Decoding Segment Trees: How Binary Structures Solve Range Queries in O(log n) Time

Segment trees are essential for efficiently handling range queries and point updates on arrays—a fundamental technique in competitive programming and technical interviews. By decomposing arbitrary ranges into logarithmically-sized precomputed intervals, they achieve O(log n) complexity per operation, dramatically outperforming O(n) brute-force approaches. This guide transforms segment trees from a mysterious black box into a clear, practical tool based on systematic divide-and-conquer logic.