(require (lib "trace.ss"))
(define (cputime f . args)
  (define-values (result cpu real gc) (time-apply f args))
  (* 1.0 cpu))

(define (factor o n f . args)
  (define-values (result cpu real gc) (time-apply f args))
  (* 1.0 (/ cpu (o n))))
;Aufgabe 1

(define (alignments m n)
  (if (or (= m 0) (= n 0)) 1
      (+ (alignments (- m 1) n) (alignments (- m 1) (- n 1)) (alignments m (- n 1)))
      )
  )

;(alignments 5 9)

(define (fak n)
  (if (<= n 1)
      1
      (* n (fak (- n 1)))))
(define (alignments-i m n)
  (define (alignments-for-length l)
    (define (sum-fak a b)
      (cond ((> a b) 0)
            (else (+ (/ (fak a) (* (fak (- a m)) (fak (- a n)) (fak (- b a)))) (sum-fak (+ a 1) (+ m n))))
            )
      )
    (sum-fak l (+ m n)) 
    )
  (alignments-for-length (max m n)) 
  )
;(alignments-i 50 90)

; ;Aufgabe 2

(define (f n)
  (if (< n 3) 1
      (+ (* 3 (f (- n 1))) (* -2 (f (- n 2))) (* 3 (f (- n 3))))
      )
  )
; Laufzeitabschätzung 
(define basis 1.84)
(define (f-o n) (expt basis n))

; Bestimmung des Proportionalitätsfaktors
(factor f-o 20 f 20)
(factor f-o 21 f 21)
(factor f-o 22 f 22)
(factor f-o 23 f 23)
(factor f-o 24 f 24)
(factor f-o 25 f 25)
(factor f-o 26 f 26)
(factor f-o 27 f 27)
(factor f-o 28 f 28)
(factor f-o 29 f 29)

; Proportionalitätsfaktor ca. 0.00067
(/ (* 0.00067 (f-o 100)) 1000 60 60 24 365)