Lab: Sorting

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Comparing Insertion Sorts
  • Exercise 2: Testing Insert
  • Exercise 3: Inserting strings
  • Exercise 4: Generalizing Insertion
  • Exercise 5: Displaying Insertion Sort
  • Exercise 6: Checking Potential Problems
  • Exercise 7: Generalizing Insertion Sort
  • Exercise 8: Inserting into Vectors
  • Exercise 9: Testing Insertion Sort

Exercises

Exercise 0: Preparation

Copy the code from the accompanying reading into DrScheme.

Exercise 1: Comparing Insertion Sorts

Discuss with your partner (and perhaps a neighboring group) the significant differences between the list-based insertion sort described in the first part of the the reading and the insertion sort we discussed in class (and that appears in the second part of the reading). What is different other than that one deals with lists and the other with vectors?

Exercise 2: 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 mixed list, arranged in ascending order;
• into a list of copies of the number to be inserted.

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

Exercise 3: Inserting strings

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

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

Exercise 4: Generalizing Insertion

a. Write a generalized insert procedure that also takes a less-than-or-equal-to predicate as a parameter.

b. Show how to call this procedure using lists of strings and numbers.

Exercise 5: Displaying 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 6: 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 7: Generalizing Insertion Sort

Write a procedure, (insertion-sort list less-than-or-equal?). that generalizes the insertion-sort-numbers procedure.

Exercise 8: Inserting into Vectors

Write the generalized insert! procedure that inserts a value into a sorted vector that has "space" at a designated position.

Exercise 9: Testing Insertion Sort

Create and name a vector containing the strings "bear", "emu", "frog", "ape", "dog", and "cat".

Rearrange the elements of the vector into alphabetical order by means of an appropriate call to insertion-sort!. (Note that the sorting occurs as a side effect of this call. Hence, to confirm that the sorting procedure worked you'll have to inspect the vector again afterwards.)