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Trees in Data Structure: 8 Types of Trees Every Data Scientist Should Know About

Introduction

In the computing domain, data structures refer to the pattern of data arrangement on a disk, which enables convenient storage and display. They pertain to the field of data science, which has been predicted to be a lucrative choice of career in 2021. Based on the predictions for the next few years, large-scale deep learning models and next-gen smart devices will pave the future of this sector.

Thus, obtaining the knowledge of data structures would be essential for finding a suitable career amidst technological advancement. As per the Data Science Industry prediction of 2021, the US and India would employ approximately 50000 data scientists and 300,000 data analysts within their 2,50,000+ firms.[1]

Data structures are applied for designing the pathways for allocation, management, and retrieval of information. Data structures are particularly necessary for drafting and improving the efficiency of the overall processed data. They manage the data by grouping and organising it to effectively facilitate the information exchange.

Trees in Data Structures

‘Trees’ are a type of ADTs (Abstract Data Types), which follow a hierarchical pattern for their data allocation. Essentially, a tree is a collection of multiple nodes connected through edges. These ‘trees’ form a data structure design that resembles a tree, where the ‘root’ node leads to ‘parent’ nodes, which eventually lead to ‘children’ nodes. The connections are made with lines known as ‘edges’.

‘Leaf’ nodes are endpoints with no further children nodes originating from them. Trees in data structures play a vital role due to the non-linear nature of their arrangement. This enables faster response time during a search, along with convenience throughout the design stages.

Types of Trees in Data Structure

The various types of trees in data structures are explained in-depth below:

1. General Tree

A general tree is characterised by the lack of any specification or constraints on the number of children a node can have. Any tree with a hierarchical structure can be classified as a general tree. A node can have multiple children, and there can be any sort of combination for the orientation of the tree. The nodes can be of any degree, from 0 to n.

Following is a classic example of a general tree in the data structure, with ‘2’ at the top being the root node.

Source

2. Binary Tree

As defined by the word ‘binary’, which means two numbers, a binary tree consists of nodes that can have 2 child nodes. Any node in a binary tree can have 0, 1, or 2 nodes at the most. Binary trees in data structures are highly functional ADTs and can be further subdivided into many types. They are primarily used in data structures for two purposes: 

  1. For accessing nodes and labelling them, as observed in Binary Search Trees.
  2. For the representation of data through a bifurcating structure.

The following is a basic diagram of a binary tree in a data structure:

Source

3. Binary Search Tree

A Binary Search Tree (BST) is a unique subtype of binary trees that are arranged in a way to facilitate faster searching/lookup or addition/removal of data. A BST is defined by the representation of the nodes based on three fields: the data, its left child, and its right child. The governing factors for BST are: 

  1. Every node on the left side (left child) must hold a value that is lesser than its parent node.
  2. Every node on the right side (right child) must hold a value that is higher than its parent node.

Such an arrangement reduces the search times to half of a linear search, as found in an array. Thus, binary search trees in data structures are widely applicable for searching and sorting compared to other ADTs.

 

Source

Even though both BTs and BSTs are essentially trees in data structures, do not get confused by the similarity in their names. Find out the difference between a binary tree and a binary search tree in detail at upGrad. 

4. AVL Tree

The AVL tree derives its name from its inventors: Adelson-Velsky and Landis. The AVL tree is characterised by a self-balancing nature. The heights of two subtrees of its root nodes are restricted to less than two. When the height difference increases above 1, the child nodes are rebalanced.

AVL trees are height-balanced, and this rebalancing occurs through single or double rotations. The balancing factor is the difference between the heights of the left subtree and the right subtree, and the values are -1, 0, and 1.

5. Red Black Tree

This type resembles the AVL trees since red black trees are also height-balanced. What separates them is that it does not require more than two rotations to balance them. They contain an extra bit that defines the red or black colour of a node, which ensures that the trees are balanced during deletions and insertions. The red black colour coding is also repainted during changes but at almost no extra cost of memory.

6. Splay Tree

Another subtype of the binary search tree, the splay tree, has a unique property of performing rotational operations to adjust the recent node. The node that is accessed recently is arranged as the root node by performing a rotation. It is a balanced tree, but not a height-balanced one.

