Solutions to the exercises due Wednesday, October 27, 2004

1. Write a command that returns the maximum of two numbers:

   (define (max_two a b)
     (if (> a b) a b))

   > (max_two  1 2)
   2

2. Using the 'factorial' function as a model, write a function
   that takes a list of numbers and returns the largest number.

   (define (factorial n)
     (if (= n 1)
         1
         (* n
            (factorial (- n 1)))))

     (- n 1)  =>  (null? (rest lst))
           1  =>  (first lst)
           *  =>  max_two 
           n  =>  (first lst)
   factorial  =>  my_max 
     (- n 1)  =>  (rest lst)

   (define (my_max lst)
     (if (null? (rest lst))
         (first lst)
         (max_two (first lst) 
                  (my_max (rest lst)))))

   > (my_max '(1 2 3))
   3
   > (my_max '(4 7 3 9 2 11 4))
   11