Description
Write C++ programs that create FIVE(5) different N*N magic squares. A square matrix
is the arrangement of the numbers 1, 2, …, N2
, in which the sum of rows, columns, and
diagonals are the same. The users (i.e., TAs) will specify the size of the square matrix:
N. The value N must be an odd number between 3 and 15.
Example Run
For example, you program is expected to run in the following way:
INPUT>> Enter the size of a magic square: 3
OUTPUT>> Magic Square #1 is:
2 7 6
9 5 1
4 3 8
OUTPUT>> Checking the sums of every row: 15 15 15
OUTPUT>> Checking the sums of every column: 15 15 15
OUTPUT>> Checking the sums of every diagnoal: 15 15
OUTPUT>> Magic Square #2 is:
8 3 4
1 5 9
6 7 2
OUTPUT>> Checking the sums of every row: 15 15 15
OUTPUT>> Checking the sums of every column: 15 15 15
OUTPUT>> Checking the sums of every diagnoal: 15 15
OUTPUT>> Magic Square #3 is:
8 1 6
3 5 7
4 9 2
OUTPUT>> Checking the sums of every row: 15 15 15
OUTPUT>> Checking the sums of every column: 15 15 15
OUTPUT>> Checking the sums of every diagnoal: 15 15
OUTPUT>> Magic Square #4 is:
2 9 4
7 5 3
6 1 8
OUTPUT>> Checking the sums of every row: 15 15 15
OUTPUT>> Checking the sums of every column: 15 15 15
OUTPUT>> Checking the sums of every diagnoal: 15 15
OUTPUT>> Magic Square #5 is:
6 1 8
7 5 3
2 9 4
OUTPUT>> Checking the sums of every row: 15 15 15
OUTPUT>> Checking the sums of every column: 15 15 15
OUTPUT>> Checking the sums of every diagnoal: 15 15
Hints to find magic squares
1. (Data Structures:) You should use arrays to generate and store the integers. You
should practice C++ modeling to create classes and methods to compile the program,
then run the executable code.
2. (Algorithms:) Many good heuristics do exist to find a magic square quickly. You
should be able to find them via Google search on Internet. However, finding ALL magic
squares requires careful examination of all permutation of all these N*N numbers (e.g.,
225! for a 15*15 matrix). When the matrix size N is big enough, the computation for
ALL magic squares will become intensive.
3. (Computation:) You are only required to find FIVE(5) magic squares for the full
credits since we just want you to get familiar with C++ programming via this assignment. However, you are encouraged to explore the computational complexity of finding
ALL magic squares, if time allows.
4. There are many ways to model/code in C++. Thus, there may not be a standard
solution. You need to explain well on your modeling and coding with comments in the
pa1.h and pa1.cpp file(s).
5. Please do not take user’s input N, then declare the size of arrays. It is not a good
practice since malicious users may input a very large number (e.g., 1,000,000).
6. Note that squares cannot be hard-coded, but must actually be computed at runtime.
Submission Guilde-lines
1. You must finish this assignment with your individual effort. Your C++ source code
file MUST be named as ”pa1.cpp” and C++ header/class file should be named as ”pa1.h”.
2. You are allowed to use any IDE. However, please test your program via g++ compiler
(i.e., g++ -Wall) on the CISE machines to make sure it runs correctly. Note the ”-std
c++11” option is acceptable by TAs. We recommend you to start the testing 48 hours
before the submission deadline.
3. Please upload the source code file(s) via the CANVAS system as the attachment(s).
Please submit the source code file(s) ONLY. NO need to compress the source code file(s)
if the size is small.
4. Please do NOT submit your source codes via smart-phones since CANVAS system
has difficulty to deal with smart-phones. Submission via WiFi is not recommended either
since your WiFi channel may be disassociated or disconnected in the middle of transmission.
5. Make sure you submit your assignment BEFORE the deadline based on CANVAS
system clock. We recommend the submission to be completed 30 minutes before the
deadline. Late submission will NOT be accepted by CANVAS system !!
Grading Criteria
1. Successful Compilation (30%): Your source code should be able to compile using ”g++
-Wall” command without any error or warning. The output should be a valid executable.
See lab tutorial for the commands. Please note that we will be using g++ compiler on
Linux to grade your programs. If you are using other compilers or IDE (e.g., Visual C++),
it is recommended that you test the source codes with g++ 48 hours before the CANVAS
submission (i.e., to make sure there is no warning). Note again the ”-std c++11” option
is acceptable by TAs.
2. Program Correctness (40%): The executable should be able to run correctly by giving
out the required output. Be sure to test all cases (e.g., 3,5,7,9,11,13 and 15) for the proper
outputs and correctness. Un-expected results may occur when the matrix size is large.
3. Programming Style (30%): Good coding style is a key to efficient programming. We
encourage you to write clear and readable codes. You should adopt a sensible set of coding
conventions, including proper indention, necessary comments and more. Here are some
guidelines of good programming style: http://en.wikipedia.org/wiki/Programming style
Final Notes
1. Remember to start the programming assignments as soon as possible. Unlike the conventional assignments, programming assignments sometimes take un-predictable amount
of time to finish. Thus, have the code running first, then polish it later with the extra
time before the deadline.
2. Remember you should always write your own code and never copy-and-paste from
other students’ work or other sources. There are indeed many tools (like Stanford Moss)
to detect the code similarity.
3. Programming assignments are usually designed by TAs. If you have any question
or concern, please feel free to contact TAs. Our goal is to let you experience the fundamentals of computer science. If you like the programming experience, you are one of us !!
4. HAPPY CODING … and GOOD LUCK !!
