(load "C:\\Documents and Settings\\mccoy\\My Documents\\CISC280-04s\\Scheme-Test-Files\\some-math-functions.scm")

; computes b to the n -- recursive process
; O(n) in both time and space
(define (exp1 b n)
  (if (= n 0)
      1
      (* b (exp1 b (dec n)))))

; computes b to the n -- iterative process
; O(n) in time, but O(1) in space (constant)
(define (exp2 b n)
  (exp-iter1 1 b n))

; product contains intermediate value
; product = b^(n - ctr)
(define (exp-iter1 product b ctr)
  (if (= ctr 0) 
      product
      (exp-iter1 (* product b)
                 b
                 (dec ctr))))

; computes b to the n -- recursive process
; more efficient calculation
; O(log(n)) in both time and space
(define (exp3 b n)
  (cond ((= n 1) b)
        ((= n 2) (* b b))
        ((even? n)
         (square (exp3 b (/ n 2))))
        (else (* b (exp3 b (dec n))))))