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queens.l
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Lisp/Scheme
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1986-08-22
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3KB
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99 lines
;
; Place n queens on a board (graphical version)
; See Winston and Horn Ch. 11
;
; Usage:
; (queens <n>)
; where <n> is an integer -- the size of the board - try (queens 4)
;
; I do not know who the original Author of this is but it was found with some
; XLISP example lisp programs. This has been slightly modified to run on
; PC-LISP V2.13.
;
; Peter Ashwood-Smith
; August 22nd, 1986
; Do two queens threaten each other ?
(defun threat (i j a b)
(or (= i a) ;Same row
(= j b) ;Same column
(= (- i j) (- a b)) ;One diag.
(= (+ i j) (+ a b)))) ;the other diagonal
; Is poistion (n,m) on the board safe for a queen ?
(defun conflict (n m board)
(cond ((null board) nil)
((threat n m (caar board) (cadar board)) t)
(t (conflict n m (cdr board)))))
; Place queens on a board of size SIZE
(defun queens (size)
(prog (n m board soln)
(setq soln 0) ;Solution #
(setq board ())
(setq n 1) ;Try the first row
loop-n
(setq m 1) ;Column 1
loop-m
(cond ((conflict n m board) (go un-do-m))) ;Check for conflict
(setq board (cons (list n m) board)) ; Add queen to board
(cond ((> (setq n (1+ n)) size) ; Placed N queens ?
(print-board (reverse board) (setq soln (1+ soln))))) ; Print it
(go loop-n) ; Next row which column?
un-do-n
(cond ((null board) (return 'Done))) ; Tried all possibilities
(setq m (cadar board)) ; No, Undo last queen placed
(setq n (caar board))
(setq board (cdr board))
un-do-m
(cond ((> (setq m (1+ m)) size) ; Go try next column
(go un-do-n))
(t (go loop-m)))))
;Print a board
(defun print-board (board soln)
(prog (size)
(setq size (length board)) ;we can find our own size
(princ "\f\n\t\tSolution: ")
(princ soln)
(princ "\n\n\t")
(print-header size 1)
(princ "\n")
(print-board-aux board size 1)
(princ "\n")
)
)
; Put Column #'s on top
(defun print-header (size n)
(cond ((> n size) (princ "\n"))
(t (prog () (patom n)
(princ " ")
(print-header size (1+ n))))))
(defun print-board-aux (board size row)
(princ "\n")
(cond ((null board) ())
(t (prog ()
(princ row) ;print the row #
(princ "\t")
(print-board-row (cadar board) size 1) ;Print the row
(print-board-aux (cdr board) size (1+ row)))))) ;Next row
(defun print-board-row (column size n)
(cond ((> n size)())
(t (prog ()
(cond ((equal column n) (princ "Q"))
(t (princ ".")))
(princ " ")
(print-board-row column size (1+ n))))))