The act of ‘splaying’ is carried out after the initial binary tree search, as tree rotations are performed in a specific fashion. After every operation, the tree is rotated to balance itself, and the searched element is arranged to the top as a root node.

7. Treap

‘Treaps’ in data structures are a combination of trees and heaps. In BSTs, the left child’s value must be less than the root node, and the right child’s value must be higher. In a heap data structure, the root node has the lowest value, and its child nodes (both left and right) have larger values.

Thus, a treap holds a value in the form of a key (resembling BSTs) and a priority (like heaps). The highest priority nodes are inserted first into a binary search tree in a way that the priority numbers are independent random numbers. They maintain a dynamic set of ordered keys and allow binary searches within their keys. 

8. B-Tree

As a self-balancing kind of tree in data structures, B-Tree sorts data to allow search, sequential access, deletions, and insertions in logarithmic time. Unlike a binary tree, a B-tree allows its nodes to have more than two children. They are compatible with databases and file systems that read and write larger blocks of data.

A B-tree in data structures is used for larger storage systems, such as disks. All of the leaves carry no information, and they appear within the same level. Internal nodes of a B-tree can have a variable size of child nodes bound by a range.

These are the trees in data structures, which are implemented by programmers who design the flow of data. Learning their unique characteristics and applications is essential to your journey of becoming a data scientist. Another method to upskill yourself would be to practice through various projects that require the knowledge of trees in data structures and other forms of ADTs. 

To apply your knowledge for DS projects, the following blog links has 13 interesting data structure project ideas and topics for beginners [2021].

Conclusion

Learning about concepts like trees in a data structure can be tricky, and programming aspirants need expert guidance for educating themselves. To learn more about trees in a data structure, check out the online courses by upGrad. Executive PG Programme in Software Development – Specialisation in DevOps with DevOps by IIIT-B & upGrad can help you build your career as a programmer.

As the proficiency of data structures is integral to the process of coding, it can help the student become an expert programmer and software developer. Programmers and data scientists are bound to be in-demand for the decades to come.

We have 500 million internet users in India, generating and consuming large quantities of data, which require thousands of data scientists to be employed to meet the demand.[2] These data scientists need the right education, with relevant technological expertise, to seek employment within this sector.

An Executive PG Programme in Software Development – Specialisation in Full Stack Development, curated by upGrad & IIIT-Bangalore, can assist you in improving your profile and securing better employment opportunities as a programmer.

What kind of trees can be used for search?<br />

- A search tree is a data structure that is used to locate certain keys within a set of data. Each node's key must be larger than any keys in subtrees on the left but less than the keys in subtrees just on right for a tree to act as a search tree.
- When the tree is fairly balanced, that is, the leaves at either end are of equivalent depths, search trees have an advantage in terms of search time. There are a variety of search-tree data structures, some of which additionally allow for efficient element insertion and deletion, which actions must then preserve tree balance.
- An associative array is frequently implemented using search trees. The search tree algorithm locates a place using the key from the key–value pair, and then the application stores the complete key–value pair at that location.
- Binary search trees, B-trees, (a,b)-trees, and Ternary search trees are examples of search trees.

What are the main applications of tree data structure?

Hierarchical data, such as folder structure, organisation structure, and XML/HTML data, should be stored in trees.
1. A Binary Search Tree is a tree that allows you to quickly search, insert, and delete data that has been sorted. It also helps you to locate the item that is nearest to you.
2. Heap is a tree data structure that uses arrays and is used to construct priority queues.
3. B-Tree and B+ Tree are two types of indexing trees used in databases.
4. Compilers use the syntax tree.
5. A space partitioning tree used to organise points in K dimensional space is known as a K-D Tree.
6. Trie is a data structure that is used to build dictionaries having prefix lookup.
7. Suffix Tree is used for quickly looking for patterns in a fixed text.
8. In computer networks, routers and bridges use spanning trees as well as shortest-path trees, respectively.

What is a perfect tree?

A perfect binary tree is one in which every interior node has two offspring and every leaf has the same depth or level. The (non-incestuous) ancestry chart of a person to a particular depth is an example of a perfect binary tree, as each person has precisely two biological parents (a mother and a father).

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