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Segment trees answer range queries and handle point updates in O(log n). Learn build, query, update.
Perfect introduction to segment trees with alternating OR/XOR operations. Teaches the fundamental concept of building a tree structure with point updates and querying.
Bottom-up construction
Combines segment tree concepts with greedy coloring strategy. Great for understanding how segment trees can be applied to non-traditional problems.
Classic problem demonstrating non-commutative merge operations in segment trees. Essential for understanding complex segment tree node merging.
Excellent problem combining segment trees with counting inversions and frequency queries. Teaches coordinate compression with segment trees.
Combines tree flattening (DFS ordering) with segment trees for subtree queries. Essential for learning Euler tour technique with segment trees.
Uses segment tree with GCD queries to solve a counting problem. Great for understanding how segment trees handle mathematical operations over ranges.
Requires coordinate compression and range update/query on large intervals. Perfect for learning sparse segment trees and memory optimization.
Teaches checking if segments form a tree structure using segment tree for interval overlap queries. Combines graph theory with segment trees.
Classic lazy propagation problem with circular array handling. Essential for mastering range updates with lazy propagation and wraparound ranges.
Advanced lazy propagation with range sorting queries on strings. Demonstrates segment tree with multiple counters and batch updates.
Mind-bending problem requiring adding Fibonacci sequences to ranges. Showcases advanced lazy propagation techniques with linear recurrences.
Introduces 'Segment Tree Beats' concept with modulo operations. Teaches amortized analysis for operations that don't fit standard lazy propagation.
The foundational segment tree problem. Perfect for learning basic segment tree implementation with point updates and range sum queries.
Applies segment trees to geometric problems with coordinate compression. Teaches handling large coordinate spaces with lazy propagation.
Requires implementing a dynamic set of intervals with segment tree. Great for understanding range assignment operations and interval tracking.
Classic problem demonstrating segment tree for counting inversions. Essential for interview preparation with coordinate compression.
Advanced application combining prefix sums with segment tree for range counting. Tests coordinate compression and complex counting strategies.
Modified inversion counting with condition nums[i] > 2*nums[j]. Reinforces coordinate compression and segment tree counting techniques.
Sweep line technique with segment tree for interval overlap counting. Perfect for learning dynamic interval insertions and maximum overlap queries.
Modern problem combining DP with segment tree for range maximum queries. Demonstrates how segment trees optimize DP transitions.
