ira/tests/report/code_brief_report_20250314_135723.md

Implementing a Binary Search Tree in Python

Introduction

A Binary Search Tree (BST) is a node-based binary tree data structure that satisfies certain properties, making it a useful data structure for efficient storage and retrieval of data [1]. In this report, we will explore the key concepts and implementation details of a BST in Python, based on information from various sources [1, 2, 3].

Definition and Properties

A Binary Search Tree is defined as a data structure where each node has a comparable value, and for any given node, all elements in its left subtree are less than the node, and all elements in its right subtree are greater [1, 2]. This property ensures that the tree remains ordered, allowing for efficient search and insertion operations. The key properties of a BST are:

• The left subtree of a node contains only nodes with keys lesser than the node's key.
• The right subtree of a node contains only nodes with keys greater than the node's key.

Implementation

To implement a BST in Python, we need to create a class for the tree nodes and methods for inserting, deleting, and searching nodes while maintaining the BST properties [1]. A basic implementation would include:

• A Node class to represent individual nodes in the tree, containing left, right, and val attributes.
• An insert function to add new nodes to the tree while maintaining the BST property.
• A search function to find a given key in the BST.

The insert function recursively traverses the tree to find the correct location for the new node, while the search function uses a recursive approach to traverse the tree and find the given key [2].

Time Complexity

The time complexity of operations on a binary search tree is O(h), where h is the height of the tree [3]. In the worst-case scenario, the height can be O(n), where n is the number of nodes in the tree (when the tree becomes a linked list). However, on average, for a balanced tree, the height is O(log n), resulting in more efficient operations [3].

Example Use Case

To create a BST, we can insert nodes with unique keys using the insert function. We can then search for a specific key in the BST using the search function [2].

Conclusion

In conclusion, implementing a Binary Search Tree in Python requires a thorough understanding of the data structure's properties and implementation details. By creating a Node class and methods for insertion, deletion, and search, we can efficiently store and retrieve data in a BST. The time complexity of operations on a BST depends on the height of the tree, making it essential to maintain a balanced tree for optimal performance.

References

[1] Binary Search Tree - GeeksforGeeks. https://www.geeksforgeeks.org/binary-search-tree-data-structure/ [2] BST Implementation - GitHub. https://github.com/example/bst-implementation [3] Binary Search Tree - Example. https://example.com/algorithms/bst