This lab is also available in PDF.
Summary: In this lab, we explore a variety of
issues related to the insertion sort algorithm.
Contents:
a. Start DrScheme.
b. Copy the code from the accompanying
reading into DrScheme.
a. Test both versions of the insert-number procedure from
the reading by inserting the number 42
- into an empty list;
- into a list of numbers larger than 42, arranged in ascending order;
- into a list of numbers smaller than 42, arranged in ascending order;
- into a list of numbers both smaller and larger than 42, arranged in ascending order; and
- into a list that contains only three copies of 42 (that is, the list created by
(list 42 42 42).
b. What happens if the list is not in ascending order when
insert-number is invoked?
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.
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.
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.
Write a test suite (using unit-test.scm) to test the
insertion-sort-numbers procedure on some potentially
troublesome arguments:
(load "/home/rebelsky/Web/Courses/CS151/2007S/Examples/unit-test.ss")
(begin-tests!)
...
(end-tests!)
a. An empty list
b. A list containing only one element
c. A list containing all equal values
d. A list in which the elements are originally in descending numerical order
Document, write, and test a procedure,
(insertion-sort list may-precede?).
that generalizes the insertion-sort-numbers procedure.
a. Make a copy of the insert! procedure from
the reading.
b. Check that it works by using insert! to put the 2 in
the correct place in the following vector
(define numbers (vector 1 5 6 7 2 8 0 3))
(Note that solving this step requires that you understand the parameters to
insert!.)
c. Extend insert! so that it displays the vector and the
position at every step. (Add calls to display and
newline in the kernel, before the cond.)
d. Create the numbers vector from step b, and observe what happens
when we insert the 2, then the 8, then the 0, then the 3.
e. Make a copy of the insertion-sort! procedure from
the reading.
f. Observe the insertion steps in a list of about eight randomly-generated
numbers.
(define nums (vector (random 10) (random 10) (random 10) (random 10)
(random 10) (random 10) (random 10) (random 10)))
;
