (< k 2) true
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(let ((kth-position (list-ref positions (- k 1)))
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(pre-kth-positions (cdr (reverse positions))))
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;; If the row, positive or negative intercept of the k-th position
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;; is equal to any of the first k-1 positions, then the k-th
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;; position is not safe.
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(if (memv (row kth-position) (map row pre-kth-positions))
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false
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(if (memv (positive-intercept kth-position)
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(map positive-intercept pre-kth-positions))
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false
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(if (memv (negative-intercept kth-position)
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(map negative-intercept pre-kth-positions))
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false
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true))))))
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(define (queens-add-columns current-queens column)
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(if (> column 8) current-queens
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(let ((new-queens
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(append current-queens
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(list (position (amb 1 2 3 4 5 6 7 8) column)))))
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(require (safe? column new-queens))
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(queens-add-columns new-queens (+ column 1)))))
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(queens-add-columns '() 1))
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