MagicSquare

0

1

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;
}
``````
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