Question

9. Lo Shu Magic Square The Lo Shu Magic Square is a grid with three rows and three columns that has the following properties: The grid contains the numbers 1 through 9 exactly. The sum of each row, each column, and each diagonal all add up to the same number. This is shown in the following figure · 15 4 9 2-15 3 5 7-15 81 615 15 15 15 15 Write a program that simulates a magic square using a two-dimensional 3 x 3 array. It should have a Boolean function isMagicSquare that accepts the array as an argument and returns true if it determines it is a Lo Shu Magic Square and false if it is not. Test the program with one array, such as the one shown in Figure 8-18, that is a magic square and one that is not. Note: you need to submit the source code and a sample output of your code

Answer 1

#include <iostream>

using namespace std;

bool isMagicSquare(int** matrix, int len) {

        

        int sum = 0;

        // row sum

        for (int i = 0; i < len; i++) {

                int rowSum = 0;

                for (int j = 0; j < len; j++) {

                        rowSum += matrix[i][j];

                }

                if (sum == 0) {

                        sum = rowSum;

                } else {

                        if (rowSum != sum) {

                                return false;

                        }

                }

        }

        // column sum

        for (int i = 0; i < len; i++) {

                int colSum = 0;

                for (int j = 0; j < len; j++) {

                        colSum += matrix[j][i];

                }

                if (colSum != sum) {

                        return false;

                }

        }

        // main diagonal

        int diaGonalSum = 0;

        for (int i = 0; i < len; i++) {

                diaGonalSum += matrix[i][i];

        }

        if (diaGonalSum != sum) {

                return false;

        }

        // reverse diagonal

        diaGonalSum = 0;

        for (int i = 0; i < len; i++) {

                diaGonalSum += matrix[i][len - 1 - i];

        }

        if (diaGonalSum != sum) {

                return false;

        }

        return true;

}

void printMatrix(int **matrix, int len) {

        for (int i = 0; i < len; i++) {

                for (int j = 0; j < len; j++) {

                        cout << matrix[i][j] << " ";

                }

                cout << endl;

        }

}

int main() {

        

        int size = 3;

        int **matrix = new int*[size];

        

        for(int i=0; i<size; i++) {

                matrix[i] = new int[size];

                for(int j=0; j<size; j++) {

                        cout << "Enter cell value at (" << i << ", " << j << "): ";

                        cin >> matrix[i][j];

                        

                        if(matrix[i][j] < 0) {

                                cout << "Invalid entry.";

                                j--; // so that this cell is repeated

                        }

                }

        }

        

        printMatrix(matrix, size);

        

        if(isMagicSquare(matrix, size)) {

                cout << "Matrix is a magic square" << endl;

        } else {

                cout << "Matrix is not a magic square" << endl;

        }

}