回溯法(scheme) -- N皇后问题

; ==========================================================
> (Queens 8)                ; 输出所有有效布局
1:      #(0 4 7 5 2 6 1 3)
2:      #(0 5 7 2 6 3 1 4)
....
91:     #(7 2 0 5 1 4 6 3)
92:     #(7 3 0 2 5 1 6 4)
total = 92

; N-Queen layout
; =============================================================
(define (Queens n)
(let ((count 0) (layout (make-vector n)))
(define (valid? col row)
(let p ((i 0) (res #t))
(if (and res (< i col))
(let ((diff (abs (- row (vector-ref layout i)))))
(p (+ i 1) (and res (not (or (= diff 0) (= diff (- col i)))))))
res)))
(let t ((col 0) (row 0))
(if (= n col)
(begin
(set! count (+ count 1))
(printf "~a:\t~a\n" count layout)))
(cond
((or (= n col) (= n row))
(if (> col 0)
(t (- col 1) (+ 1 (vector-ref layout (- col 1))))))
(else
(if (valid? col row)
(begin
(vector-set! layout col row)
(t (+ col 1) 0))
(t col (+ row 1))))))
(printf "total = ~a\n" count)))