Segment Tree & Fenwick Tree Patterns — DSA Pattern
The Segment Tree & Fenwick Tree Patterns pattern applies when you need range queries, point updates, and inversion counting. Its time complexity is O(log n) per query/update, O(n) build and space complexity O(n). Common variations are Fenwick Tree (BIT) - Prefix Queries / Inversions and Segment Tree - Range Sum with Point Update.
Master advanced data structures for range queries and point updates. Learn Fenwick Tree (Binary Indexed Tree) for prefix queries and Segment Tree for range sum operations.
Segment Tree & Fenwick Tree Patterns is pattern 16 of 16 in the Thita.ai DSA course. It covers range queries, point updates, and inversion counting, split into 2 subpatterns and about 2 hours of study. It is a depth pattern: reach for it once the interview-critical patterns are solid.
Subpatterns of Segment Tree & Fenwick Tree Patterns
Each subpattern below has its own theory page and problem set. They are listed in the order the course teaches them.
- Fenwick Tree (BIT) - Prefix Queries / Inversions — Master Fenwick Tree (Binary Indexed Tree) for efficient prefix sum queries and counting inversions in O(log n) time. (depth topic)
- Segment Tree - Range Sum with Point Update — Build and query segment trees for range sum queries with point updates. Essential for competitive programming and advanced interviews. (depth topic)
How to practise Segment Tree & Fenwick Tree Patterns on Thita.ai
Read the theory for a subpattern, then solve its problems in the browser editor. Your solution runs against the problem's test cases, and the AI coach gives a hint on the technique you are missing rather than the finished answer. Progress is tracked per subpattern, so the tracker shows which of the 2 Segment Tree & Fenwick Tree Patterns subpatterns you have covered. Topics covered here include segment tree, Fenwick tree, binary indexed tree, BIT, range query, point update, range sum query, inversion count.
Related DSA patterns
- Bit Manipulation Patterns — XOR tricks, counting bits, power-of-two checks, and Hamming weight.
- Design Patterns — Tries, LRU/LFU cache, and data structure design.
- All 16 DSA patterns
- The DSA patterns sheet
- Coding practice