Two-Dimensional Arrays

A two-dimensional array extends the concept of a one-dimensional array by adding a second dimension. While a one-dimensional array can be thought of as a single row of elements, a two-dimensional array organizes data in rows and columns, forming a matrix-like structure.

Declaration Methods

There are four primary ways to declare a two-dimensional array:

1. dataType arrayName[rows][cols]; — Declares without initialization.
2. dataType arrayName[rows][cols] = {{row1}, {row2}}; — Initializes with nested braces for clarity.
3. dataType arrayName[rows][cols] = {values}; — Initializes with a flat list.
4. dataType arrayName[][cols] = {values}; — Omits row count, letting the compiler infer it.

Method 1: Declaration with Manual Assignment

#include <iostream>
using namespace std;

int main() {
    int matrix[2][2];
    matrix[0][0] = 10;
    matrix[0][1] = 20;
    matrix[1][0] = 30;
    matrix[1][1] = 40;
    
    cout << matrix[0][0] << endl;
    cout << matrix[1][1] << endl;
    return 0;
}

Method 2: Initialization with Nested Braces

#include <iostream>
using namespace std;

int main() {
    int matrix[2][3] = {
        {5, 10, 15},
        {20, 25, 30}
    };
    
    for (int r = 0; r < 2; r++) {
        for (int c = 0; c < 3; c++) {
            cout << matrix[r][c] << " ";
        }
        cout << endl;
    }
    return 0;
}

Method 3: Flat Initialization

#include <iostream>
using namespace std;

int main() {
    int matrix[2][2] = {1, 2, 3, 4};
    
    for (int r = 0; r < 2; r++) {
        for (int c = 0; c < 2; c++) {
            cout << matrix[r][c] << " ";
        }
        cout << endl;
    }
    return 0;
}

Method 4: Automatic Row Detection

#include <iostream>
using namespace std;

int main() {
    int matrix[][4] = {1, 2, 3, 4, 5, 6, 7, 8};
    
    for (int r = 0; r < 2; r++) {
        for (int c = 0; c < 4; c++) {
            cout << matrix[r][c] << " ";
        }
        cout << endl;
    }
    return 0;
}

Memory and Address Information

The array name provides access to memory-related information:

#include <iostream>
using namespace std;

int main() {
    int matrix[2][3] = {
        {1, 2, 3},
        {4, 5, 6}
    };
    
    cout << "Total memory: " << sizeof(matrix) << " bytes" << endl;
    cout << "Memory per row: " << sizeof(matrix[0]) << " bytes" << endl;
    cout << "Memory per element: " << sizeof(matrix[0][0]) << " bytes" << endl;
    cout << "Number of rows: " << sizeof(matrix) / sizeof(matrix[0]) << endl;
    cout << "Number of columns: " << sizeof(matrix[0]) / sizeof(matrix[0][0]) << endl;
    
    cout << "Array address: " << matrix << endl;
    cout << "First row address: " << matrix[0] << endl;
    cout << "First element address: " << &matrix[0][0] << endl;
    return 0;
}

Practical Example: Student Grades

#include <iostream>
#include <string>
using namespace std;

int main() {
    int grades[3][3] = {
        {85, 92, 78},
        {90, 88, 95},
        {75, 80, 85}
    };
    string students[] = {"Alice", "Bob", "Charlie"};
    
    for (int i = 0; i < 3; i++) {
        int total = 0;
        for (int j = 0; j < 3; j++) {
            total += grades[i][j];
        }
        cout << students[i] << " - Total Score: " << total << endl;
    }
    return 0;
}

Functions

Functions encapsulate reusable blocks of code, reducing redundancy and improving maintainability.

Function Definition

A function consists of:

• Return type
• Function name
• Parameter list
• Function body
• Return statement

returnType functionName(parameterType paramName) {
    // function body
    return value;
}

Example of an addition function:

#include <iostream>
using namespace std;

int add(int x, int y) {
    return x + y;
}

Function Invocation

#include <iostream>
using namespace std;

int add(int x, int y) {
    return x + y;
}

int main() {
    int num1 = 15;
    int num2 = 25;
    int result = add(num1, num2);
    cout << "Sum: " << result << endl;
    return 0;
}

Parameters defined in the function signature are formal parameters, while values passed during the call are actual parameters (arguments).

Pass by Value

When passing by value, the function receives a copy of the argument. Modifications to the parameter do not affect the original variable.

#include <iostream>
using namespace std;

void swapValues(int a, int b) {
    int temp = a;
    a = b;
    b = temp;
    cout << "Inside function: a=" << a << ", b=" << b << endl;
}

int main() {
    int x = 5, y = 10;
    cout << "Before: x=" << x << ", y=" << y << endl;
    swapValues(x, y);
    cout << "After: x=" << x << ", y=" << y << endl;
    return 0;
}

Function Declaration (Prototype)

A function must be declared before it is used. If the definition appears after main(), a forward declaration is required.

#include <iostream>
using namespace std;

int findMaximum(int x, int y); // Function prototype

int main() {
    int a = 42, b = 17;
    cout << "Maximum: " << findMaximum(a, b) << endl;
    return 0;
}

int findMaximum(int x, int y) {
    return (x > y) ? x : y;
}

Header File Organization

For larger projects, functions can be separated into header and source files:

1. Create a header file (e.g., operations.h) with function declarations.
2. Create a source file (e.g., operations.cpp) with function definitions.
3. Include the header in the main file.

operations.h:

#ifndef OPERATIONS_H
#define OPERATIONS_H
int findMaximum(int x, int y);
#endif

operations.cpp:

#include "operations.h"

int findMaximum(int x, int y) {
    return (x > y) ? x : y;
}

main.cpp:

#include <iostream>
#include "operations.h"
using namespace std;

int main() {
    cout << findMaximum(25, 40) << endl;
    return 0;
}