Converting tree recursive process into iterative process

crazy-function-iter-and-rec.lisp

(defun crazy-func (n)
  (cond ((< n 3) n)
        (t (+ (crazy-func (- n 1))
            (* 2 (crazy-func (- n 2) ))
            (* 3 (crazy-func (- n 3)))))))
(defun crazy-func-iter (n)
  (crazy-iter 2 1 0 3 n))


;;; iter alogrithm:
;     let us store cf of n-1, n-2 and n-3 as state variables. At any point, we can
;     return the caly of crazy-func if we have these values.
;     let a=n-1, b=n-2 c=n-3, cf(n) = a+2b+3c
;     cf(n+1) = a+2b+3c + a + b

(defun crazy-iter (a b c count n)
  (if (> count n)
      a
      (crazy-iter (+ a (* 2 b) (* 3 c)) a b (1+ count) n )))