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You know the fundamentals. Now explore AVL trees, red-black trees, and other self-balancing structures.
Excellent introduction to implicit treap with split/merge and range reverse operations. Teaches implicit key concepts where positions aren't stored explicitly.
Why O(log n)?
Perfect for learning order statistics trees with dynamic updates. Requires counting inversions after swaps using treaps or policy-based data structures.
Dynamic segment trees with coordinate compression for large ranges (n ≤ 10^9). Great for learning split and merge on intervals.
Advanced 2D range query solvable with nested treaps. Teaches transforming permutation problems into geometric queries.
Practice for order statistics trees (policy-based data structures). Requires coordinate compression and range counting.
Dynamic position tracking ideal for order statistics trees. Teaches efficient element movements and position queries in O(log n).
Binary trie for maximum XOR queries. Teaches tree-based approaches to bit manipulation problems as specialized tree structures.
Classic persistent segment trees (Cartesian tree variant). Teaches handling range majority queries efficiently with small k.
Solvable with 26 segment trees or implicit treaps for range sorting. Excellent for understanding lazy propagation and range modifications.
Teaches coordinate compression with balanced trees for DP optimization. Reduces O(n²) solutions to O(n log n) using trees.
Part of SecondThread's dedicated Treap contest. Designed specifically to teach treap concepts with split/merge operations.
Greedy problem benefiting from balanced BST operations. Teaches maintaining dynamic segments with optimal decisions using ordered structures.
Classic order statistics problem solvable with AVL/Red-Black trees. Perfect for learning self-balancing BST implementations.
Requires balanced BST with coordinate compression for range counting. Teaches transforming prefix sum problems into tree-based queries.
Excellent for learning interval trees and TreeMap operations. Requires efficient interval merging and splitting.
Teaches segment trees with coordinate compression and lazy propagation. Great for handling large coordinate spaces efficiently.
Perfect introduction to TreeSet/TreeMap (Red-Black trees). Teaches efficient interval management with O(log n) insertions and merges.
Greedy problem requiring TreeSet for efficient 'next available' queries. Demonstrates practical use of balanced BST higher() operations.
Advanced segment tree with candidate tracking. Teaches building trees for complex queries where nodes maintain aggregate information.
Solvable with dynamic segment trees or balanced TreeMap. Excellent for learning lazy propagation with sparse ranges.
