CS 9-2
Chapter 5 Quiz


Question: Write a function such that when given a non-empty list of numbers,
it will return the largest number on the list.  For example, 
(max-lst '(5 10 9 6 2)) will return 10. (max-lst '(2)) will return 2.




Hint: First, try to write a function that given 2 numbers, will return the 
larger of the two numbers. Let's call it max2. Here is the skeleton.

(define max2
  (lambda (a b)
    (your comparison function)
  ))

(max2  5 10)
> 10

Then, think about if you have an arbitrary list, e.g. (5 10 3 2 9), how would
you go about finding the largest number of the list? Break the problem down
into a smaller question. You just wrote max2, which finds the larger of the 
two numbers.  Now, what is the larger number between 5 and the first number of
the rest of the list (10 3 2 9)? It's 10. Then what is the larger number 
between 10 and the first number of the rest of the list? So on and so forth.




Here is some Scheme help.

List:
Examples of list in Scheme:
(1 2 3), (a b c), (1 b)

We call things in the list elements, since they can be integers, alphabets, 
words or anything. Just like in math, elements in a list do not have to be of
the same type.

'() is an empty list. You can check whether a list is an empty list by the 
function empty? for example: (empty? '(1 2 3)) will return #f which means 
false. (empty? '()) will return #t which means true.

'() is different from (   ) without the tick. If Scheme sees a tick, it does 
not evaluate the elements inside the list. However, without the tick, Scheme 
will evaluate the list. 

Operators:
The first element of the list should always be an operator, e.g. mathematical
 operators such as +, -, *, /, or list operators such as car, cdr, cadr and 
empty? Therefore, you should write 1+2 as (+ 1 2), not (+ 1 2), (1+2), 
(+ (1 2)) or (+ 1 2). Similarly, if you want to express if a is bigger than b,
 then return 1, or else return 0, you write 
(if (> a b)  
   1 
   0)

List operators:
(car (1 2 3)) will return the first element of a list. In this example, it 
will return integer 1
(cdr (1 2 3)) will return the a list containing everything but the first 
element of the list. In this example, it will return list (2 3)
(car (cdr (1 2 3))) is equivalent to (cadr (1 2 3)) and will return 2
(cdr (car (1 2 3))) will return an error. Because (car (1 2 3)) returns 1 and
 cdr only works on lists.