Segment Tree Basics and Visualization
Prerequisite Knowledge
Before reading this article, you should first study:
Summary in One Sentence
Segment trees are a derivative of the binary tree structure, designed for efficient interval queries and dynamic updates. The time complexity for interval queries is , and for updating a single element is .
The visualization panel supports the creation and usage of segment trees. The panel below demonstrates the logical structure, underlying array, and basic operations like query and update for segment trees:
Considering this is the first chapter, I do not intend to delve deeply into the implementation details of segment trees. Instead, I aim to provide an understanding of the basic principles and application scenarios of segment trees, giving you an intuitive grasp of the concept. Detailed code implementation will be covered in the data structure design section following the binary tree series exercises. It is not necessary to go in-depth here.
Let me start with an optimization idea mentioned in Selection Sort to gradually introduce the principles of segment trees and explain why this data structure is needed.
Previous Context
In the previous article on Selection Sort, I suggested an optimization using a suffixMin array. By precomputing a suffixMin array such that suffixMin[i] = min(nums[i..]), you can query the minimum value of nums[i..] in time: