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If I had to pick the single most important topic in software development, it would be data structures. One of the most common and easiest ones is a tree – a hierarchical data structure. In this article, let’s explore Trees in Java.

- What is a Binary Tree?
- Types of Binary Tree
- Binary Tree Implementation
- Tree Traversals
- Applications of Binary Tree

A *Tree*** **is a non-linear data structure where data objects are generally organized in terms of hierarchical relationship. The structure is non-linear in the sense that, unlike Arrays, Linked Lists, Stack and Queues, data in a tree is not organized linearly. **A binary tree is a recursive tree data structure where each node can have 2 children at most. **

Binary trees have a few interesting properties when they’re perfect:

**Property 1: The number of total nodes on each “level” doubles as you move down the tree.****Property 2: T****he number of nodes on the last level is equal to the sum of the number of nodes on all other levels, plus 1**

Each data element stored in a tree structure called a *node. *A Tree node contains the following parts:

1. Data2. Pointer to left child

3. Pointer to the right child

In Java, we can represent a tree node using class. Below is an example of a tree node with integer data.

static class Node { int value; Node left, right; Node(int value){ this.value = value; left = null; right = null; }

Now that you know what is a binary tree, let’s check out different types of binary trees.

A full binary tree is a binary tree where every node has exactly 0 or 2 children. The example of fully binary tress is:

A binary tree is perfect binary Tree if all internal nodes have two children and all leaves are at the same level. The example of perfect binary tress is:

A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. An example of a complete binary tree is:

Now that you are aware of different types of binary trees, let’s check out how to create a binary tree.

For the implementation, there’s an auxiliary *Node* class that will store *int* values and keeps a reference to each child. The first step is to find **the place where we want to add a new node in order to keep the tree sorted**. We’ll follow these rules starting from the root node:

- if the new node’s value is lower than the current node’s, go to the left child
- if the new node’s value is greater than the current node’s, go to the right child
- when the current node is
*null,*we’ve reached a leaf node, we insert the new node in that position

Now let’s see how we can implement this logic with the help of an example:

package MyPackage; public class Tree { static class Node { int value; Node left, right; Node(int value){ this.value = value; left = null; right = null; } } public void insert(Node node, int value) { if (value < node.value) { if (node.left != null) { insert(node.left, value); } else { System.out.println(" Inserted " + value + " to left of " + node.value); node.left = new Node(value); } } else if (value > node.value) { if (node.right != null) { insert(node.right, value); } else { System.out.println(" Inserted " + value + " to right of " + node.value); node.right = new Node(value); } } } public void traverseInOrder(Node node) { if (node != null) { traverseInOrder(node.left); System.out.print(" " + node.value); traverseInOrder(node.right); } } public static void main(String args[]) { Tree tree = new Tree(); Node root = new Node(5); System.out.println("Binary Tree Example"); System.out.println("Building tree with root value " + root.value); tree.insert(root, 2); tree.insert(root, 4); tree.insert(root, 8); tree.insert(root, 6); tree.insert(root, 7); tree.insert(root, 3); tree.insert(root, 9); System.out.println("Traversing tree in order"); tree.traverseLevelOrder(); } }

**Output:**

Binary Tree Example Building tree with root value 5 Inserted 2 to left of 5 Inserted 4 to right of 2 Inserted 8 to right of 5 Inserted 6 to left of 8 Inserted 7 to right of 6 Inserted 3 to left of 4 Inserted 9 to right of 8 Traversing tree in order 2 3 4 5 6 7 8 9

In this example, we have used in-order traversal to traverse the tree. The in-order traversal consists of first visiting the left sub-tree, then the root node, and finally the right sub-tree. There are more ways to traverse a tree. Let’s check them out.

Trees can be traversed in several ways: Let’s use the same tree example that we used before for each case.

Depth-first search is a type of traversal where you go as deep as possible down one path before backing up and trying a different one. There are several ways to perform a depth-first search: **in-order**, **pre-order** and **post-order**.

We already checked out in-order traversal. Let’s check out **pre-order** and **post-order **now.

**Pre-Order Traversal**

In Pre-order traversal you visit the root node first, then the left subtree, and finally the right subtree. Here’s the code.

public void traversePreOrder(Node node) { if (node != null) { System.out.print(" " + node.value); traversePreOrder(node.left); traversePreOrder(node.right); } }

**Output:**

5 2 4 3 8 6 7 9

**Post-Order Traversal**

In Post-order traversal you visit left subtree first, then the right subtree, and the root node at the end. Here’s the code.

public void traversePostOrder(Node node) { if (node != null) { traversePostOrder(node.left); traversePostOrder(node.right); System.out.print(" " + node.value); } }

**Output:**

3 4 2 7 6 9 8 5

This type of traversal visits all the nodes of a level before going to the next level. It is like throwing a stone in the center of a pond. The nodes you explore “ripple out” from the starting point. Breadth-First Search is also called level-order and visits all the levels of the tree starting from the root, and from left to right.

Applications of binary trees include:

- Used in many search applications where data is constantly entering/leaving
- As a workflow for compositing digital images for visual effects
- Used in almost every high-bandwidth router for storing router-tables
- Also used in wireless networking and memory allocation
- Used in compression algorithms and many more

This brings us to the end of this ‘Trees in Java’ article.

**Data Structures in Java | Stack, Queue, LinkedList, Tree in Data Structures | Edureka**

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