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Columbia University
cs3157 – Advanced Programming
Summer 2014, Lab #3, 40 points
June 10, 2014
This lab is due June 23rd 11:59 pm.
• lab in C. We will be using Makefiles.
• Don’t forget to FREE up any memory you request!!
• Make sure you complete the relevant reading on pointers.
• This is a long lab, please start early. Please also work on the homework project concurrently.
• Please make sure to run the debugger when you run into issues.
• Some code was developed in class, please indicate in the README etc
Step 1 - Puzzles (35 points)
In this step, you will develop code that computes a magic square. A magic square is a n× nmatrix filled
with integers in the range [1 – n2] so that each entry in the matrix has a unique value. The sum of each of
the rows and each of the columns and each of the two diagonals must be equal the same number. The
number is known as the magic constant Example for n=3 the magic
constant is 15, for n=4 it will be 34 etc. Also Note that there not a single unique solution to the magic
square problem.
think of Typedef as a shortcut so instead of having to type out a full type you can use the shortcut. For
example
typedef int XX[15];
XX yyy;
will make yyy a shortcut for a 15 array int. So can say yyy[0] etc
Create a file called Maintest1.c/Magicsquare1.c/Magicsquare.h and (to help you get started) start by
putting the following code/declarations in each file (where appropriate):
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#define MAGICSIZE 3
typedef int MSQUARE_TYPE[MAGICSIZE][ MAGICSIZE];
typedef MSQUARE_TYPE * MagSquare_PTR;
void initSquare( MagSquare_PTR, int magicsquaresize );
void printSquare( MagSquare_PTR, int magicsquaresize );
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int main() {
srand( time( NULL )); /* seed the random number gen */
MagSquare_PTR mptr = /* replace with something with malloc to create
space to point at*/;
initSquare( mptr, MAGICSIZE );
printSquare( mptr , MAGICSIZE);
} // end of main()
Define the function initSquare(MagSquare_PTR, int size) which takes the magic square pointer
argument (as above) and the size of the n by n array and fills it with values in the range [1 - 9]. These
values must be assigned RANDOMLY, but make sure that no number appears more than once in the
array.
Also Define the function printSquare(MagSquare_PTR, int size) which takes the magic square
pointer argument (as above) and the n for the n by n size, and prints out its contents to the screen in a nice
n rows by n columns format.
You should test your code with just these 2 functions to make sure each is working (before adding the rest
of the functions).
Hint: To get random numbers look up lookup rand() and srand() from the stdlib libary.
1. maintest1.c – this will contain the main function
2. magicsquare.h – this will contain the functions declarations that you will be using.
3. magicsquare.c – this will contain the function definitions from above including the following
methods:
a. void initSquare(MagSquare_PTR, int)
(see above)
b. void printSquare(MagSquare_PTR, int)
(see above)
c. int sumColumn( int column, MagSquare_PTR, int size )
The function takes the 2-dimensional magic square array and a column number and returns
the sum of the 3 values in that column
d. int sumRow(int row, MagSquare_PTR, int size)
see above.
e. int sumDiagonal( int diagonal, MagSquare_PTR, int size )
The function takes the 2-dimensional magic square array and a diagonal number and
returns the sum of the n values in that diagonal. Use diagonal = 0 to refer to the diagonal
that runs from the northwest corner down to the southeast corner. Use diagonal = 1 to refer
to the diagonal that runs from the northeast corner down to the southwest corner.
f. Create a function called int isMagic(MagSquare_PTR, int size) which takes the
magic square pointer as an argument and checks each of the rows and columns and
diagonals to see if all the sums equal 15. The function should return 0 if the argument is
not a magic square and 1 if it is a magic square.
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g. Modify the above main() so that it calls isMagic and prints out whether the square is a
magic square or not.
h. Modify the main() program so that after it prints out the square, it computes (using the
functions above) and prints out the sum of each of the 3 rows and each of the 3 columns
and each of the 2 diagonals.
Compile and test your program.
Here's a sample output:
the square is not a magic square of size 3
here is your square:
2 8 3
1 4 5
7 9 6
sum of row 1 = 13
sum of row 2 = 10
sum of row 3 = 22
sum of column 1 = 10
sum of column 2 = 21
sum of column 3 = 14
sum of diagonal 0 = 12
sum of diagonal 1 = 14
Note: you will need to create a makefile for this lab too. For example
make step1_run
would compile and execute the step1 code.
Hint: here is a sample of a more complicated Makefile:
CC = gcc
CCFLAGS = -Wall –lm
step1_run: maintest1.c magicsquare1.o
$(CC) $(CCFLAGS) -o test1 maintest1.c magicsquare1.o
./test1
magicsquare1.o: magicsquare1.c magicsquare1.h
$(CC) $(CCFLAGS) –c magicsquare1.c
clean:
rm –f *.o test1
(make clean
will just clean up all the temp .o files and executables, should run it before submission, if you used emacs,
you should probably include *~ also).
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Step 2 create a running program (20 points)
Now copy maintest1.c to maintest2.c and magicsquare1.c to magicsquare2.c, and magicsquare1.h to
magicsquare1.h modify them as follows:
1. Create a function called permuteSquare(MagSquare_PTR) which takes the magic square
pointer as an argument and randomly switches two entries in the array. Do this by randomly
picking two sets of row and column indices (in the range [0 - 2]) and then swapping the entries
located at each pair of indices. Check to make sure you aren’t picking the same spot .. that is
swapping the same location with itself J
2. Modify the main() so that after it calls isMagic(), if the square is not magic, then it calls
permuteSquare() to switch around two entries in the square and then test again to see if the
square is magic. Do this repeatedly until a magic square is found. When a magic square is found,
call printSquare() again to print out the magic square.
3. Have the program count the number of times it has to permute the square in order to find a magic
square. Print that out too (Hint: count it where you call method permutesquare).
Compile and test your code. Please ask for help as you need etc
Good luck.