Objectives: C++

Define a two dimensional array

Understand how to traverse a two dimensional array

Code and run a program that processes a two dimensional array

Instructions:

A magic square is a matrix (two dimensional arrays) in which the sum of each row, sum of each column, sum of the main diagonal, and sum of the reverse diagonal are all the same value.

You are to code a program to determine if a given two-dimensional array (that will be read in from a file) is a magic square or not. The functions you will need to code are as follows:

Code a function/method for each of the following:

Read data into the matrix

Print the matrix on the screen

Sum a row given the index for that row

Sum a column given the index for that column

Sum the main diagonal

Sum the reverse diagonal

Determine if the two dimensional array is a magic square

The main method will read the size of the array outside of the while loop. Then inside the while loop it will callall the methods given above to read the data into the matrix, print the matrix, print all the row sums, print all the column sums, and print both diagonals. Then the program will determine if the matrix is a magic square and print an appropriate message. The next size should be read in at the end of the while loop. The main willcontinue with the next matrix in the data file, until a size of -1 is reached. See the Additional Notes on Two Dimension Arrays for more help with this assignment.

Sample Output:

The first part of the output should look similar to this:

=========

= Square 1=

=========

8 1 6

3 5 7

4 9 2

The sum of row 0 is 15

The sum of row 1 is 15

The sum of row 2 is 15

The sum of column 0 is 15

The sum of column 1 is 15

The sum of column 2 is 15

The main diagonal is 15

The other diagonal is 15

This matrix is a magic box!

Data File:

Paste everything below this block of text into a notepad file. Your input file must appear exactly as it below and include all of this data in the same file.

3

8 1 6

3 5 7

4 9 2

7

30 39 48 1 10 19 28

38 47 7 9 18 27 29

46 6 8 17 26 35 37

5 14 16 25 34 36 45

13 15 24 33 42 44 4

21 23 32 41 43 3 12

22 31 40 49 2 11 20

4

48 9 6 39

27 18 21 36

15 30 33 24

12 45 42 3

3

6 2 7

1 5 3

2 9 4

4

3 16 2 13

6 9 7 12

10 5 11 8

15 4 14 1

5

17 24 15 8 1

23 5 16 14 7

4 6 22 13 20

10 12 3 21 19

11 18 9 2 25

7

30 39 48 1 10 28 19

38 47 7 9 18 29 27

46 6 8 17 26 37 35

5 14 16 25 34 45 36

13 15 24 33 42 4 44

21 23 32 41 43 12 3

22 31 40 49 2 20 11

-1

Run:

Run the program to see if your results are correct.