As a data structure, the binary tree is ubiquitous in modern computing. It is found in various applications, from compilers and operating systems to artificial intelligence and big data. Despite its omnipresence, many programmers have only a rudimentary understanding of how binary trees work. This blog post is aimed at rectifying that situation by providing a complete guide to the binary tree.

We will start with an overview of what binary trees are and how they are used before delving into the internals of the data structure. Finally, we will cover some common implementations that can be performed on binary trees. By the end of this blog post, you should understand how binary trees work and be able to use them in your own applications.

## What is Binary Tree in Data Structure?

In computer science, a binary tree is a structurally complete data structure in which each node has at most two children. A binary tree usually has two nodes, called the left and right nodes, with the left being less than the right. The topmost node in the tree is called the root node. Binary trees are generally used for quick storage and retrieval of data. Because each node can only have two children, it is easy to find a particular data piece without searching through the entire structure. Additionally, binary trees can be traversed using either a recursive or iterative algorithm. As a result, a binary tree in the data structure is often used when performance is critical, such as in real-time applications.

## Terminologies Associated with Binary Trees

Here, we'll define some of the most important terms you need to know to understand binary trees.

**Binary Tree:** A tree is a data structure that consists of nodes connected by edges. A binary tree is a type of tree in which each node has at most two child nodes, often referred to as left and right child nodes.**Root Node:** The root node is the topmost node in a tree. It doesn't have a parent node since it's at the top of the tree.**Child Node:** A child node is any node with a parent node. Each node can have at most two child nodes in a binary tree.**Sibling Nodes:** Sibling nodes are nodes that have the same parent node. In other words, they're siblings.**Ancestor Nodes:** Ancestor nodes are defined in terms of child nodes and parent nodes. An ancestor node is any node that is higher up in the tree than a given child node. For example, if Node Cis a child node of Node B, then Node B is an ancestor node of Node C.**Descendant Nodes: **Descendant nodes are also defined in terms of child nodes and parent nodes. A descendant node is any node that is lower down in the tree than a given parent node. So, continuing with our previous example, if Node Bis is a parent node of Node C, then Node Cis a descendant node of Node B.**Leaf Nodes:** Leaf nodes are nodes that don't have any children. In other words, they're at the bottom of the tree!**Internal Nodes:** Internal nodes are all nodes that are not leaf nodes. Therefore, they're all non-leaf nodes that have one or more child nodes.**Height:** The height of a particular node is the number of edges on the longest path from that node to a leaf node. The tree's height is defined as the height of the root node.**Depth:** The depth of a node refers to its level in the tree and is equal to the number of edges on the path from the root node to that particular node counted using only downward edges.

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## Components of Binary Tree

Source

A binary tree is a data structure that allows two nodes to be linked together by a path from the root to the leftmost child and from the leftmost child to the rightmost child. The different components of a binary tree are the root, the left subtree, and the right subtree.

### 1. The Root

The root of a binary tree is the topmost node in the tree. The root node has no parents and is the ancestor of all other nodes in the tree. The root node contains data and links to its left and right children.

### 2. The Left Subtree

The left subtree is a binary tree that consists of all nodes to the left of the root node. The left subtree's root node is the left child of the original tree's root node. All nodes in the left subtree are less than or equal to the original tree's root node.

### 3. The Right Subtree

The right subtree is a binary tree that consists of all nodes to the right of the root node. The right subtree's root node is the right child of the original tree's root node. All nodes in this subtree are greater than or equal to the original tree's root node.

If you're working with binary trees, it's important to understand the different components that make up this data structure. By understanding the root, left subtree, and right subtree, you'll be well on your way to becoming a binary tree expert.

## Properties of Binary Tree in Data Structure

Here are some key properties of binary trees in the data structure.

**Efficient Insertion and Deletion:** One of the advantages of using a binary tree is that insertion and deletion can be done quite efficiently. If the correct position for insertion or deletion is known, then it can be done in O(log n) time. This is because you only need to traverse down the tree to the correct position.**Efficient Searching:** Another feature of using a binary tree is that searching can be done quite efficiently as well. If the value searched for is known, it can be found in O(log n) time. This is because you only need to traverse down the tree until you find the correct value.**Data Structure:** A binary tree is also a very powerful data structure. It can be used to store data in an efficient way. For example, a binary tree can be used to store information about a family tree. Each person in the family would be represented by a node in the tree, and the relations between them would be represented by the edges between the nodes.

## Types of Binary Tree

There are several different types of binary trees in the data structure, each with its own characteristics. The most common types are full binary tree, perfect binary tree, complete binary tree, degenerate binary tree, & balanced binary tree in the data structure. Let's take a closer look at each one.

