Complexity Analysis of Persistent Segment Tree
Operation | Time Complexity | Space Complexity (per update) | Description |
---|---|---|---|
Build | O(n log n) | O(n log n) | Construct the initial segment tree from an array of size n |
Update | O(log n) | O(log n) | Create a new version of the tree with an updated value at a specific index |
Query | O(log n) | O(1) | Perform a range query on any version of the tree |
Persistent Segment Tree in Python
Persistent data structures are a powerful tool in computer science, enabling us to maintain and access multiple versions of a data structure over time. One such structure is the Persistent Segment Tree. Segment trees are versatile data structures that allow efficient querying and updating of array intervals. By making a segment tree persistent, we enhance its capability to maintain historical versions, which is particularly useful in competitive programming and real-time applications where rollback and point-in-time queries are needed. This article explores the concept, implementation in Python.
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