;
; Place n queens on a board
;  See Winston and Horn Ch. 11
; 
; Usage:
;	(queens <n>)
;          where <n> is an integer -- the size of the board - try (queens 4)

; Do two queens threaten each other ?
(defun threat (i j a b)
  (or (eql i a)			;Same row
      (eql j b)			;Same column
      (eql (- i j) (- a b))	;One diag.
      (eql (+ i j) (+ a b))))	;the other diagonal

; Is position (n,m) on the board not 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 (board n m)
	(setq board nil)
	(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 (reverse board))))           ; Print config
	(go loop-n)			           ; Next row which column?
	un-do-n
	(cond ((null board) (return 'Done)) 	   ; Tried all possibilities
	      (t (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)))))