Question

How to check whether a matrix is a magic square or not in C++

Answer 1

#include <iostream>
#include <vector>

// Function to check if the matrix is a magic square
bool isMagicSquare(const std::vector<std::vector<int>>& matrix) {
    int size = matrix.size();

    int sumDiagonal1 = 0, sumDiagonal2 = 0;

    // Calculate the sum of the primary diagonal
    for (int i = 0; i < size; i++) {
        sumDiagonal1 += matrix[i][i];
    }

    // Calculate the sum of the secondary diagonal
    for (int i = 0; i < size; i++) {
        sumDiagonal2 += matrix[i][size - i - 1];
    }

    // If the two diagonals don't have the same sum, it's not a magic square
    if (sumDiagonal1 != sumDiagonal2) {
        return false;
    }

    // Check sums of each row and column
    for (int i = 0; i < size; i++) {
        int sumRow = 0, sumCol = 0;

        for (int j = 0; j < size; j++) {
            sumRow += matrix[i][j];  // Sum of the current row
            sumCol += matrix[j][i];  // Sum of the current column
        }

        // If any row or column sum is not equal to the diagonal sum, it's not a magic square
        if (sumRow != sumDiagonal1 || sumCol != sumDiagonal1) {
            return false;
        }
    }

    // If all checks pass, it's a magic square
    return true;
}

int main() {
    std::vector<std::vector<int>> matrix = {
        {8, 3, 4},
        {1, 5, 9},
        {6, 7, 2}
    };

    // Check if the matrix is a magic square
    if (isMagicSquare(matrix)) {
        std::cout << "The given matrix is a magic square." << std::endl;
    } else {
        std::cout << "The given matrix is NOT a magic square." << std::endl;
    }
}


/*
run:

The given matrix is a magic square.

*/

 

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