In this problem you are asked to build several Scheme functions and analyze the performance of these functions.

Define a procedure subst-1st which takes three arguments: an item new, and item old, and a list of items list. The procedure subst-1st looks for the first occurence of item old in list and replaces it with the item new.

Test your procedure on:

(subst-1st 'dog 'cat '(my cat is clever)
	==> (my dog is clever)

(subst-1st 'b 'a '(c a b a c))
	==> (c b b a c)

(subst-1st '(0) '(*) '((*) (1) (*) (2)))
	==> ((0) (1) (*) (2))

(subst-1st 'two 'one '())  ==> ()

In order to be able to include lists as possible arguments to which the parameters new and old are bound, use equal? to test for sameness. Also define procedures substq-1st and substv-1st that use eq? and eqv? respectively instead of equal? to test for sameness.

Finally, analyze the performance of your subst-1st functions. On the average, how many and what kind of operations are performed when applied to a list on n items? Construct a function count which takes a single non-negative integer argument, n, and produces the list of items 1, 2, ..., n. For example,

(count 1)  ==> (1)
(count 0)  ==> ()
(count 5)  ==> (1 2 3 4 5)

Use count as a source of lists to do performance testing of your subst-1st functions.

Lab 2 Scheme Code