; Additional Examples from Lecture 4, Mon., Sept. 15, 2008

(load "tester.scm")

(define (insert-nth n x L)
  (if (= n 0)
      (cons x L)
      (if (null? L)
          (error "no nth position in list" n L)
      (cons (first L) (insert-nth (- n 1) x (rest L)))))
  )

(test (insert-nth 3 'x '(a b c e f g)) '(a b c x e f g))
;(test (insert-nth 13 'x '(a b c e f g)) '(a b c x e f g))

; tail-recursive summation of a list
; using a nested definition

(define (sum L)
  (define (sum2 L Acc)
    (if (null? L)
        Acc
        (sum2 (rest L) (+ (first L) Acc))))
  (sum2 L 0))

(test (sum '(1 2 3 4 5 6 7 8 9 10)) 55)


; tail-recursive version of factorial

(define (fac n) (trfac n 1))

(define (trfac n acc)
  (if (< n 2)
      acc
      (trfac (- n 1) (* n acc))))

(test (fac 5) 120)
  
(tester 'show)