Matrix: Given a matrix, check if it is a magic square or not

Problem Statement:

You are given a matrix, you need to check if the matrix is a Magic Square or not.

A matrix is a magic square of n * n, satisfies below conditions:

1. It has distinct elements from 1 to n^2.

2.The sum of any row, column or diagonal is equal to the same number.

Example:

Input:

  2   7   6
  9   5   1
  4   3   8

Output:

 Yes.

Sum of each row and column and diagonal is 15

Solution Explanation:

For the solution calculate below steps:

1. Find the sum of prime diagonal and secondary diagonal
2. Find the sum of each row and column.

If all the sum are same, then it is a magic matrix.

Time Complexity: O(1)
Space Complexity: O(1)

Code Solution

#include <iostream>
#include <queue>
#include <stack>
using namespace std;


bool solution(int mat[3][3])
{
    
    int n = 3;
    int i = 0;
    int j = 0;

    int sumd1 = 0;
    int sumd2 = 0;

    for (i = 0; i < n; i++)
    {
        sumd1 += mat[i][i];
        sumd2 += mat[i][n-1-i];
    }

    if(sumd1!=sumd2)
        return false;

    for (i = 0; i < n; i++) {
        
        int rowSum = 0, colSum = 0;    
        for (j = 0; j < n; j++)
        {
            rowSum += mat[i][j];
            colSum += mat[j][i];
        }
        if (rowSum != colSum || colSum != sumd1)
            return false;
    }
   return true;
}

int main()
{
    int mat[3][3] = {{ 2, 7, 6 },
                     { 9, 5, 1 },
                     { 4, 3, 8 }};
    
    if (solution(mat))
        cout << "Magic Square";
    else
        cout << "Not a magic Square";
    
    return 0;
}

Output

Magic Square