Ex-2.42

;positions on the board are represented using pair
;(row col) where 1<=row,col<= board-size
(define empty-board '())
(define (adjoin-position row col rest-of-queens)
  (cons (cons row col) rest-of-queens))
(define (safe? k positions)
  ;returns #t if a pos is safe with respect to other
  ;positions
  (define (safe-position? pos positions)
    (if (null? positions) true
        (and (safe-two-positions? pos (car positions))
             (safe-position? pos (cdr positions)))))

  ;returns #t if two positions are safe for each other
  (define (safe-two-positions? pos1 pos2)
    (cond
     ((= (car pos1) (car pos2)) #f)
     ((= (cdr pos1) (cdr pos2)) #f)
     ((same-diagonal? pos1 pos2) #f)
     (else #t)))

  ;returns #t if two positions are on same diagonal
  (define (same-diagonal? pos1 pos2)
    (= (abs (- (car pos1) (car pos2)))
       (abs (- (cdr pos1) (cdr pos2)))))

  ;here we made the assumption that first position
  ;in given positions is the one which has queen
  ;on k'th column, this holds true because of the
  ;way code written in procedure queens, this is
  ;not really right assumption to make but then we
  ;can change that anytime.
  (safe-position? (car positions) (cdr positions)))