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Analysis of Algorithms Asymptotic Notation and Sorting Project

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COT 4400 Project 1
COT 4400: Analysis of Algorithms
Asymptotic Notation and Sorting Project
You are not allowed to use the Internet. You may only consult approved references1
.
This is an individual project.
This policy is strictly enforced.
You must submit a hard copy of all of the items requested below. You must also submit your code2
to Canvas.
For full credit, the code that is submitted must:
• Use the specified signature, if applicable.
• Be implemented in a file using the specified file name, if applicable.
• Be correct (i.e., it must always return the correct result).
• Be efficient (i.e., it must use the minimum amount of time and the minimum amount of space necessary to be a
correct implementation).
• Be readable and easy to understand. You should include comments to explain when needed, but you should not
include excessive comments that makes the code difficult to read.
– Every class definition should have an accompanying comment that describes what is for and how it should be
used.
– Every function should have declarative comments which describe the purpose, preconditions, and post conditions for the function.
– In your implementation, you should have comments in tricky, non-obvious, interesting, or important parts of
your code.
– Pay attention to punctuation, spelling, and grammar.
• Follows ALL coding guidelines from section 1.3 of the textbook. Additional coding guidelines:
– No magic numbers. Use constants in place of hard-coded numbers.
– No line of the text of your source code file may have more than 80 characters (including whitespace).
– All header files should have #define guards to prevent multiple file inclusion. The form of the symbol name
should be <FILENAME> H
– Do not copy and paste code. If you need to reuse a section of code, then write a function that performs that
code.
– Define functions inline only when they are small, say, 10 lines or less
– Function names, variable names, and filenames must be description. Avoid abbreviation.
– Use only spaces (no tabs), and indent 3 spaces at a time.
• Compile and run on the C4 Linux Lab machines (g++ compiler, version 4.8.2). The shell script and makefile that
I will use to compile and run your code will be posted on Canvas. Please note that I may use my own main.cpp file
to test the code you submit.
• Have no memory leaks.
1The list of approved references is posted on Canvas. You must cite all references used.
2Your code must compile and run on the C4 Linux Lab machines
Page 1 of 4
COT 4400 Project 1 Fall 2014
Project Description
A magic square is an n × n matrix in which each of the integers 1, 2, 3, . . . , n2 appears exactly once an all column sums,
row sums, and diagonal sums are equal. For example, the following is a 5 × 5 magic square in which all rows, columns,
and diagonals add up to 65:
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
The following is a procedure for constructing an n × n magic square for any odd integer n. Place 1 in the middle of the
top row. Then, after integer k has been placed, move up one row and move one column right to place the next integer,
k + 1, unless one of the following occurs:
• If a move takes you above the top row in the j
th column, move to the bottom of the j
th column and place k + 1
there.
• If a move takes you outside to the right of the square in the i
th row, place k + 1 in the i
th row at the left side.
• If a move takes you to an already filled square or if you move out of the square at the upper right-hand corner, place
k + 1 immediately below k
Page 2 of 4 Project continues. . .
COT 4400 Project 1 Fall 2014
Project Tasks
1. Define a class to hold a MagicSquare object in file magicSquare.h. The implementation of each of the member
functions will be in file magicSquare.cpp.
(a) [5 points] The default public constructor should generate a 5 × 5 magic square.
MagicSquare()
(b) [5 points] Implement a public constructor that takes an odd integer, n, as a parameter, which should generate
an n × n magic square. You should assume that n will always be an odd integer.
MagicSquare(const int& n)
(c) [10 points] Implement a private generator function to create a magic square using the procedure described in the
project description. You should assume that you are only using this function to create magic squares for an odd
n. Hint: your constructors should call this function.
void generateMagicSquare()
(d) [4 points] Overload the << operator to output the magic square to an ostream.
Magic Squares are output on n + 1 lines. The first list should indicate n, the size of the magic square. The next
n lines should each have n integers, separated by one space, which is the magic square. For example, the output
for a 5×5 magic square would be:
5
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
(e) [4 points] Overload the >> operator to input a magic square from istream. The magic square will be input in
the same format as it was output.
(f) [10 points] Implement a public function to test whether the object is a magic square. This function must test
all of the criteria that we used to define a magic square. The function should return true if the object meets the
criteria for a magic square and false otherwise.
This function would be useful to verify that a magic square that was input using the overloaded >> is valid.
bool isMagicSquare()
(g) [10 points] If some n×n matrix is a magic square, then rotating the matrix by 900 would also be a magic square.
Implement a public function to create a new magic square object that rotates the calling magic square object
MagicSquare rotate()
For example, below is the 900
rotation of the 5 × 5 magic square provided in the project description:
11 10 4 23 17
18 12 6 5 24
25 19 13 7 1
2 21 20 14 8
9 3 22 16 15
You should implement additional helper functions as needed. Helper functions must also be located in the magicSquare.h
and magicSquare.cpp files.
Page 3 of 4 Project continues. . .
COT 4400 Project 1 Fall 2014
2. Write a main function to test each of the member functions of your MagicSquare class in file main.cpp.
(a) [2 points] Create a magic square object using the default constructor.
i. Verify that the magic square object is in fact a magic square.
ii. If the object is a valid magic square, then output the magic square to file output.txt
(b) [5 points] Create magic squares of sizes 7,9,11,13,15,17,19,21,23,25. For each magic square:
i. Verify that the object created is in fact a magic square.
ii. If the object is a valid magic square, then output the magic square to file output.txt (There should be a
blank line between each magic square output)
iii. Rotate the magic square. Verify that the result is in fact a magic square. If the result is a valid magic square,
then output the magic square to file output.txt otherwise, output the magic square to console.
(c) [5 points] Test all instances of magic squares that are in input file named input.txt.
i. The format of the input file is as follows. The first line of the input file indicates the number of instances
in the file followed by a blank line. Each instances consists of n + 1 lines, where n denotes the size of
the instance. The following n lines are a row from the magic square instance, where each line contains n
integers which are separated by spaces. There is a blank line between consecutive instances. For example,
an input.txt file with two 5 × 5 instances could be:
2
5
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
5
11 10 4 23 17
18 12 6 5 24
25 19 13 7 1
2 21 20 14 8
9 3 22 16 15
ii. For each instance, test that is a valid magic square.
If instance i is a magic square you should output (to console): i: is valid If instance i is not a magic
square you should output (to console): i: is not valid For example, one sequence of outputs might be:
0: is valid
1: is valid
2: is not valid
3: is not valid
4: is valid
iii. You should create your own input.txt file to test various potential matrices to determine if they are a magic
square – you must submit your input.txt file. Note that I will be using my own input.txt to test your
code.
Page 4 of 4 End of Project

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