Example: Check Matrix Equality in C++

// Check Matrix Equality
#include <iostream>
#include <vector>

// Function to check if two matrices are equal
bool areMatricesEqual(const std::vector<std::vector<int>>& mat1,
                      const std::vector<std::vector<int>>& mat2) {
    // Step 1: Check if the number of rows are equal
    if (mat1.size() != mat2.size()) {
        return false;
    }

    // Step 2: If rows are 0 (empty matrices), they are equal
    if (mat1.empty()) {
        return true; // Both are empty, or one is empty and the other checked empty.
                     // The first check `mat1.size() != mat2.size()` handles cases
                     // where one is empty and other is not.
    }

    // Step 3: Check if the number of columns are equal for each row
    // Assuming matrices are rectangular (all rows have same number of columns)
    if (mat1[0].size() != mat2[0].size()) {
        return false;
    }

    // Step 4: Iterate through each element and compare
    for (size_t i = 0; i < mat1.size(); ++i) { // Iterate through rows
        for (size_t j = 0; j < mat1[i].size(); ++j) { // Iterate through columns
            if (mat1[i][j] != mat2[i][j]) {
                return false; // Found a differing element
            }
        }
    }

    // Step 5: If all checks pass, matrices are equal
    return true;
}

int main() {
    // Test Case 1: Equal Matrices
    std::vector<std::vector<int>> matrixA = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    std::vector<std::vector<int>> matrixB = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

    std::cout << "Test Case 1 (Equal Matrices): " << std::endl;
    if (areMatricesEqual(matrixA, matrixB)) {
        std::cout << "Matrices A and B are equal." << std::endl;
    } else {
        std::cout << "Matrices A and B are NOT equal." << std::endl;
    }
    std::cout << std::endl;

    // Test Case 2: Unequal Matrices (different element)
    std::vector<std::vector<int>> matrixC = {{1, 2, 3}, {4, 5, 0}, {7, 8, 9}}; // Element (1,2) is 0
    std::vector<std::vector<int>> matrixD = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};

    std::cout << "Test Case 2 (Unequal Matrices - different element): " << std::endl;
    if (areMatricesEqual(matrixC, matrixD)) {
        std::cout << "Matrices C and D are equal." << std::endl;
    } else {
        std::cout << "Matrices C and D are NOT equal." << std::endl;
    }
    std::cout << std::endl;

    // Test Case 3: Unequal Matrices (different number of rows)
    std::vector<std::vector<int>> matrixE = {{1, 2}, {3, 4}};
    std::vector<std::vector<int>> matrixF = {{1, 2}, {3, 4}, {5, 6}};

    std::cout << "Test Case 3 (Unequal Matrices - different rows): " << std::endl;
    if (areMatricesEqual(matrixE, matrixF)) {
        std::cout << "Matrices E and F are equal." << std::endl;
    } else {
        std::cout << "Matrices E and F are NOT equal." << std::endl;
    }
    std::cout << std::endl;

    // Test Case 4: Unequal Matrices (different number of columns)
    std::vector<std::vector<int>> matrixG = {{1, 2, 3}, {4, 5, 6}};
    std::vector<std::vector<int>> matrixH = {{1, 2}, {4, 5}};

    std::cout << "Test Case 4 (Unequal Matrices - different columns): " << std::endl;
    if (areMatricesEqual(matrixG, matrixH)) {
        std::cout << "Matrices G and H are equal." << std.endl;
    } else {
        std::cout << "Matrices G and H are NOT equal." << std::endl;
    }
    std::cout << std::endl;
    
    // Test Case 5: Empty Matrices
    std::vector<std::vector<int>> matrixI = {};
    std::vector<std::vector<int>> matrixJ = {};

    std::cout << "Test Case 5 (Empty Matrices): " << std::endl;
    if (areMatricesEqual(matrixI, matrixJ)) {
        std::cout << "Matrices I and J are equal." << std::endl;
    } else {
        std::cout << "Matrices I and J are NOT equal." << std::endl;
    }
    std::cout << std::endl;

    // Test Case 6: One empty, one not
    std::vector<std::vector<int>> matrixK = {{1}};
    std::vector<std::vector<int>> matrixL = {};

    std::cout << "Test Case 6 (One empty, one not): " << std::endl;
    if (areMatricesEqual(matrixK, matrixL)) {
        std::cout << "Matrices K and L are equal." << std::endl;
    } else {
        std::cout << "Matrices K and L are NOT equal." << std::endl;
    }
    std::cout << std::endl;

    return 0;
}