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Binary search tree

Last updated on Friday, April 26, 2024.

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A binary search tree is a data structure in computer science used to store and organize data efficiently. It consists of nodes with at most two children, where the left child node contains a value smaller than the parent node, and the right child node contains a value larger than the parent node. This structure allows for fast search, insertion, and deletion operations on the data stored in the tree.

The Binary Search Tree: A Fundamental Data Structure in Computer Science

A binary search tree, often abbreviated as BST, is a fundamental data structure in computer science that facilitates efficient searching, insertion, and deletion of elements.

Structure of a Binary Search Tree

In a binary search tree, each node has at most two child nodes, referred to as the left child and the right child. The key property of a BST is that for every node n, all elements in the left subtree of n are less than the value of n, and all elements in the right subtree of n are greater than the value of n.

Operations on a Binary Search Tree

One of the key advantages of a binary search tree is its efficient operations:

Search: Searching for a specific element in a BST is done by comparing the element with the value of the current node and recursively traversing either the left or right subtree until the element is found or determined to be absent.
Insertion: To insert a new element into a BST, the tree is traversed similarly to searching, but when the element is not found, it is added as a leaf node in the appropriate position to maintain the tree's ordering.
Deletion: Deleting an element from a BST involves three main cases:
1. If the node to be deleted has no children, it is simply removed.
2. If the node has one child, the child is moved up to take the place of the deleted node.
3. If the node has two children, the node's successor (the smallest node in the right subtree) is moved to its position.

Applications of Binary Search Trees

Binary search trees have various applications in computer science and software development, including:

Implementing efficient search algorithms like binary search.
Dictionary implementations, where keys are stored in a BST for quick retrieval.
Compiler implementations to store identifiers for quick access.
Efficient database operations like indexing and searching.

Overall, the binary search tree is a versatile and powerful data structure that forms the basis for many essential algorithms and applications in the field of computer science.

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