N queens Scheme

gistfile1.txt

#lang racket
(define (iqueens L a d) ;; gives all of the queen solutions
        (if (null? L)
            (list a)
            (append-map (λ(x) 
                  (if(diagonal? x a 1)
                        '()
                         (iqueens (remove x L) (cons x a) 1))
                          )
                        L)))                       

(define (enumerate-interval l h) ;; produces a list from l to h
        (if (> l h)
            '()
        (cons l (enumerate-interval (+ l 1) h))))

(define (diagonal? col a d) 
        (if (null? a) ;; base case 1 no queens can be attacked
              #F
        (if (=(abs(- col (car a)))d) ;; base case 2 queens can be attacked
              #T
              (diagonal? col (cdr a) (+ d 1) ;; recursive callto diagonal
        )
        )
        ))
         

(define (q n)
        (define initialsize (enumerate-interval 1 n)) ;;determines the size of the board to pass into iqueens
        (define resultsofq (iqueens initialsize '() 1));; calling iqueens
        resultsofq)

(define (test n)
        (define boardsize (enumerate-interval 0 n))
        (define finallist (map q boardsize)) ;; run the function q on all of the various boardsizes 
        (define testresults (map length finallist)) ;;determine length of all the results
        testresults)
          
(test 12) ;; lists the number of solutions from sizes 0 to 12
         ;; '(1 1 0 0 2) corresponds to 1 solution for size 0, 1 solution for size 1, etc...