Question

C++

Magic Squares. An n x n matrix that is filled with the numbers 1,2,3,…,n² is a magic square if the sum of the elements in each row, in each column, and in the two diagonals is the same value.
The following algorithm will construct magic n x n squares; it only works if n is odd: Place 1 in the middle of the bottom row. After k has been placed in the (i,j) square, place k+1 into the square right and down, wrapping around the borders. However, if you reach a square that has already been filled, then you must move one square up instead.
Here is the 5 x 5 square that you get if you follow this method:

11 18 25 2 9

10 12 19 21 3

4 6 1320 22

23 5 7 14 16

17 24 1 8 15

Make a function with an array argument that will make a magic square.

Make another function that will check if its array argument is a magic square.

Make a third function that can be passed a matrix of the same size as the magic squares created by your first function, and will allow the user to enter any number of changes the user wants to make to the values of the matrix.

Make a main function that will make a magic square, print it, check if it is a magic square, allow the user to change it, print it again, and check if it is a magic square after the changes. Do not use global variables.

Answer 1

SOLUTION-
I have solve the problem in C ++ code with comments and screenshot for easy understanding :)

CODE-

// C++ program
//headerfile
#include <iostream>
using namespace std;

class MagicSquare
{
   private:
   int **magic; // dynamic array to store the magic square
   int size; // size of the matrix
   public:
      MagicSquare(int n); //constructor
      ~MagicSquare();      //destructor
   bool isMagic() const;
   void setValues();
   void display() const;
};

// constructor that takes as input the size of the matrix and generate the magic square according to the given algorithm
MagicSquare::MagicSquare(int n)
{
    // check if input is odd, then set size to n else by default set n to 5
    if(n%2 != 0)
     size = n;
    else
     size = 5;
    // create the dynamic array of size*size
    magic = new int*[size];
    for(int i=0;i<size;i++)
    {
      magic[i] = new int[size];
    for(int j=0;j<size;j++)
    {
      magic[i][j] = 0; // initialize all entries to 0
    }
}

   // populate the matrix according to the algorithm
   int row=size-1; // set row to last row
   int col=size/2; // set col to middle column

   // loop size*size times
   for(int cnt = 1;cnt<=size*size;)
   {
   // if location (row,col) is filled, then move one square up
   if(magic[row][col] != 0)
{
row--;
if(row == -1) // if row reached outside matrix, then wrap around
row = size-1;
row--;

if(row == -1) row= size-1;

col--;
if(col == -1) // if col reached outside matrix, then wrap around
col = size-1;
continue;
}
   else // if not filled, populate the location with cnt and increment cnt
magic[row][col] = cnt++;

// move into square right and down
row++;
   if(row == size) // if row reached outside matrix, then wrap around
row = 0;
   col++;

   if(col == size) // if col reached outside matrix, then wrap around
col = 0;
   }
}

// function to check and return if the matrix is a magic square or not
bool MagicSquare:: isMagic() const
{
int sum = 0, rowSum, colSum;
// calculate the sum of first row
for(int i=0;i<size;i++)
sum += magic[0][i];

// loop to calculate row sum and column sum
for(int i=0;i<size;i++)
{
   rowSum = 0 ;
   colSum = 0;
for(int j=0;j<size;j++)
{
    rowSum += magic[i][j];
    colSum += magic[j][i];
}

// check if sum of ith row and ith column is equal to sum
if((rowSum != sum) || (colSum != sum))
return false; // if not return false
}

// calculate main diagonal sum

int diagonalSum = 0;
for(int i=0;i<size;i++)
diagonalSum += magic[i][i];

if(diagonalSum != sum) // check diagonal sum = sum
return false;

// calculate other diagonal sum
diagonalSum = 0;

for(int i=0;i<size;i++)
diagonalSum += magic[i][size-1-i];
// check other diagonal sum = sum
if(diagonalSum != sum)
return false;

return true; // it is a magic square

}

// function to display the matrix
void MagicSquare:: display() const
{
for(int i=0;i<size;i++)
{
for(int j=0;j<size;j++)
cout<<magic[i][j]<<" ";
cout<<endl;
}
}

// function to allow user to modify the values of the matrix
void MagicSquare:: setValues()
{
int row, col, value;
char choice;

// loop till the user wants
do
{
// input the row and column of matrix which needs to be changed
cout<<"Enter row(1-"<<size<<") and column(1-"<<size<<") for the element to change (separated by a space): ";
cin>>row>>col;
// input the value to set
cout<<"Enter the value to set: ";
cin>>value;
// update the value at given position
magic[row-1][col-1] = value;

// ask if user wants to change more
cout<<"Do you want to make more changes? (y/n) ";
cin>>choice;
}while(choice == 'y' || choice == 'Y');
}

// destructor to delete the dynamically allocated array
MagicSquare::~MagicSquare()
{
for(int i=0;i<size;i++)
delete [] magic[i];
delete[] magic;
}

int main()
{
   MagicSquare magic(5); // generate magic square of size 5
   magic.display(); // display the array
   // check and display if the matrix is magic square or not
   if(magic.isMagic())
   cout<<endl<<"The above matrix is a MAGIC SQUARE: "<<endl;
   else
   cout<<endl<<"The above matrix is not a MAGIC SQUARE: "<<endl;

   magic.setValues(); // allow user to update the values
   magic.display(); // display the updated array
   // check and display if updated matrix is magic square or not
   if(magic.isMagic())
   cout<<endl<<"The above matrix is a MAGIC SQUARE: "<<endl;
   else
   cout<<endl<<"The above matrix is not a MAGIC SQUARE: "<<endl;

return 0;
}
//end of program

SCREENSHOT-

11 18 25 2 9 10 12 19 21 3 4 6 13 20 22 23 5 7 14 16 17 24 1 8 15 The above matrix is a MAGIC SQUARE: Enter row (1-5) and column (1-5) for the element to change (separated by a space) : 2 1 Enter the value to set: 15 Do you want to make more changes? (y/n) y Enter row(1-5) and column(1-5) for the element to change (separated by a space): 5 4 Enter the value to set: 16 Do you want to make more changes? (y/n) y Enter row (1-5) and column (1-5) for the element to change (separated by a space) : 5 5 Enter the value to set: 44 Do you want to make more changes? (y/n) n 11 18 25 2 9 15 12 19 21 3 4 6 13 20 22 23 5 7 14 16 17 24 1 16 44 The above matrix is not a MAGIC SQUARE: ... Program finished with exit code o Press ENTER to exit console.

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