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How to Solve N-Queens Problem in Scheme?

- by Philip

Hi, I'm stuck on the extended exercise 28.2 of How to Design Programs. Here is the link to the question: http://www.htdp.org/2003-09-26/Book/curriculum-Z-H-35.html#node_chap_28 I used a vector of true or false values to represent the board instead of using a list. This is what I've got which doesn't work: #lang Scheme (define-struct posn (i j)) ;takes in a position in i, j form and a board and returns a natural number that represents the position in index form ;example for board xxx ; xxx ; xxx ;(0, 1) - 1 ;(2, 1) - 7 (define (board-ref a-posn a-board) (+ (* (sqrt (vector-length a-board)) (posn-i a-posn)) (posn-j a-posn))) ;reverse of the above function ;1 - (0, 1) ;7 - (2, 1) (define (get-posn n a-board) (local ((define board-length (sqrt (vector-length a-board)))) (make-posn (floor (/ n board-length)) (remainder n board-length)))) ;determines if posn1 threatens posn2 ;true if they are on the same row/column/diagonal (define (threatened? posn1 posn2) (cond ((= (posn-i posn1) (posn-i posn2)) #t) ((= (posn-j posn1) (posn-j posn2)) #t) ((= (abs (- (posn-i posn1) (posn-i posn2))) (abs (- (posn-j posn1) (posn-j posn2)))) #t) (else #f))) ;returns a list of positions that are not threatened or occupied by queens ;basically any position with the value true (define (get-available-posn a-board) (local ((define (get-ava index) (cond ((= index (vector-length a-board)) '()) ((vector-ref a-board index) (cons index (get-ava (add1 index)))) (else (get-ava (add1 index)))))) (get-ava 0))) ;consume a position in the form of a natural number and a board ;returns a board after placing a queen on the position of the board (define (place n a-board) (local ((define (foo x) (cond ((not (board-ref (get-posn x a-board) a-board)) #f) ((threatened? (get-posn x a-board) (get-posn n a-board)) #f) (else #t)))) (build-vector (vector-length a-board) foo))) ;consume a list of positions in the form of natural number and consumes a board ;returns a list of boards after placing queens on each of the positions on the board (define (place/list alop a-board) (cond ((empty? alop) '()) (else (cons (place (first alop) a-board) (place/list (rest alop) a-board))))) ;returns a possible board after placing n queens on a-board ;returns false if impossible (define (placement n a-board) (cond ((zero? n) a-board) (else (local ((define available-posn (get-available-posn a-board))) (cond ((empty? available-posn) #f) (else (or (placement (sub1 n) (place (first available-posn) a-board)) (placement/list (sub1 n) (place/list (rest available-posn) a-board))))))))) ;returns a possible board after placing n queens on a list of boards ;returns false if all the boards are not valid (define (placement/list n boards) (cond ((empty? boards) #f) ((zero? n) (first boards)) ((not (boolean? (placement n (first boards)))) (first boards)) (else (placement/list n (rest boards)))))

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