Types of Binary Trees
Various data structures in computer science aid in the organization of data in various forms. Trees are popular abstract data structures that simulate a hierarchical tree structure. A tree typically has a root value and subtrees formed by child nodes from parent nodes. Non-linear data structures are trees.
The number of child nodes that a general tree data structure can hold is not limited. This, however, is not the case with a binary tree. This article will teach you about a specific tree data structure - binary trees - and the different types of binary trees.
What exactly is the Binary Tree Data Structure?
There can be a maximum of two children for each parent in a binary tree, which is a non-linear data structure of the tree type.
Every node in a binary tree has a left and right reference in addition to the data element. The node at the top of a tree's hierarchy is known as the root node. The nodes that contain other sub-nodes are the parent nodes.
The left and right children are the two children of a parent node. Hashing, data compression, network traffic routing, setting up binary heaps, and building binary search trees are just a few of the uses for a binary tree.
Terminologies related to Binary Trees and Binary Tree Types
Binary Tree Types:
There are several types of binary trees, and each has its own set of characteristics. Each binary tree type is described in detail below:
1. Full Binary Tree
It is a specific type of binary tree with either zero or two children. It means that every node in that binary tree should have two child nodes, or the parent node should be the leaf node or the external node.
A full binary tree is a singular binary tree in which every node contains two children aside from the exterior node, to put it another way. A binary tree is not a full binary tree if it only has one child. In this instance, there are exactly as many leaf nodes as there are internal nodes, plus one. L=I+1, where I is the total number of nodes and L is the number of leaf nodes.
2. Complete Binary Tree
A type of binary tree known as a complete binary tree has all tree levels-all save the lowest-completely filled with nodes. Furthermore, every node in the bottom or final level of this binary tree should be on the left.
3. Perfect Binary Tree
When all of a binary tree's internal nodes have exactly two offspring and all of its leaf or exterior nodes are located at the same level or depth in the tree, the binary tree is said to be "perfect."
Two nodes make create a perfect binary tree of height 'h'.
4. Balanced Binary Tree
A binary tree is considered "balanced" if its height is O(logN), where N is the number of nodes. Each node's left and right subtrees should have height differences between them of no more than one in a balanced binary tree. Typical examples of data structures that can produce a balanced binary search tree include the AVL Tree and the Red-Black Tree.
5. Degenerate Binary Tree
A binary tree is said to as degenerate or pathological if each internal node has only one child. These trees are comparable to a linked list in terms of performance.
Balanced Vs Unbalanced Binary Tree
Binary tree traversals frequently encounter pointers that are null and so useless. An array has a faster access operation than a Binary Search Tree (BST). The height of the tree determines a fundamental option.
Not an easy node to delete.
The height of the tree is a fundamental option.
Time Complexity BST:
Binary Tree Traversal:
The linear data structure, such as linked list, queue, and stack, only has one method to be traversed. While there are numerous ways to move through a tree, some of which are given below:
Therefore, we will talk about the tree traversal methods stated above in this post. Let's get to the topic of tree traversal now.
This method follows to the "root left, right" principle. It indicates that the left subtree is initially traversed recursively, followed by the visit to the root node, and then the right subtree. Preorder traversal is the process of traversing the root node before (or prior to) the left and right subtrees.
Therefore, each node is visited before both of them in a preorder traversal.
Preorder traversal has a variety of uses, including:
Post order navigation
This method adheres to the "left-right root" principle. This indicates that the root node's first left subtree is explored, followed by a recursive traversal of the right subtree, and then the root node itself. It is referred to as postorder traversal because the root node is explored after (or post) the left and right subtrees.
Each node is therefore visited after both of its subtrees in a postorder traverse.
Among the uses for postorder traversal are:
This method follows to the "left root right" principle. It indicates that the root node is traversed first, followed by the first left subtree, and then the right subtree. It is known as inorder traversal because the root node is travelled between the left and right subtrees.
Each node is therefore visited between each of its subtrees throughout the inorder traversal.
Among the uses for inorder traversal are:
Application of Binary Trees:
Applications of Binary Trees in Real Time:
Binary Tree's benefits include:
Binary Tree disadvantages:
Next TopicB Tree Insertion