;; Iterative Version
;; Return the nth harmonic number
(define iter-harm
  (lambda (n)
    (harm-helper 0 n)))

(define harm-helper
  (lambda (sum n)  ; compute (sum + H_n) as (sum + 1/n) + H_{n-1}
    (if (= n 0)
        sum
        (harm-helper (+ (/ 1 n) sum) (- n 1)))))

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;; Iterative Version
;; Return m*n, whre m is a number
;; and n is a nonnegative integer
(define iter-mult
  (lambda (m n)
    (mult-helper 0 m n)))

;; Add m*n to product and return it
(define mult-helper
  (lambda (prod m n) ; compute prod + m*n as (prod + m) + m*(n-1)
    (if (= n 0)
        prod
        (mult-helper (+ prod m) m (- n 1)))))

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;; Iterative Version
;; Count the number of 6's in the decimal representation
;; of nonnegative number n
(define iter-number-of-6s
  (lambda (n)
    (number-of-6s-helper 0 n)))

;; Add the number of 6's in the decimal representation (D.R.) of n to count
;; and return it
(define number-of-6s-helper
  ;; computes (count + number of 6's in the D.R. of n) as
  ;;  (count + 1 + (number of 6's in the D.R. of floor(n/10)) if the last digit of n is 6
  ;;  (count + (number of 6's in the D.R. of floor(n/10)) otherwise
  (lambda (count n)
    (if (= n 0)
        count
        (number-of-6s-helper (+ count (if (= (remainder n 10) 6) 1 0))
                             (quotient n 10)))))

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;; Iterative Version
;; Russian Multiplication
;; Return m*n, whre m is a number
;; and n is a nonnegative integer
(define iter-r-mult
  (lambda (m n)
    (r-mult-helper 0 m n)))

;; Add m*n to prod and return it
(define r-mult-helper
  ;; computes (prod + m*n) as
  ;;   (prod + m) + (2*m + floor(n/2)) if n is odd
  ;;   prod + (2*m + floor(n/2))       if n is even
  (lambda (prod m n)
    (if (= n 0)
        prod
        (r-mult-helper (+ prod (if (odd? n) m 0))
                       (+ m m)
                       (quotient n 2)))))

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;; Iterative Version
;; Return sum of digits in the decimal representation of a
;; nonnegative integer n
(define iter-sum-of-digits
  (lambda (n)
    (sum-of-digits-helper 0 n)))
  
;; Add the sum of digits in the decimal representation (D.R.) of n to sum
;; and return it
(define sum-of-digits-helper
  ;; computes (sum + sum of digits of n) as
  ;; (sum + the rightmost digit in the D.R. of n)
  ;; + (sum of digits in the D.R. of floor(n/10))
  (lambda (sum n)
    (if (= n 0)
        sum
        (sum-of-digits-helper (+ sum (remainder n 10)) (quotient n 10)))))