## 1. Overview

Creating a multidimensional *ArrayList* often comes up during programming. In many cases, there is a need to create a two-dimensional *ArrayList* or a three-dimensional *ArrayList*.

In this tutorial, we'll discuss how to create a multidimensional *ArrayList* in Java.

## 2. Two-Dimensional *ArrayList*

Suppose we want to represent a graph with 3 vertices, numbered 0 to 2. In addition, let's assume there are 3 edges in the graph (0, 1), (1, 2), and (2, 0), where a pair of vertices represents an edge.

**We can represent the edges in a 2-D ArrayList by creating and populating an ArrayList of ArrayLists.**

First, let's create a new 2-D *ArrayList*:

```
int vertexCount = 3;
ArrayList<ArrayList<Integer>> graph = new ArrayList<>(vertexCount);
```

Next, we'll initialize each element of *ArrayList* with another *ArrayList*:

```
for(int i=0; i < vertexCount; i++) {
graph.add(new ArrayList());
}
```

Finally, we can add all the edges (0, 1), (1, 2), and (2, 0), to our 2-D *ArrayList*:

```
graph.get(0).add(1);
graph.get(1).add(2);
graph.get(2).add(0);
```

Let us also assume that our graph is not a directed graph. So, we also need to add the edges (1, 0), (2, 1), and (0, 2), to our 2-D *ArrayList*:

```
graph.get(1).add(0);
graph.get(2).add(1);
graph.get(0).add(2);
```

Then, to loop through the entire graph, we can use a double for loop:

```
int vertexCount = graph.size();
for (int i = 0; i < vertexCount; i++) {
int edgeCount = graph.get(i).size();
for (int j = 0; j < edgeCount; j++) {
Integer startVertex = i;
Integer endVertex = graph.get(i).get(j);
System.out.printf("Vertex %d is connected to vertex %d%n", startVertex, endVertex);
}
}
```

## 3. Three-Dimensional *ArrayList*

In the previous section, we created a two-dimensional *ArrayList.* Following the same logic, let's create a three-dimensional *ArrayList*:

Let's assume that we want to represent a 3-D space. **So, each point in this 3-D space will be represented by three coordinates, say, X, Y, and Z.**

In addition to that, let's imagine each of those points will have a color, either Red, Green, Blue, or Yellow. Now, each point (X, Y, Z) and its color can be represented by a three-dimensional *ArrayList.*

For simplicity, let's assume that we are creating a (2 x 2 x 2) 3-D space. It will have eight points: (0, 0, 0), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, 0), and (1, 1, 1).

Let's first initialize the variables and the 3-D *ArrayList*:

```
int x_axis_length = 2;
int y_axis_length = 2;
int z_axis_length = 2;
ArrayList<ArrayList<ArrayList<String>>> space = new ArrayList<>(x_axis_length);
```

Then, let's initialize each element of *ArrayList* with *ArrayList<ArrayList<String>>*:

```
for (int i = 0; i < x_axis_length; i++) {
space.add(new ArrayList<ArrayList<String>>(y_axis_length));
for (int j = 0; j < y_axis_length; j++) {
space.get(i).add(new ArrayList<String>(z_axis_length));
}
}
```

Now, we can add colors to points in space. Let's add Red color for points (0, 0, 0) and (0, 0, 1):

```
space.get(0).get(0).add(0,"Red");
space.get(0).get(0).add(1,"Red");
```

Then, let's set Blue color for points (0, 1, 0) and (0, 1, 1):

```
space.get(0).get(1).add(0,"Blue");
space.get(0).get(1).add(1,"Blue");
```

And similarly, we can continue to populate points in the space for other colors.

Note that a point with coordinates (i, j, k), has its color information stored in the following 3-D *ArrayList* element:

```
space.get(i).get(j).get(k)
```

As we have seen in this example, the *space* variable is an *ArrayList*.** Also, each element of this ArrayList is a 2-D ArrayList** (similar to what we saw in section 2).

**Note that the index of elements in our space ArrayList represents the X coordinate, while each 2-D ArrayList, present at that index, represents the (Y, Z) coordinates.**

## 4. Conclusion

In this article, we discussed how to create a multidimensional *ArrayList* in Java. We saw how we can represent a graph using a 2-D *ArrayList*. Moreover, we also explored how to represent 3-D space coordinates using a 3-D *ArrayList*.

The first time, we used an *ArrayList* of *ArrayList,* while the second time, we used an *ArrayList* of 2-D *ArrayList*. Similarly, **to create an N-Dimensional ArrayList, we can extend the same concept.**

The full implementation of this tutorial can be found on GitHub.