Multidimensional Arrays

Arrays in C++ may have more than one dimension. Two-dimensional arrays are the most common example, but larger numbers of dimensions are possible.

Declaring a Two-Dimensional Array

When a two-dimensional array is declared, we must specify two different dimensions for the array: the number of rows, and the number of columns in each row.

As with a one-dimensional array, the number of rows and the number of columns must be specified as integers. You may use an integer literal, a symbolic constant, a variable, a function call that returns an integer, or an expression that resolves to an integer. For example:

int numbers[2][4];    // Two-dimensional array of two rows and
                      // four columns in each row.

Initializing a Two-Dimensional Array

int numbers[2][4] = {{1, 3, 5, 7}, {2, 4, 6, 8}};

Accessing an Element of a Two-Dimensional Array

To access an individual element of a two-dimensional array, we must code two subscripts - one to specify the row and the other to specify the column within the row:

cout << numbers[1][2] << endl;    // Print column 2 of row 1, the
                                  // integer value 6.

Iterating over the Elements of a Two-Dimensional Array

We usually use two nested for loops to iterate over the elements of a two-dimensional array. For example, to find the sum of all elements of the array numbers, we might code the following loops:

int sum = 0;
for (int row = 0; row < 2; row++)
{
    for (int col = 0; col < 4; col++)
    {
        sum += numbers[row][col];
    }
}

We typically loop through the rows of the array in the outer loop and the columns of a row in the inner loop, but it's certainly possible to reverse that pattern and loop through the columns of the array in the outer loop and then the rows of a column in the inner loop.

Passing Two-Dimensional Arrays to Functions

Like one dimensional arrays, two-dimensional arrays are passed to functions by address by default. This means that the function will be able to modify the elements of the original array in the calling routine. For example, the following example program:

#include <iostream>
        
using std::cout;
using std::endl;
        
void print_array(const int[][4]);
void increment_array(int[][4]);
        
int main()
{
    int numbers[2][4] = {{1, 3, 5, 7}, {2, 4, 6, 8}};

    print_array(numbers);

    increment_array(numbers);

    print_array(numbers);

    return 0;
}

void print_array(const int array[][4])
{
    for (int row = 0; row < 2; row++)
    {
        for (int col = 0; col < 4; col++)
            cout << array[row][col] << ' ';
    
        cout << endl;
    }
    
    cout << endl;
}
    
void increment_array(int array[][4])
{
    for (int row = 0; row < 2; row++)
        for (int col = 0; col < 4; col++)
            array[row][col] += 10;
}