Interval Tree

Description

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An interval tree is a specialized type of binary search tree that's used to hold intervals and allows for efficiently querying all intervals that overlap with any given interval or point. Here's a bit more about how it works and what it's good for: Structure:

Nodes: Each node in an interval tree stores an interval (e.g., [start, end]) and a reference to the maximum endpoint of any interval stored in the subtree rooted at this node. This helps in efficient searching.
Balancing: To ensure efficient operations, the tree is generally kept balanced, often implemented as a red-black tree.

Operations:

Insertion: You can insert a new interval into the tree, updating the necessary max values.
Deletion: You can remove an interval, again adjusting the max values in nodes accordingly.
Searching: The primary feature of the interval tree is searching for all intervals that overlap with a given interval or point. This is done by exploring branches of the tree based on comparisons with interval endpoints and the max values in nodes.

Use Cases:

Computer Graphics: Used for handling overlapping regions in graphics.
Genomics: Useful in managing genomic ranges and querying overlaps.
Network Scheduling: Helps in managing tasks in time intervals and checking for conflicts.

This structure is powerful for scenarios where you need to manage and query overlapping segments efficiently, reducing the potential complexity from linear (in naive approaches) to logarithmic with respect to the number of intervals in the tree.


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