Question

C++

Lab 11 – Is This Box a Magic Box?

Objectives:

• 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 call all 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 will continue 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. Do not use dynamic arrays or pointers in this solution. Follow the solution given in the video and in Additional Notes on Two Dimension Arrays.

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.

Answer 1

SOLUTION;-

-;GIVEN DATA;-

*include <iostream>
*include <fstream>

using namespace std;

void readData(int** mat, int size, std::fstream &myfile) {
int n;
for(int i=0; i<size; i++) {
for(int j=0; j<size; j++) {
// read from file
myfile >> n;
  
// assign to matrix
mat[i][j] = n;
}
}
}

void printMatrix(int** mat, int size) {
for(int i=0; i<size; i++) {
for(int j=0; j<size; j++) {
  
cout << mat[i][j] << " ";
}
cout << endl;
}
cout << endl;
}

int rowSum(int** mat, int row, int size) {
int sum = 0;
for(int j=0; j<size; j++) {
sum += mat[row][j];
}
return sum;
}

int colSum(int** mat, int col, int size) {
int sum = 0;
for(int j=0; j<size; j++) {
sum += mat[j][col];
}
return sum;
}

int mainDiaSum(int** mat, int size) {
int sum = 0;
for(int j=0; j<size; j++) {
sum += mat[j][j];
}
return sum;
}

int revDiaSum(int** mat, int size) {
int sum = 0;
for(int j=size-1; j>=0; j--) {
sum += mat[j][j];
}
return sum;
}

int main()
{
std::fstream myfile("data.txt", std::ios_base::in);

int size, a;
int squareNo = 0;
myfile >> size;
  
while (size > 0)
{
squareNo++;
  
// create matrix
int** mat = new int*[size];
for(int i = 0; i < size; ++i) {
mat[i] = new int[size];
}
  
int sum;
  
readData(mat, size, myfile);
cout << "========================\n";
cout << "====== Square " << squareNo << " ======" << endl;
cout << "========================\n";
  
printMatrix(mat, size);
  
bool isMagic = true;
  
// assigning row 0 sum as magic sum..
// if matrix is not magic, we will set above boolean as false
int magicSum = rowSum(mat, 0, size);
  
for(int i=0; i<size; i++) {
sum = rowSum(mat, i, size);
if(sum != magicSum)
isMagic = false;
cout << "The sum of row " << i << " is " << sum << endl;
}
cout << endl;
  
for(int j=0; j<size; j++) {
sum = colSum(mat, j, size);
if(sum != magicSum)
isMagic = false;
cout << "The sum of col " << j << " is " << sum << endl;
}
cout << endl;
  
sum = mainDiaSum(mat, size);
if(sum != magicSum)
isMagic = false;
cout << "The sum of main diagonal is " << sum << endl;
  
sum = mainDiaSum(mat, size);
if(sum != magicSum)
isMagic = false;
cout << "The sum of other diagonal is " << sum << endl;
  
if(isMagic)
cout << "The matrix is a magic Box" << endl << endl;
else
cout << "The matrix is not a magic Box" << endl << endl;
  
for(int i = 0; i < size; ++i) {
delete [] mat[i];
}
delete [] mat;

// get next matrix size
myfile >> size;
}

return 0;
}

data.txt:
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

Sample output:

Sh-4.2$ main

=======================

=======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 sum of main diagonal is 15

The sum of other diagonal is 15

This matrix is a magic box

=====================

===== Square 2 =======

====================

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

The sum of row 0 is 175

The sum of row 1 is 175

The sum of row 2 is 175

The sum of row 3 is 175

The sum of row 4 is 175

The sum of row 5 is 175

The sum of row 6 is 175

''The sum of column 0 is 175''

The data .txt in same folder....