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# 5 Types of Binary Tree in Data Structure Explained

Last updated:
3rd Apr, 2023
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8 Mins    View All  A binary tree is a non-linear tree data structure that contains each node with a maximum of 2 children. The binary name suggests the number 2, so any binary tree can have a left and right child.

A pointer depicts a binary tree to the uppermost node, usually known as the tree’s root. Every node in a binary tree contains data, a pointer to the left child, and a pointer to the right child. Pointers are used to implement a binary tree. The root pointer denotes the first node in the tree. In order to create a binary tree, you need to first create a node.

After being familiar with what is binary tree in data structure, you also need to know the basic operations performed on a binary tree. You can perform functions like inserting an element, removing an element, searching for an element, and traversing the binary tree.

Any binary tree in data structure is used in two different ways in computing. Firstly, they are used to access nodes depending on specific labels or values linked with each node. Secondly, they are used as data representations with a relevant branched structure.

Before going through various binary tree types, let’s first get familiar with the terminologies used in a binary tree.

Node: It holds a data value in a binary tree.

Root: Topmost node in any binary tree is called the root of a tree.

Size: It denotes the number of nodes in a binary tree.

Parent node: A node in a binary tree with a child.

Child node: It is a node that originates from a parent node moving away from the root of the binary tree.

Internal node: It is a node with at least one child in a binary tree.

Leaf node: It is a node with no child. It is alternatively an external node.

Depth of a node tree: It is calculated in the context of a particular node. It is referred to as the number of edges from a particular node to the root.

Internal path length of a tree: It refers to the sum of the levels of every internal node in a binary tree.

External path length of a tree: It is defined as the sum of the levels of every external node in a binary tree.

Height of node in a tree: It is the number of edges from a specific node to the deepest leaf node of the binary tree. The height of the root will always be more than that of other nodes in the binary tree.

Now let’s check out the details of 5 types of binary tree.

## Types of Binary Tree

### 1. Full Binary Tree

This binary tree in data structure is also known by the names -Proper binary tree and Strict binary tree. It is one of the most fundamental types of binary tree in data structure. A Full binary tree is defined as a binary tree where each node should have two or no children at all.

It is alternatively characterized as a binary tree in which every node comprises two children except the leaf nodes. The nodes in which the address of the root node is stored are called children nodes of the root. Those nodes devoid of children are called leaf nodes.

You need to travel all the nodes to check whether a tree is a binary tree. The code will return “False” if any node has one child. It will return “True” if all nodes have 0 or 2 children.

Here are the properties of a full binary tree:

• The number of leaf nodes equals the number of internal nodes + 1. For instance, if the number of internal nodes is 4, the number of leaf nodes equals 5.
• The maximum number of nodes and the number of nodes in a binary tree are equal. It is represented as 2h+1 -1.
• The minimum number of nodes in a full binary tree is 2h-1.
• The minimum height of a full binary tree is log2(n+1) – 1.
• The maximum height of a full binary tree is h = (n+1)/2.

### 2. Perfect Binary Tree

A Perfect binary tree is one of those types of binary trees wherein every node must have 0 or 2 children, and each leaf node’s level must be the same. In other words, perfect binary trees in data structure are defined as those trees where all interior nodes possess two branches and those nodes with no branches (leaf nodes) exist at the same level.

In this context, the level of a node is the distance or height from the root node. You can consider a perfect binary tree as a complete binary tree wherein the last level is also completely occupied.

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### 3. Complete Binary Tree

A Complete binary tree is one of those types of binary tree in data structure wherein all the levels of the tree are fully filled. The binary tree’s last level may or may not be completely filled. However, every node must be located at the leftmost position in the node’s last level. The nodes must be included from the left.

They are one of the essential types of binary trees because they offer the best ratio between the number of nodes and a tree’s height.

Here are the key properties of a complete binary tree:

• The maximum number of nodes is 2h+1 – 1.
• The minimum number of nodes is 2h.
• The minimum height is log2(n+1) – 1.

### 4. Balanced Binary Tree

In Balanced binary trees, a tree’s height is log2 of the total number of nodes. Suppose the tree’s height is h and the tree’s total number of nodes is n. The equation to calculate height is h = log(n). The maximum difference in height between a right sub-tree and a left sub-tree must be “1”.

The difference can have other values like 0 and -1. These types of binary trees are also called AVL trees. One of the well-known examples of balanced binary trees is the Red-Black tree.

You can implement the following code to run a balanced binary tree.

private class Node {

private int value;

private Node left;

private Node right;

}

public boolean isBalanced(Node n) {

if (balancedtreeHeight(n) > -1)

return true;

return false;

}

public int balancedtreeHeight(Node n) {

if (n == null)

return 0;

int h1 = balancedtreeHeight(n.right);

int h2 = balancedtreeHeight(n.left);

if (h1 == -1 || h2 == -1)

return -1;

if (Math.abs(h1 – h2) > 1)

return -1;

if (h1 > h2)

return h1 + 1;

return h2 + 1;

}

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### 5. Degenerate Binary Tree

A Degenerate binary tree is one of the less frequently used types of binary search tree. It is a binary tree in which each node has only one child, i.e., a left or right child. No node should have both left and right children.

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## Conclusion

It is essential to understand what is binary tree in data structure if you want to use it for various applications. Implementing different functions on binary trees can assist you in efficiently organizing and storing data.

Studying multiple types of binary trees helps you to perform operations more effectively in time complexity. The data science fundamentals, including binary tree data structure, help you start your data science journey easily. Subsequently, you can work on advanced data science projects to enhance your skills and portfolio.

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1Q1. How to search a binary search tree

A. You can follow the below steps to search a binary search tree. (i) Compare the element with the tree’s root. (ii) If the item matches, return the node’s location. (iii) If the item doesn’t match, you need to check if the item is less than the element existing on the root. If so, you need to move to the left sub-tree. But if the item is more than the element existing on the root, move to the right sub-tree. (iv) Iterate this process until a match is found. (v) If no element is found, NULL is returned.

2Q2. What are the applications of a self-balancing binary search tree?

A. A self-balancing binary search tree is used to preserve a sorted data stream. Let’s understand this with an example. Suppose a company receives online orders being placed and wants to store the live data by sorting its price in RAM. A self-balancing binary search tree executes a double-ended priority queue. You can use a Binary Heap to implement a priority queue through extractMax() or exctractMin().

3Q3. What are the benefits of binary trees?

A. The following list discusses the benefits of binary trees. (i) They perfectly implement the hierarchical approach of storing data. (ii) They represent structural relationships in the given data set. (iii) They make insertion and deletion faster than arrays and linked lists. (iv) They provide a flexible approach to data handling and movement. (v) They are used to store as many nodes as possible. (vi) They remove half sub-tree at every step in the searching process.

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