nqueens.scm

;;; NQUEENS -- Compute number of solutions to 8-queens problem.

(import (rnrs))

(define trace? #f)

(define (nqueens n)

  (define (iota1 n)
    (let loop ((i n) (l '()))
      (if (= i 0) l (loop (- i 1) (cons i l)))))

  (define (my-try x y z)
    (if (null? x)
        (if (null? y)
            (begin
              (when trace? (begin (write z) (newline)))
              1)
            0)
        (+ (if (ok? (car x) 1 z)
               (my-try (append (cdr x) y) '() (cons (car x) z))
               0)
           (my-try (cdr x) (cons (car x) y) z))))

  (define (ok? row dist placed)
    (if (null? placed)
        #t
        (and (not (= (car placed) (+ row dist)))
             (not (= (car placed) (- row dist)))
             (ok? row (+ dist 1) (cdr placed)))))

  (my-try (iota1 n) '() '()))

(nqueens 14)