MagicSquare

Mahendra Kumar

matrixDSA

To verify whether the given matrix(square) is a magic square or not. Magic Square of size 3

2 7 6 9 5 1 4 3 8 Sum in each row & each column = 3*(32+1)/2 = 15

Magic Square of size 5

9 3 22 16 15 2 21 20 14 8 25 19 13 7 1 18 12 6 5 24 11 10 4 23 17 Sum in each row & each column = 5*(52+1)/2 = 65

Magic Square of size 7

20 12 4 45 37 29 28 11 3 44 36 35 27 19 2 43 42 34 26 18 10 49 41 33 25 17 9 1 40 32 24 16 8 7 48 31 23 15 14 6 47 39 22 21 13 5 46 38 30 Sum in each row & each column = 7*(72+1)/2 = 175

#include <bits/stdc++.h>
using namespace std;
void generateSquare(int n)
{
    int magicSquare[n][n];
    memset(magicSquare, 0, sizeof(magicSquare));
    int i = n / 2;
    int j = n - 1;
    // One by one put all values in magic square
    for (int num = 1; num <= n * n;) {
        if (i == -1 && j == n) // 3rd condition
        {
            j = n - 2;
            i = 0;
        }
        else {
            // 1st condition helper if next number
            // goes to out of square's right side
            if (j == n)
                j = 0;
            // 1st condition helper if next number
            // is goes to out of square's upper side
            if (i < 0)
                i = n - 1;
        }
        if (magicSquare[i][j]) // 2nd condition
        {
            j -= 2;
            i++;
            continue;
        }
        else
            magicSquare[i][j] = num++; // set number
        j++;
        i--; // 1st condition
    }
    // Print magic square
    cout << "The Magic Square for n=" << n
         << ":\nSum of "
            "each row or column "
         << n * (n * n + 1) / 2 << ":\n\n";
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++)
            cout << setw(4) << magicSquare[i][j] << " ";
        cout << endl;
    }
}
int main()
{
  int n;
  cout<<"Enter an odd number:";
  cin>>n;
  generateSquare(n);
  return 0;
}