Interesting Solutions to SICP Chapter 1

I have started working through SICP chapter 1, using the Dr Scheme interactive environment. I will post my more interesting solutions and comments.

Ken Dyck gives a more complete solution set.

Comment: Rather than finding the larger two explicitly, I find the smallest and use a simple mathematical identity.

My solutions:

Exercise 1.3. Define a procedure that takes three numbers as arguments and returns the sum of the squares of the two larger numbers.

(define (f a b c)
(define (lt a b) (if (> a b) b a))
(define (least a b c) (lt a (lt b c)))
(define (square x) (* x x))

(+ (square a)
  (square b)
  (square c)
  (- (square (least a b c)))))

Comment: Rather than finding the larger two explicitly, I find the smallest and use a simple mathematical identity.

Exercises 1.17 & 1.18: Devise recursive and iterative algorithms for multiplication that take a logarithmic number of steps.

(define (mul-recursive a b)
 (cond ((= b 0) 0)
       ((even? b) (mul-recursive (double a) (halve b)))
       (else (+ a (mul-recursive a (- b 1))))))

(define(* a b)
 (define (mul-iterative r a b)
   (cond ((= b 0) r)
         ((even? b) (mul-iterative r (double a) (halve b)))
         (else (mul-iterative (+ r a) a (- b 1)))))

 (mul-iterative 0 a b))

Comments: Observe how similar the two solutions are. The iterative solution is especially easy to follow if you expand out an example.