In computer science, many data structures assist in organizing and storing data in various methods. Data structures are collections of data values, their connections, and multiple functions that we can use to process data and manipulate it using particular methods. One of the different forms of data structures is the binary search tree. A binary tree data structure called Binary Search Tree is built on nodes.

In this blog of Java Homework Help, we will discuss the Binary search tree in detail. Since technical education is a prerequisite for enrollment in this course, technical students will find this material to be highly useful and educational. However, first, let’s briefly overview the tree in data structure before moving on directly to the binary search tree.

## What is a Tree?

A particular type of data structure used to represent data in a hierarchical format is a tree. It can be described as a group of nodes—collections of things or entities—that are connected to one another to create the illusion of a hierarchy. Trees are non-linear data structures because their data is not organized in a linear or sequential manner.

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**What is a Binary Search Tree?**

An extensive approach for examining nodes and their left and right branches—which are portrayed as branches of a tree—and delivering values is called a binary search tree. The BST was developed using the architecture of a fundamental binary search algorithm, allowing for quicker node lookups, insertions, and removals.

In addition, a binary search tree (BST) has the following two features:

- There can be a maximum of two children per node.
- Each node’s values are lower than those of the current node, which are lower than those of the right descendent nodes (if any).

Furthermore, each node consists of three parts:

- An arrow pointing to the left subtree
- The appropriate subtree with a pointer
- Data component

The root of a tree is the highest node in the structure. The NULL pointer represents an empty tree.

The BST is based on the concept of the binary algorithm, which enables quick node insertion and removal. Because of the way they are configured, each search, insertion, or deletion takes time proportional to the logarithm of the number of items kept in the tree. On average, each comparison enables the operations to skip around half of the tree.

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## Types of Binary Trees

There are various types of binary trees, and each has particular qualities. The following list provides an overview of the various kinds of binary trees:

### Rooted Binary Tree

A rooted binary tree is a kind of binary tree in which the root is only permitted to have degree 2. Meaning that each node can only have a maximum of two offspring. Moreover, each edge in a connected acyclic graph known as a rooted binary tree originates either directly or indirectly from the root, which is a specific node in the graph.

**Full Binary Tree**

Two children or none can be found in a full binary tree. To put it another way, every node in a full binary tree is either the external or lead node, or it has two children. As a result, every node has two children aside from the external node.

**Balanced Binary Tree**

If the following restrictions are met, a binary tree is height-balanced. This include there is no more than one height difference between the left and right subtrees. Secondly, both the right and left subtrees are in balance. Furthermore, the height of an empty tree is balanced.

**Infinite Complete Binary Tree**

An infinite full binary tree has two children at each node. The continuum’s cardinality causes the set of all nodes to be countably infinite. However, the set of all infinite pathways from the root is uncountably infinite. This is because these paths relate via an order-preserving bijection to the points of the Cantor set or to the set of positive irrational numbers.

### Degenerate Binary Tree

In a binary tree data structure, a degenerate tree is one where each parent node has just one child node connected with it. A tree of this type will function like a linked list data structure. A left-skewed tree is one in which every node in the degenerate tree has exclusively left children. The tree is referred to as being right-skewed if all of the nodes have exclusively right children.

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## Operations in Binary Search Tree

Let’s now quickly go through some of the fundamental operations you can execute on a binary search tree:

### Search Operation

The BST requirement that each left subtree must have values below the root and each right subtree must have values above the root is what drives the algorithm.

If the value is above the root, we can be certain that it is not in the left subtree and only need to search in the right subtree. Likewise, if the value is below the root, we can rest assured that it is not in the right subtree and only need to search in the left subtree.

### Insert Operation

In a binary search tree, a new element is always inserted at the leaf. In order to enter an element into a binary search tree, simply begin the search at the root node.

Look for an empty space in the left subtree if the inserting node’s value is smaller than the root. In comparison, if the value of the data element exceeds that of the node. Then look for an empty space in the appropriate subtree and put the element there.

### Deletion Operation

A node in a binary search tree can be removed in three different cases.

**Case I**

The leaf node in the first case is the node that has to be eliminated. In this situation, just remove the node from the tree.

**Case II**

The node that needs to be eliminated in the second scenario has just one child node. In this situation, take the following actions:

- Put its descendant node in its place.
- The child node should be moved from its starting position.

**Case III**

In the third case, the node that is being eliminated has two offspring. In such a situation, proceed as follows:

- Discover that node’s in-order successor.
- Substitute the in-order successor for the node.
- From its initial place, remove the in-order successor.

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## Terminologies Commonly Used in Binary Search Tree

Let’s take a closer look at each terminology used to illustrate binary tree data structures in tabular form.

Parent | A directed edge originates from precisely one other node and connects each node in a tree (aside from the root). |

Node | In a binary tree, a node denotes a point of termination. |

Root | It is the node at the top of a tree. |

Child | A node that, when removed from the root, is directly connected to another node. |

Internal node | These are child nodes that have at least one child node. |

Leaf/External node | These are Nodes that are empty. |

Height of a node | The number of edges from the node to the deepest leaf. The root’s height is equal to the height of the tree. |

**Also Read: A Guide on Sequel Programming Language For Beginners**

**Conclusion**

A sophisticated level technique called BST compares node values with the root node to carry out a variety of operations. Many different search methods are implemented using binary search trees. Furthermore, insertion and deletion operations in BST are quicker than those in arrays and linked lists. Hence, we can say it plays a major role in the world of computer science.

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**FAQs**

Q: What is a perfect binary tree?A: When all leaf nodes are at the same tree level and every internal node has a maximum of two child nodes, a binary tree is said to be perfect. |

Q: What is the Predecessor of a node in a binary search tree?A: The node that would come immediately before the node you are at can be referred to as a predecessor. Look at the largest/rightmost leaf node in the left subtree to find the predecessor of the current node. |