COMP 2103X1 Assignment 6 Due Thursday, March 2 by 7:00 PM General information about assignments (important!): http://cs.acadiau.ca/~jdiamond/comp2103/assignments/General-info.html Information on passing in assignments: http://cs.acadiau.ca/~jdiamond/comp2103/assignments/Pass-in-info.html Information on coding style: http://cs.acadiau.ca/~jdiamond/comp2103/assignments/C-coding-style-notes [1] Searching for strings is an extremely common operation in a lot of programs. For this problem you will write a program which accepts two strings as command-line arguments and output some information as described below. Consider the following text (written by a famous mathematician/logician) There was one who was famed for the number of things He forgot when he entered the ship: His umbrella, his watch, all his jewels and rings, And the clothes he had bought for the trip. (I’ve written this on four lines, but it is really one string with a “\n” character following each of the lines.) Now suppose our search string is “forgotten”. In this case, the word we want is not in the text, but various prefixes of the string are. Your program should find the rightmost occurrence of the search string, if it exists, and otherwise of all instances of the longest prefix of the search string in the text, it should find the rightmost one. In either case, your program then outputs two numbers, as shown below in the examples. The first number is the number of characters of the search string which match, and the second number is how many characters from the right end of the text to go backwards (to find the match). For example, the prefix “forgot” (of “forgotten”) is found 128 characters back from the end of the string, and the length of this longest matched prefix is 6. Thus your program will output “6;128”. Here are some examples of how your program should operate. You must include these samples, as well as some of your own creation, when you create your script file. $ a6p1 ’twas brillig’ ’was not’ 4;11 $ a6p1 ’aaron aardvark’ ’aaabbb’ 2;8 $ a6p1 ’aaron aardvark’ ’qwerty’ 0;q $ a6p1 hicdefghi hi 2;2 $ a6p1 ’A two-line text string’ inky 2;3 1 http://cs.acadiau.ca/~jdiamond/comp2103/assignments/General-info.html http://cs.acadiau.ca/~jdiamond/comp2103/assignments/Pass-in-info.html http://cs.acadiau.ca/~jdiamond/comp2103/assignments/C-coding-style-notes You will notice that if there is no (non-empty) prefix of the search string in the text that the program outputs 0 for the matched length (as expected) but instead of outputting the distance from the end, it outputs the first character of the search string. Your program must do this as well. What other unusual cases should your program deal with? If there are any that you can think of, the comment at the top of your program should describe these cases and what your program does with them. Your program should never “blow up”. Finally, notice that by surrounding the text and search string with single quotes, t.

1. COMP 2103X1 Assignment 6
Due Thursday, March 2 by 7:00 PM
General information about assignments (important!):
http://cs.acadiau.ca/~jdiamond/comp2103/assignments/General-
info.html
Information on passing in assignments:
http://cs.acadiau.ca/~jdiamond/comp2103/assignments/Pass-in-
info.html
Information on coding style:
http://cs.acadiau.ca/~jdiamond/comp2103/assignments/C-
coding-style-notes
[1] Searching for strings is an extremely common operation in a
lot of programs. For this problem
you will write a program which accepts two strings as
command-line arguments and output some
information as described below.
Consider the following text (written by a famous
mathematician/logician)
There was one who was famed for the number of things
He forgot when he entered the ship:
His umbrella, his watch, all his jewels and rings,
And the clothes he had bought for the trip.
(I’ve written this on four lines, but it is really one string with a
“n” character following each of
the lines.) Now suppose our search string is “forgotten”. In this
case, the word we want is not in