### 1. Full/Proper/Strict Binary Trees

A full or proper binary tree is a tree in which every node has either zero or two child nodes. There are exactly two child nodes for each internal node in a strict binary tree.

### 2. Complete Binary Trees

A complete binary tree is a tree where all levels are fully filled, with the exception of the last level, and all nodes on the last level are as far left as possible.

### 3. Perfect Binary Trees

A perfect binary tree is a special type of complete binary tree where every internal node has exactly two children & all leaves are at the same level.

### 4. Degenerate Binary Tree

A degenerate or pathologic binary tree is one where there exists only one path from the root to any leaf node. In other words, it is a tree in which each node has only one child node.

### 5. Balanced Binary Trees

A balanced tree in the data structure is one in which the height of the right & left subtrees differ by at most 1 level and in which the left & right subtrees are also evenly balanced. The height of a balanced tree with n nodes is O (logn).

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## Implementation of Binary Trees with Examples

A binary tree refers to a data structure that allows the two nodes to be easily linked together by a path from the root to the leftmost child, known as the left path, & from the leftmost child to the rightmost child, known as the right path. The path is called a path because it can be followed from one node to another. A binary tree is thus defined as a finite set of nodes with the following properties:

- The data in each node is greater than all data in the left subtree and less than all data in the right subtree.
- The left and right subtrees are themselves binary trees.

Here we are now with the binary tree example in the data structure. A binary tree can be represented by an array in which the elements are stored in level order, i.e., the root is at index 0, the left child of the root is at index 1, the right child of the root is at index 2, and so on. For example, an array [3, 9, 20, null, null, 15, 7] represents the following binary tree:

3

/ \

920

/ \

15 7

An empty binary tree is represented by an empty array [ ].

A full binary tree is a binary tree in which each node has exactly two children. A perfect binary tree is a full binary tree in which all leaves are at the same level.

3 Perfect Binary Tree Full Binary Tree Complete Binary Tree

/ \ 3 5 11 23 15 31 27 19 16 8 4 2 1 25 2930 26 24 28 20 18 17 14 12 10 9 8 6 4 2 1

## What are the Applications of Binary Trees?

There is a multitude of applications of binary trees in computer science. They are often used to store data in a database, allowing for efficient insertion and deletion of data. Additionally, binary trees can be used to efficiently search through large amounts of data. For example, if you were looking for a specific word in a dictionary, you could use a binary tree to find where that word is located quickly.

Binary trees are also used in operating systems to manage memory allocation. When a new process is created, it is stored in a memory block called a "page". Each page has a certain amount of memory allocated to it. When the operating system needs to allocate more memory to a process, it will first check if any available pages are large enough to satisfy the request. The operating system will create a new page and allocate the memory if there are no available pages. This process is much more efficient than searching through all of the memory for an available block of sufficient size; using a binary tree helps reduce search time from O(n) (linear search) to O(log n) (binary search).

## Benefits of a Binary Tree in Data Structure

There are many reasons why you might want to use a binary tree over other data structures like arrays or linked lists. Some advantages of binary trees in data structure include the following:

**Faster search time:** Since each node in a binary tree can be quickly accessed by its unique key, search times are much faster than with other data structures. For example, if you wanted to find a specific record in an array, you would have to scan through the entire array until you found the desired record. With a binary tree, you can start at the root node and quickly traverse the tree until you find the desired record.**Increased flexibility:** Unlike an array, a binary tree is not confined to being stored in sequential memory locations. This means that binary trees can be easily implemented on systems with limited memory resources.**Efficient insertion and deletion:** Insertion and deletion operations can be performed on a binary tree in O(log n) time, where n is the number of nodes in the tree. This is much faster than the O(n) time required for these operations on an array.**Reduced storage requirements:** Since each node only has two child pointers, a binary tree requires less storage space than other data structures such as an array or linked list.

## Disadvantages of Binary Trees

Despite their advantages, there are also some disadvantages associated with using binary trees:

**Difficult to implement: **Since each node can only have two children, it can be difficult to correctly implement all the required functionality for a binary tree (e.g., inserting and deleting nodes).**Limited to balancing algorithms:** A binary tree can become unbalanced if left unchecked, resulting in decreased performance. Balancing algorithms (such as AVL trees and red-black trees) can be used to keep a binary tree balanced, but these algorithms add complexity to the implementation.

## Conclusion

A tree data structure is one of the most powerful tools that you can use to store and organize data. A binary tree is a particularly efficient type of tree data structure, which makes it an important tool for computer science applications. This guide should have given you a good understanding of what a binary tree is, how it works, and how you can use it to store and retrieve data. Moreover, you should also look to widen your knowledge with a quality Java Certification Course. With this knowledge in hand, you should be able to start using binary trees in your projects.