Multi-Dimensional Arrays

Overview

We have looked at arrays in one dimension. As we have seen, these can be used for lots of purposes.

Sometimes, however, we want to use a multi-dimensional array which is an array that has more than one index.

Two-Dimensional Arrays

The simplest type of multi-dimensional array is a two dimensional one. In declaring a 2D array, we need to give two sizes, one for the number of rows, and one for the number of columns. For example:

int array[][] = new int[3][5];

This would create a two-dimensional grid that would look something like this:

When using the array, we specify both the row and column to be used:

array[0][2] = 9;
array[2][4] = 18;

You can also think of a multi-dimensional array as an "array of arrays".

The Indexing Formula

Multi-dimensional arrays allow us to view our data in an intuitive way, but memory is really one dimensional. The 2D array:

Would actually be stored in memory as follows:

In order to convert a two-dimensional address such as:

array[row][column]

array[row*COLUMNS + column]

Example: Times Table

The example below stores a multiplication table in a 2D array. It also demonstrates passing 2d arrays to and from functions:

class TimesTable {
    // function which creates a 2d times table of a given size
    public static int[][] createTimesTable(int size) {
        int times_table[][];
        times_table = new int[10][10];

        for (int i = 0; i < 10; i++) {
            for (int j = 0; j < 10; j++) {
                times_table[i][j] = (i + 1) * (j + 1);
            }
        }

        return times_table;
    }

    // function which prints out a 2d table of integers
    public static void printTimesTable(int table[][]) {
        for (int i = 0; i < 10; i++) {
            for (int j = 0; j < 10; j++) {
                System.out.print(table[i][j] + " ");
            }
            System.out.println();
        }
    }

    public static void main(String args[]) {
        // build the times table
        int times_table[][] = createTimesTable(10);

        // print it out
        printTimesTable(times_table);
    }
}

This example also demonstrates nested for loops which is a very common pattern when using multi-dimensional arrays.

Mazes

We can also use 2d arrays to represent mazes. Here, the start of the maze is the upper-left corner, and the finish is the bottom right of the maze.

class Maze {
    // function which returns a (hard-coded) 2d maze
    public static char[][] getMaze() {
        return new char [] []
        {
            {'-','#','#','#','#','-','-','-','-','-','-','#','#','#','#','#','#','#'},
            {'-','-','-','-','#','-','#','#','#','#','-','-','-','-','-','-','#','#'},
            {'-','#','#','-','#','-','-','-','#','#','#','#','#','#','#','-','#','#'},
            {'-','#','#','#','#','-','#','-','#','#','#','-','-','-','#','-','-','-'},
            {'-','-','-','-','-','-','#','-','#','#','#','-','#','#','#','-','#','#'},
            {'#','#','-','#','#','#','#','-','#','#','#','-','#','#','#','-','#','#'},
            {'#','#','#','#','#','#','#','-','-','-','-','-','-','-','#','-','-','-'},
            {'#','#','-','-','-','-','-','-','#','#','#','#','#','#','#','#','#','#'},
            {'-','-','-','#','#','#','#','#','#','#','-','-','-','-','#','#','#','#'},
            {'-','#','-','-','-','-','-','-','-','-','-','#','#','-','-','-','-','#'},
            {'-','#','#','#','#','#','#','#','#','#','#','#','#','#','#','#','#','#'},
            {'-','-','-','-','-','-','-','-','-','-','-','-','#','#','#','#','#','#'},
            {'#','#','#','#','#','#','#','#','#','#','#','-','-','-','-','-','-','-'},
        };
    }

    // function which prints out a 2d maze
    public static void printMaze(char maze[][]) {
        for (int i = 0; i < maze.length; i++) {
            for (int j = 0; j < maze[0].length; j++) {
                System.out.print(maze[i][j]);
            }
            System.out.print('\n');
        }
    }

    public static void main(String args[]) {
        char maze[][] = getMaze();
        printMaze(maze);
    }
}

Any kind of grid-like information can be represented with 2d arrays.

Solving a Maze

How can we develop an algorithm to solve a maze stored in a 2d array like this?

Arrays of More than Two Dimensions

We can also have arrays that have even more dimensions. A three-dimensional array can be declared as:

int array[][][] = new int[10][10][10];

This will create a three dimensional array containing 1,000 integers.

Arrays of more than two dimensions are not very commonly done, but there is no limit to the number of dimensions you could create.