4 Types of Trees in Data Structure Explained: Properties & Applications

To make effective use of information, it must be stored and managed in a structured format. Numerous algorithms and software applications rely heavily on data structures. They are a useful tool for programmers who are tasked with creating efficient software. All areas of computer science, from AI to operating systems, rely on data structures. Here, you'll get some insight into Trees, one of the most often-used non-linear data structures. In this article, we'll take a look at the many varieties of trees that exist as data structures, as well as their characteristics and potential uses.

Varieties of Trees in Data Structure

In the data structure, there are several distinct kinds of trees:

Binary tree

Each element/parent node in a binary tree can only have a maximum of two children. Any given node may have zero, one, or two offspring. The two kids are commonly referred to as the "left child" and "right child."

Binary tree characteristics

• A binary tree is either empty or has a single node (the root node), two child nodes (the left and right subtrees), and a parent node (the center node). There will be one instance where each of the subtrees performs the function of a binary tree.
• The root is the highest-level node.
• The phrase "leaf node" is used to describe a node that has no children.
• Each level of i can have no more than 2i nodes.
• The length of the longest path from the tree's root to its leaves is equal to the tree's height.
• A node's depth is equal to the sum of the distances from its leaves to its center.

There are several distinct categories of binary trees.

• Perfect binary tree: A perfect binary tree would have two child nodes for each internal node. There is a uniform ground level for all leaf nodes.
• Full binary tree: To define a full binary tree, each parent or internal node must have exactly two children or none at all.
• Complete binary tree: All levels of the binary tree, except for the last one, have nodes, making it complete.
• Degenerate binary tree: A degenerate binary tree is a tree in which every internal node has exactly one child.
• Balanced binary tree: Trees on the left and right have a difference of 0 or 1.

Binary Tree Applications

• Decision Trees
• Routing Tables
• Data Compression
• Sorting

Binary Search Tree (BST)

Each leaf in a Binary Search Tree is labeled with a key and is assigned a value. This facilitates easy access for editing, removing, and looking up information. Similar to binary trees, a BST can only contain two nodes at most. It's impossible to distinguish between binary trees and binary search trees. Contrary to popular belief, nevertheless, not all binary trees can be used as search trees. Where is the distinction? The key distinction is that a BST requires the value of the left child node to be less than the parent, whereas a BST allows the value of the right child node to be greater than the parent.

Binary Search Tree Properties

• Each left subtree node's value must be smaller than that of the root node.
• Any right subtree will have nodes whose values are greater than the root node.

Binary Search Tree Applications

• Indexing and multi-level indexing
• Put in place searching algorithms
• Keep an organized flow of information

AVL Tree

In the data structure, an AVL tree is a binary tree where the balance factor of each node is checked to ensure the tree remains stable. Having equal heights for the left and right subtrees. One of three numbers (-1, 0, or 1) should be entered for the balance factor. It is only possible for there to be a one-level difference in height between the left and right sub-trees. If the discrepancy is more than 1, we will need to rotate the tree to restore its integrity.

AVL Tree Properties

• The maximum allowed difference in height between any node's two child subtrees is one.
• Balance Factor = (Height of Left Subtree – Height of Right Subtree).
• The right subtree is one level higher than the left subtree, which is represented by the Balance factor being -1.
• When the balance factor is 0, it means that the left and right subtrees are of equal height.
• When there is a 1 balance factor, the left subtree is one level above the right subtree.

AVL Tree Applications

• In-memory sorts of sets and dictionaries
• Any database-based program that has to look up data frequently

B-Tree

Each leaf node in a B tree can have multiple keys and several leaf nodes can have multiple offspring. It is a generalization of the binary search tree and a subclass of the m-way tree. Multiple keys can be stored in a single B-tree node, and each node can have multiple children. This makes it possible to access the disk faster while also decreasing its height.

B-Tree Properties

• There are no more than m children in every given node.
• Minimum of m2/n children in every node (except the root node and the leaf node).
• At least two nodes at the root level are required.
• All leaf nodes must be at the same level.

B-Tree Application

• File and database management systems
• Indexing at several levels
• To get to the information contained on the drives quickly
• To keep data in chunks

Final Words

We reach the final parts of the article, having discussed the different trees in the data structure. If you have an interest in the tech domain and are good with data and numbers, data science can help you have a good career path and Skillslash can help you achieve it with its Data Science Course In Noida with placement guarantee. Contact the support team to know more.

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