ゼル伝

gistfile1.scm

;;; ゼルダの伝説 (SFC) で、鍵と扉がそれぞれ n 個のとき、
;;; ダンジョンのとりうる状態数を返す zelda 関数 (仮)

(use srfi-1)

(define (zelda n)
  (define (combination n m)
    (/ (apply * (iota m (+ (- n m) 1) 1))
       (apply * (iota m 1 1))))
  (define (sum list)
    (apply + list))
  (sum (map (lambda (k)
              (* (combination n k)
                 (sum (map (cut combination n <>)
                           (iota (+ k 1))))))
            (iota (+ n 1)))))

(define (main args)
  (print (zelda (string->number (cadr args)))))