2. the text, but various prefixes of the string are. Your program
should find the rightmost occurrence
of the search string, if it exists, and otherwise of all instances
of the longest prefix of the search
string in the text, it should find the rightmost one.
In either case, your program then outputs two numbers, as
shown below in the examples. The first
number is the number of characters of the search string which
match, and the second number is
how many characters from the right end of the text to go
backwards (to find the match).
For example, the prefix “forgot” (of “forgotten”) is found 128
characters back from the end of the
string, and the length of this longest matched prefix is 6. Thus
your program will output “6;128”.
Here are some examples of how your program should operate.
You must include these samples,
as well as some of your own creation, when you create your
script file.
$ a6p1 ’twas brillig’ ’was not’
4;11
$ a6p1 ’aaron aardvark’ ’aaabbb’
2;8
$ a6p1 ’aaron aardvark’ ’qwerty’
0;q
$ a6p1 hicdefghi hi
2;2

3. $ a6p1 ’A two-line
text string’ inky
2;3
1
http://cs.acadiau.ca/~jdiamond/comp2103/assignments/General-
info.html
http://cs.acadiau.ca/~jdiamond/comp2103/assignments/Pass-in-
info.html
http://cs.acadiau.ca/~jdiamond/comp2103/assignments/C-
coding-style-notes
You will notice that if there is no (non-empty) prefix of the
search string in the text that the program
outputs 0 for the matched length (as expected) but instead of
outputting the distance from the end,
it outputs the first character of the search string. Your program
must do this as well.
What other unusual cases should your program deal with? If
there are any that you can think of,
the comment at the top of your program should describe these
cases and what your program does
with them. Your program should never “blow up”.
Finally, notice that by surrounding the text and search string
with single quotes, the spaces be-
come part of their respective command-line argument, rather
than acting as argument separators.
Similarly, an embedded newline character becomes part of the
argument when enclosed in quotes,
rather than completing the command.
[2] Write a program which does the following things.

4. — Declares a 4�4 matrix of ints.
— Reads in such a matrix (from stdin).
— Prints out the matrix in a rectangular array (see examples and
further directions below).
— Prints out “It is upper triangular.” if the matrix is all zeroes
below the main diagonal.
— Prints out “It is lower triangular.” if the matrix is all zeroes
above the main diagonal.
— Prints out “It is not triangular” if it is not all zeroes either
above or below the main diagonal.
— Prints out a blank line and then the transpose of the matrix.
— Prints out a blank line and then “It is symmetric.” if the
transpose of the matrix is equal to the
matrix, otherwise “It is not symmetric.”
You should test your program on enough matrices to show that
your program detects all the different
possibilities. Naturally, you should use good programming
practices when writing your program.
You might want to store test data in files, rather than repeatedly
typing matrix data in. If so, in your
script file you should display the contents of your test files with
cat.
If your program is reading from the keyboard, you must print
out a prompt, asking the user for
the data. If the program is reading from a re-directed file (e.g.,
a6p2 < test1) or from a pipe
(e.g., cat test1 | a6p2 ) then DO NOT print out a prompt. You
can use the isatty() library
function (see man 3 isatty) to determine whether you are
reading from the keyboard or not.
Note that isatty() takes fd (“file descriptor”) as its parameter.
You can get the correct fd by
using the return result of fileno(stdin).�

5. Here is an example of what running this program might look
like.
% a6p2
Please enter 16 integers:
1 0 3 4 0 4 5 6 0 0 9 0 0 0 0 8
The matrix is:
1 0 3 4
0 4 5 6
� Note that some historically significant early computer
terminals were made by Teletype Corpora-
tion, and consequently “tty” became a generic short form for
“computer terminal”. Thus “isatty”
means “is a tty”, i.e., “is a terminal”.
2
0 0 9 0
0 0 0 8
It is upper triangular.
Its transpose is:
1 0 0 0
0 4 0 0

6. 3 5 9 0
4 6 0 8
It is not symmetric.
%
% a6p2 < test2
The matrix is:
1 233 6666 -4
0 4 5 236
0 0 9 0
77 0 0 8
It is not triangular.
Its transpose is:
1 0 0 77
233 4 0 0
6666 5 9 0
-4 236 0 8
It is not symmetric.
For this assignment, you should ensure that you were able to

