Is my implementation of SICP Exercise 1.3 going in the right direction?

Question

Exercise 1.3 in SICP asks to define a procedure that takes 3 numbers as arguments and returns the sum of the squares of the 2 largest numbers. I think I've gotten it correct but I wasn't totally sure if I've covered all cases. My implementation is as follows:

(define (bigsq a b c)
    (cond ((and (> a b) (> b c)) (+ (* a a) (* b b)))
          ((and (> a b) (not (> b c))) (+ (* a a) (* c c)))
          ((> c a) (+ (* b b) (* c c)))
          (else (+ (* a a) (* b b))))

Is there a way to write those first 2 conditions as one, as well? Also any comments on efficiency are welcome as well.

Answer 1

For starters, we could use a helper procedure for implementing the sum just once:

(define (sum x y)
  (+ (* x x) (* y y)))

Now, for the conditions: given that the order doesn't matter - (sum a b) is the same as (sum b a), there's only 4 cases to consider, and we can avoid repeating some of the comparisons by nesting ifs:

(define (sum-max a b c)
  (if (>= a b)
      (if (>= b c)
          (sum a b)
          (sum a c))
      (if (>= a c)
          (sum b a)
          (sum b c))))