Tail Recursion

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Identifying Tail-Recursive Procedures
  • Exercise 2: Does Tail Recursion Really Make a Difference?
  • Exercise 3: Finding the Longest String on a List
  • Exercise 4: Finding the Index
  • Exercise 5: Iota, Once Again
  • Exercise 6: Reverse
  • Exercise 7: Append

Exercises

Exercise 0: Preparation

a. Go over the short reading on tail recursion.

b. Start DrScheme.

Exercise 1: Identifying Tail-Recursive Procedures

Identify three (or more) tail-recursive procedures you've already written.

Exercise 2: Does Tail Recursion Really Make a Difference?

In DrScheme, you can find out how long it takes to evaluate an expression by using (time expression). The time procedure prints out the time it takes to evaluate and then returns the value computed. If you care only about the time it takes, you can write

> (let ((junk (time expression))))

a. Try the two versions of factorial on some large numbers. Does one seem to be faster than the other?

b. Try the three versions of add-to-all on some lists of varying sizes (you'll probably need at least a hundred values in each list, and possibly more) until you can determine a difference in running times.

Exercise 3: Finding the Longest String on a List

Write a tail-recursive longest-string-on-list procedure.

Exercise 4: Finding the Index

Define a tail-recursive procedure index that has two arguments, an item a and a list of items ls, and returns the index of a in ls, that is, the zero-based location of a in ls. If the item is not in the list, the procedure returns -1. Test your procedure on:

  (index 3 (list 1 2 3 4 5 6)) --> 2
  (index 'so (list 'do 're 'mi 'fa 'so 'la 'ti 'do)) --> 4
  (index "a" (list "b" "c" "d")) --> -1
  (index 'cat null) --> -1

Exercise 5: Iota, Once Again

Define and test a tail-recursive version of Iota.

Exercise 6: Reverse

Write your own tail-recursive version of reverse.

Exercise 7: Append

This is an optional extra-credit exercise.

Here's a non-tail-recursive version of append.

(define append
  (lambda (list-one list-two)
    (if (null? list-one) list-two
        (cons (car list-one)
              (append (cdr list-one) list-two)))))

a. Write your own tail-recursive version.

b. Determine experimentally which of the three versions (built-in, given above, tail-recursive) is fastest.