7. correctly read 16 integers, but you
do not need to do sophisticated error handling; if stdin does not
have 16 consecutive integers for
you, write out an error message and terminate the program.
You should write a function which takes two 4 � 4 matrices and
stores the transpose of the first
matrix into the second matrix.
Your code to perform the tests on the matrix should be in one or
more functions, not in the main
program. Similarly, good design practices should lead you to
put the code to read the matrix in its
own function.
When printing the matrix, make the columns as narrow as
possible, as shown above. That is, find
the number with the largest printed width, and print all of the
numbers in fields that wide. (And
separate columns with one space.)
3
[3] When you study algorithm analysis, you will find (or
attempt to find) mathematical functions which
describe how long a given algorithm will take to work on a
problem of a given size. Sometimes this
is easy, sometimes it is more difficult, and sometimes it may be
extremely difficult or impossible.
Sorting is a very important and well-studied problem in
computer science. Consider the following
algorithm, which sorts an array of n numbers, using the
following idea. First, find the smallest

8. number in the array and save it as the first sorted number. Then,
find the smallest number in the
rest of the array and save that as the smallest number. Continue
doing this until there are only two
numbers left; when you have found the smallest of those two
numbers, the remaining number is
the largest.
This idea can be formalized as follows:
SelectionSort(array[1..n])
for i = 1 to n-1
minpos = i
for j = i+1 to n
if array[j] < array[minpos]
minpos = j
if minpos != i
swap(array[minpos], array[i])
In sorting algorithms we often count the number of comparisons
of data items and use that as the
measure of how long an algorithm takes. In this case, we can
see that the inner for loop does n�1
comparisons the first time, n � 2 comparisons the second time,
and so on down to 1 comparison
the last time. Thus we can say that the amount of time used by
selection sort to sort n numbers is
T .n/ D

9. n�1X
iD1
i for n > 0
which is a sum we can solve with elementary mathematics,
giving us T .n/ D n.n � 1/=2.
I told you that story so I can tell you this story.
Some algorithms operate by breaking down a big problem into
two or more smaller problems,
of more or less equal size. (This breaking down may or may not
require some work to be done,
depending on the situation.) Then the sub-problems are solved,
which takes some time, and the
solutions are combined to give us a solution to the original
problem, which may also take some
time. Such techniques fall into a class of algorithms known as
divide and conquer.
The equations describing divide and conquer algorithms (and
some other classes) are much more
complex than the one given above. For example, the time
required by one well-known algorithm
can be described as follows
T .n/ D
�
0 if n < 2
T .dn=2e/ C T .bn=2c/ C n � 1 otherwise
.�/

10. In other words, we break the problem into two sub-problems
whose sizes are as equal as possible,
we solve those problems, and we use another n � 1 operations
in the “break apart” and/or “put
together” phases.
4
These equations can be difficult to solve sometimes. Since this
is COMP 2103, instead of solving
equation .�/, write a program which
(i) prompts the user for two numbers,
(ii) inputs two numbers, and
(iii) outputs a table of n versus T .n/ for all numbers between
the two input numbers.
For example, here is a possible terminal session, user input in
red:
$ a6p3
Enter two numbers: 2 4
n | T(n)
------+--------
2 | 1
3 | 3
4 | 5
Your table doesn’t have to look like mine, but try to make it
something you’d be proud of, not

11. something you’d try to hide. Also, keep in mind that T .n/ will
get large sooner or later, so try to
keep that in mind while designing your table layout.
To solve this problem, create a recursive function which, when
given a non-negative integer n,
returns T .n/. Then call this function as needed from the place in
your program where you are
printing out the table.
When creating your script file run your program a few times
with different inputs to test boundary
conditions, invalid inputs, and so on. And, of course, at least
one case where everything is correct.
Did you use functions in any of these questions? Should you
have? Did you document them
correctly?
Does you program “blow up” on unexpected input, or does it
deal with bad input in a “graceful”
way?
How does your program deal with boundary conditions, if there
are any?
Did you remember to put all required comments in? Does your
program call out for any other
comments in the body of the code?
5