Example: Determinant of NxN Matrix in C++

// Determinant of NxN Matrix
#include <iostream>
#include <vector>
#include <iomanip> // For std::setw

// Function to get a sub-matrix (minor matrix) by removing a specified row and column
std::vector<std::vector<int>> getSubMatrix(const std::vector<std::vector<int>>& matrix, int row, int col, int N) {
    std::vector<std::vector<int>> subMatrix(N - 1, std::vector<int>(N - 1));
    int sub_i = 0; // Row index for subMatrix
    for (int i = 0; i < N; ++i) {
        if (i == row) continue;
        int sub_j = 0; // Column index for subMatrix
        for (int j = 0; j < N; ++j) {
            if (j == col) continue;
            subMatrix[sub_i][sub_j] = matrix[i][j];
            sub_j++;
        }
        sub_i++;
    }
    return subMatrix;
}

// Recursive function to calculate the determinant
int calculateDeterminant(const std::vector<std::vector<int>>& matrix, int N) {
    // Base case 1: For a 1x1 matrix, the determinant is the single element
    if (N == 1) {
        return matrix[0][0];
    }

    // Base case 2: For a 2x2 matrix, use the formula (ad - bc)
    if (N == 2) {
        return (matrix[0][0] * matrix[1][1]) - (matrix[0][1] * matrix[1][0]);
    }

    int det = 0;
    int sign = 1; // Used for alternating signs (+ - + - ...)

    // Iterate through the first row to apply cofactor expansion
    for (int j = 0; j < N; ++j) {
        // Get the sub-matrix by excluding the first row and current column 'j'
        std::vector<std::vector<int>> subMatrix = getSubMatrix(matrix, 0, j, N);

        // Recursively calculate the determinant of the sub-matrix
        // Add or subtract (based on 'sign') the product of the element and its sub-matrix's determinant
        det += sign * matrix[0][j] * calculateDeterminant(subMatrix, N - 1);

        // Toggle the sign for the next element
        sign = -sign;
    }

    return det;
}

// Function to print a matrix (for debugging/display)
void printMatrix(const std::vector<std::vector<int>>& matrix, int N) {
    for (int i = 0; i < N; ++i) {
        for (int j = 0; j < N; ++j) {
            std::cout << std::setw(4) << matrix[i][j] << " ";
        }
        std::cout << std::endl;
    }
}

int main() {
    // Step 1: Define the matrix size and elements.
    // Example 1: 3x3 matrix
    std::vector<std::vector<int>> matrix3x3 = {
        {1, 2, 3},
        {4, 5, 6},
        {7, 8, 9}
    };
    int N3 = 3;

    std::cout << "Matrix 1 (" << N3 << "x" << N3 << "):" << std::endl;
    printMatrix(matrix3x3, N3);
    std::cout << "Determinant: " << calculateDeterminant(matrix3x3, N3) << std::endl << std::endl;

    // Example 2: 4x4 matrix
    std::vector<std::vector<int>> matrix4x4 = {
        {1, 0, 2, -1},
        {3, 0, 0, 5},
        {2, 1, 4, -3},
        {1, 0, 5, 0}
    };
    int N4 = 4;

    std::cout << "Matrix 2 (" << N4 << "x" << N4 << "):" << std::endl;
    printMatrix(matrix4x4, N4);
    std::cout << "Determinant: " << calculateDeterminant(matrix4x4, N4) << std::endl << std::endl;

    // Example 3: 2x2 matrix
    std::vector<std::vector<int>> matrix2x2 = {
        {4, 2},
        {-1, 3}
    };
    int N2 = 2;

    std::cout << "Matrix 3 (" << N2 << "x" << N2 << "):" << std::endl;
    printMatrix(matrix2x2, N2);
    std::cout << "Determinant: " << calculateDeterminant(matrix2x2, N2) << std::endl << std::endl;

    // Example 4: 1x1 matrix
    std::vector<std::vector<int>> matrix1x1 = {
        {7}
    };
    int N1 = 1;

    std::cout << "Matrix 4 (" << N1 << "x" << N1 << "):" << std::endl;
    printMatrix(matrix1x1, N1);
    std::cout << "Determinant: " << calculateDeterminant(matrix1x1, N1) << std::endl << std::endl;

    return 0;
}