Lab: Merge Sort

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Merging
  • Exercise 2: Reflecting on Merging
  • Exercise 3: Splitting
  • Exercise 4: Splitting, Revisited
  • Exercise 5: Sorting
  • Exercise 6: Special Cases
  • Exercise 7: Sorting Students
  • Exercise 8: Verifying Sorts
  • Exercise 9: Comparing Sorts
  • Exercise 10: Experimentally Comparing Sorts

Exercises

Exercise 0: Preparation

a. Make a copy of mergesort.ss, my implementation of merge sort. Scan through the code and make sure that you understand all the procedures.

b. Start DrScheme

Exercise 1: Merging

a. Write an expresssion to merge the lists (1 2 3) and (1 1.5 2.3).

b. Write an expression to merge two lists that contain the same values.

c. Write an expression to merge two lists of words. (You may choose the words yourself. Each list should have at least three elements. You can represent names as strings.)

d. Assume that we represent names as lists of the form (last-name first-name). Write an expression to merge the following two lists

(define cs-faculty
  (list (list "Bishop" "David")
        (list "Gum" "Ben")
        (list "Rebelsky" "Samuel")
        (list "Stone" "John")
        (list "Walker" "Henry")))

(define young-cs-kids
  (list (list "Rebelsky" "Daniel")
        (list "Rebelsky" "Jonathan")
        (list "Rebelsky" "William")))

Exercise 2: Reflecting on Merging

a. What will happen if you call merge with unsorted lists as the first two parameters?

b. Verify your answer by experimentation.

c. What will happen if you call merge with sorted lists of very different lengths as the first two parameters?

d. Verify your answer by experimentation.

Exercise 3: Splitting

Use split to split:

a. A list of numbers of length 6

b. A list of numbers of length 5

c. A list of strings of length 6

d. A length-4 list of lists (each sublist should have length 2 or more).

Exercise 4: Splitting, Revisited

One of my colleagues prefers to define split something like the following

(define split
  (lambda (ls)
    (let kernel ((rest ls)
                 (left null)
                 (right null))
      (if (null? rest)
          (list left right)
          (kernel (cdr rest) (cons (car rest) right) left)))))

a. How does this procedure split the list?

b. Why might you prefer one version of split over the other?

Exercise 5: Sorting

a. Run merge-sort on a list you design of fifteen integers.

b. Run new-merge-sort on a list you design of twenty strings.

c. Uncomment the lines in new-merge-sort that print out the current list of lists. Rerun new-merge-sort on a list you design of twenty strings. Is the output what you expect?

Exercise 6: Special Cases

a. Run both versions of merge sort on the empty list.

b. Run both versions of merge sort on a one-element list.

c. Run both versions of merge sort on a list with duplicate elements.

Exercise 7: Sorting Students

Assume that we represent students with a list of the form

(lastname firstname id major)

a. Create a list of ten or more students.

b. Write an expression to sort that list by first name.

c. Write an expression to sort that list by id number.

d. Write an expression to sort that list so that students are arranged alphabetically by major and then alphabetically by last name within each major.

Exercise 8: Verifying Sorts

a. Write a procedure, verify-sort, that verifies the postconditions of merge-sort. That is, (verify-sort unsorted sorted may-precede?) should return true (#t) if sorted in sorted order and sorted is a permutation of unsorted. It should return false (#f) otherwise.

Note that (verify-sort '(1 1 2) '(1 2 2) <=) should return false (#f).

b. Use verify-sort to verify that merge-sort correctly sorts lists of 1000 random numbers.

b. Use verify-sort to verify that new-merge-sort correctly sorts lists of 1000 random numbers.

Exercise 9: Comparing Sorts

Which version of the merge sort algorithm do you prefer, merge-sort or new-merge-sort? Why?

Exercise 10: Experimentally Comparing Sorts

a. Using DrScheme's built-in timing mechanism (you may have to look through the online help to find information about that mechanism), make a table of the running time of insertion sort, merge-sort and new-merge-sort on inputs of size 0, 1, 10, 100, 500, 1000, 2000, and 5000.

b. Graph your data.

c. Based on your data, what can you say about the relative speeds of the three sorting methods?