Question

I’m working my way through How to Design Programs on my own. I haven’t quite grasped complex linear recursion, so I need a little help.

The problem:
Define multiply, which consumes two natural numbers, n and x, and produces n * x without using Scheme’s *. Eliminate + from this definition, too.

Straightforward with the + sign:

(define (multiply n m)
  (cond
    [(zero? m) 0]
    [else (+ n (multiply n (sub1 m)))]))

(= (multiply 3 3) 9)

I know to use add1, but I can’t it the recursion right.

Thanks.

Answer 1

Split the problem in two functions. First, you need a function (add m n) which adds m to n. What is the base case? when n is zero, return m. What is the recursive step? add one to the result of calling add again, but decrementing n. You guessed it, add1 and sub1 will be useful.

The other function, (mul m n) is similar. What is the base case? if either m or n are zero, return 0. What is the recursive step? add (using the previously defined function) m to the result of calling mul again, but decrementing n. And that’s it!