;; sumNr: num --> n
;; sums all the numbers from 1 to n
(define (sumNr n)
  (cond
    [(zero? n) 0]
    [else (+ n (sumNr (sub1 n)))]))

"Reverse accumulation tests:"
(time (sumNr 5))
(time (sumNr 5000))
(time (sumNr 500000))

;; sumNf: num --> n
;; sums all the numbers from 1 to n
(define (sumNf n)
  (cond
    [(zero? n) 0]
    [else (sumNf_help (sub1 n) n)]))

;; sumNf_help: num, num --> n
;; adds acc to the sum of all the numbers from 1 to n
(define (sumNf_help n acc)
  (cond
    [(zero? n) acc]
    [else (sumNf_help (sub1 n) (+ n acc))]))

""
"Forward accumulation tests:"
(time (sumNf 5))
(time (sumNf 5000))
(time (sumNf 500000))