# What Is Binary Search Tree and Its Operations in Data Structure?

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Heather Bennett

A binary search tree (BST) is a type of data structure that organizes data in a hierarchical order. It is widely used in computer science and is efficient for searching, inserting, and deleting elements. In a BST, each node has at most two children, referred to as the left child and the right child.

## Operations in Binary Search Tree:

### 1. Searching:

To search for an element in a binary search tree, we start at the root node and compare the Target value with the current node’s value.

If they match, we have found the element. If the Target value is less than the current node’s value, we move to its left child. Otherwise, if it is greater, we move to its right child.

This process continues recursively until we find the desired element or reach a null pointer (indicating that no such element exists in the tree).

### 2. Insertion:

Adding elements to a binary search tree involves finding their appropriate position based on their values and maintaining the BST property.

To insert an element into an empty tree, we simply create a new node and make it the root.

If the tree is not empty, we compare the value of the new element with each node starting from the root.

If it is less than or equal to a node’s value, we move to its left child. If it is greater than a node’s value, we move to its right child.

We repeat this process until reaching an empty spot where we can insert our new node while preserving the binary search tree property.

### 3. Deletion:

The deletion operation in a binary search tree involves removing a specific element while maintaining its structure.

There are three cases to consider:

• Case 1: The node to be deleted is a leaf node (has no children).

In this case, we simply remove the node from the tree.

• Case 2: The node to be deleted has one child. We replace the node with its child and update the necessary links.
• Case 3: The node to be deleted has two children. In this case, we need to find the in-order predecessor or in-order successor, replace the value of the node to be deleted with that of its predecessor or successor, and then delete the predecessor or successor node instead.

### 4. Traversal:

In order to process or print all elements in a binary search tree, we can use different traversal techniques:

• In-order traversal: In this traversal, we recursively traverse the left subtree, visit the current node, and then recursively traverse the right subtree.

This results in elements being printed in ascending order.

• Pre-order traversal: Here, we visit the current node before traversing its children. This can be useful for creating a copy of a binary search tree.
• Post-order traversal: In this traversal, we first visit both children of a node before visiting the node itself. It is commonly used in deleting nodes from a binary search tree.

## Conclusion:

A binary search tree provides an efficient way of organizing data while performing various operations like searching, insertion, deletion, and traversal. Its hierarchical structure enables faster searching compared to other data structures. By understanding and implementing the operations discussed above, you can effectively work with binary search trees in your programs.