Example: Naive Matrix Multiplication in C

// Naive Matrix Multiplication
#include <iostream>
#include <vector>

// Helper function to print a matrix
void printMatrix(const std::vector<std::vector<int>>& matrix) {
    // Step 1: Iterate through each row of the matrix.
    for (const auto& row : matrix) {
        // Step 2: Iterate through each element in the current row.
        for (int val : row) {
            // Step 3: Print the element followed by a space.
            std::cout << val << " ";
        }
        // Step 4: Move to the next line after printing all elements in a row.
        std::cout << std::endl;
    }
}

// Function to perform naive matrix multiplication
std::vector<std::vector<int>> multiplyNaive(const std::vector<std::vector<int>>& A,
                                           const std::vector<std::vector<int>>& B) {
    int n = A.size(); // Assuming square matrices of size n x n
    
    // Step 1: Initialize the result matrix C with dimensions n x n, filled with zeros.
    std::vector<std::vector<int>> C(n, std::vector<int>(n, 0));

    // Step 2: Iterate through rows of matrix A.
    for (int i = 0; i < n; ++i) {
        // Step 3: Iterate through columns of matrix B.
        for (int j = 0; j < n; ++j) {
            // Step 4: Iterate through elements for the sum of products.
            for (int k = 0; k < n; ++k) {
                // Step 5: Accumulate the product A[i][k] * B[k][j] into C[i][j].
                C[i][j] += A[i][k] * B[k][j];
            }
        }
    }
    // Step 6: Return the resulting product matrix C.
    return C;
}

int main() {
    // Step 1: Define matrices A and B (2x2 example).
    std::vector<std::vector<int>> A = {{1, 2}, {3, 4}};
    std::vector<std::vector<int>> B = {{5, 6}, {7, 8}};

    int n = A.size();
    if (n == 0 || A[0].size() != n || B.size() != n || B[0].size() != n) {
        std::cout << "Invalid matrix dimensions for square matrices." << std::endl;
        return 1;
    }

    // Step 2: Print original matrices for clarity.
    std::cout << "Matrix A:" << std::endl;
    printMatrix(A);
    std::cout << "\nMatrix B:" << std::endl;
    printMatrix(B);

    // Step 3: Perform naive matrix multiplication.
    std::vector<std::vector<int>> C = multiplyNaive(A, B);

    // Step 4: Print the result matrix.
    std::cout << "\nResult of Naive Multiplication (C = A * B):" << std::endl;
    printMatrix(C);

    return 0;
}