# Java: Arrays -- Multi-dimensional

All arrays in Java are really linear, one-dimensional arrays. However, you can easily build multi-dimensional arrays from these, and Java has features in the language to help you do this.

These examples all use two-dimensional arrays, but the same syntax and coding can easily be extended to arrays of any dimension. By convention two dimensional arrays have rows (horizontal) and columns (vertical). The first subscript selects the row (which is a one-dimensional array itself), and the second subscript selects the element in that row/array.

## Visualizing two-dimensional arrays

Assume we have an array, `a`, with three rows and four columns.

a[0][0] | a[0][1] | a[0][2] | a[0][3]
a[1][0] | a[1][1] | a[1][2] | a[1][3]
a[2][0] | a[2][1] | a[2][2] | a[2][3]

Two-dimensional arrays are usually visualized as a matrix, with rows and columns. This diagram shows the array `a` with its corresponding subscripts.
        +-----+
        |     |    +-----+-----+-----+-----+
        |a[0] | -> | [0] | [1] | [2] | [3] |
        |     |    +-----+-----+-----+-----+
        +-----+
        |     |    +-----+-----+-----+-----+
        |a[1] | -> | [0] | [1] | [2] | [3] |
        |     |    +-----+-----+-----+-----+
        +-----+
        |     |    +-----+-----+-----+-----+
        |a[2] | -> | [0] | [1] | [2] | [3] |
        |     |    +-----+-----+-----+-----+
        +-----+
| In Java two-dimensional arrays are implemented is a one-dimensional array of one-dimensional arrays -- like this.

## Declaring and Allocating a two-dimensional array

Let's declare a board for playing the game of tic-tac-toe. It will have three rows (the first subscript) and three columns (the second subscript) and contain an int in each element.

    int[][] board = new int[3][3];

## Initial values

It's possible to assign initial values to an array when you declare it in a manner very similar to one-dimensional arrays, but with an extra level of braces. The dimension sizes are computed by the compiler from the number of values.

    int[][] board = new int[][] {{0,0,0},{0,0,0},{0,0,0}};

You must assign values to an element before you use it, either with an initializer as above or assignment.

## Example -- drawing the tic-tac-toe board

It's often easiest to use two-dimensional arrays with nested `for` loops. For example, the following code draws the tic-tac-toe board in a `paint` method. It assumes that a cell is 10 pixels on a side, and that a positive number represents an X and a negative number represents a O.

    for (int row=0; row<3; row++) {
        for (int col=0; col<3; col++) {
            if (board[row][col] > 0) { // draw X
                g.drawLine(col*10, row*10  , col*10+8, row*10+8);
                g.drawLine(col*10, row*10+8, col*10+8, row*10  );
            } else if (board[row][col] < 0) { // draw O
                g.drawOval(col*10, row*10, 8, 8);
            }
        }
    }