Lab: Insertion Sort

Summary: In this lab, we explore a variety of issues related to the insertion sort algorithm.

Contents:

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Testing Insert
  • Exercise 2: Inserting Strings
  • Exercise 3: Generalizing Insertion
  • Exercise 4: Displaying Steps in Insertion Sort
  • Exercise 5: Checking Potential Problems
  • Exercise 6: Generalizing Insertion Sort

Exercises

Exercise 0: Preparation

a. Start DrScheme.

b. Copy the code from the accompanying reading into DrScheme.

Exercise 1: Testing Insert

a. Test both versions of the insert-number procedure from the reading by inserting a number

• into an empty list;
• into a list of larger numbers, arranged in ascending order;
• into a list of smaller numbers, arranged in ascending order;
• into a list of both larger and smaller numbers, arranged in ascending order; and
• into a list the contains multiple copies of the number to be inserted.

b. What happens if ls is not in ascending order when insert-number is invoked?

Exercise 2: Inserting Strings

Write a new insert-string procedure that inserts a string into a list of strings that are in alphabetical order:

> (insert-string "dog" (list "ape" "bear" "cat" "emu" "frog"))
("ape" "bear" "cat" "dog" "emu" "frog")

In case you've forgotten, string<? and string-ci<? are useful predicates for comparing strings for order.

You may not use the generalized insert procedure in writing this procedure.

Exercise 3: Generalizing Insertion

a. Show how to call the generalized insert procedure using lists of strings.

b. Show how to call the generalized insert procedure using lists of numbers.

c. Redefine insert-string so that it uses insert as a helper procedure.

Exercise 4: Displaying Steps in Insertion Sort

a. Add calls to the display and newline procedures to the body of the helper in insertion-sort-numbers so that it displays the values of unsorted and sorted, appropriately labeled, at each step of the sorting process.

b. Use the revised insertion-sort-numbers procedure to sort the values 7, 6, 12, 4, 10, 8, 5, and 1.

Exercise 5: Checking Potential Problems

Test the insertion-sort-numbers procedure on some potentially troublesome arguments:

• an empty list,
• a list containing only one element,
• a list containing all equal values,
• a list in which the elements are originally in descending numerical order.

Exercise 6: Generalizing Insertion Sort

Document, write, and test a procedure, (insertion-sort list may-precede?). that generalizes the insertion-sort-numbers procedure.