This lab is also available in PDF.
Summary: In this laboratory, we consider
merge sort, a more efficient technique for sorting lists
of values.
Contents:
a. Make a copy of mergesort.scm,
my implementation of merge sort. Scan through the code and make
sure that you understand all the procedures.
b. Start DrScheme.
a. Write an expresssion to merge the lists (1 2 3) and
(1 1.5 2.3).
b. Write an expression to merge two identical lists of numbers. For example, you might merge the lists (1 2 3 5 8 13 21) and
(1 2 3 5 8 13 21)
c. Write an expression to merge two lists of strings. (You may choose the
strings yourself. Each list should have at least three elements.)
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 mathstats-faculty
(list (list "Chamberland" "Marc")
(list "French" "Chris")
(list "Jager" "Leah")
(list "Kornelson" "Keri")
(list "Kuiper" "Shonda")
(list "Moore" "Emily")
(list "Moore" "Tom")
(list "Mosley" "Holly")
(list "Romano" "David")
(list "Shuman" "Karen")
(list "Wolf" "Royce")))
(define more-faculty
(list (list "Moore" "Ed")
(list "Moore" "Jonathan")
(list "Moore" "Peter")))
a. What will happen if you call merge with unsorted
lists as the list 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.
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
a. Run merge-sort on a list you design of fifteen integers.
b. Run new-merge-sort on a list you design of ten 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 ten strings. Is the output what you expect?
d. Rerun new-merge-sort on a list of twenty integers.
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.
As you've probably noticed, there are two key postconditions of a
procedure that sorts lists: The result is a permutation of the original
list and the result is sorted. We're fortunate that the unit
test framework lets us test permutations (with test-permutation!).
Hence, if we wanted to test merge sort in the unit test framework, we
might write
(define some-list ...)
(test-permutation! (merge-sort some-list pred?) some-list)
However, we still need a way to make sure that the result is sorted,
particularly if the result is very long.
Write a procedure, (sorted? lst may-precede?) that checks
whether or not lst is sorted by may-precede?.
For example,
> (sorted? (list 1 3 5 7 9) <)
#t
> (sorted? (list 1 3 5 4 7 9) <)
#f
> (sorted? (list "alpha" "beta" "gamma") string<?)
Note that we can use that procedure in a test suite for merge sort with
(test! (sorted? (merge-sort some-list may-precede?) may-precede?) #t)
>
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?
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