AP Computer Science Quiz (Relax, it's just a quiz.)

1. The function, factorial, as written below, is a recursive process.

(define (factorial n)
  (cond ((or (= n 1) (= n 0)) 1)
        (else (* n (factorial (- n 1))))))

It is a recursive process because of the space it takes up when invoked. Consider (factorial 4):

(factorial 4)
(* 4 (factorial 3))
(* 4 (* 3 (factorial 2)))
(* 4 (* 3 (* 2 (factorial 1))))
(* 4 (* 3 (* 2 1)))
(* 4 (* 3 2))
(* 4 6)
24

Write a different version of factorial that uses an iterative process. factorial should still be called the same way (eg., (factorial 4)), so you will need to write a helper function that has one more variable.

2. Here is a definition of accumulate:

(define (accumulate combiner null-value term a next b)
  (cond ((> a b) null-value)
        (else (combiner (term a)
                        (accumulate combiner null-value term (next a) next b)))))

Write factorial in terms of accumulate. Here's a skeleton of part of what your answer must look like:

(define (factorial n) (accumulate <??> <??> <??> <??> <??> <??>))

You have to fill in the <??>s. Any attempt to write factorial as a recursive procedure will earn a score of zero.