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🗂️Data StructureAdvanced

Sqrt Tree

A sqrt tree is a layered block-decomposition data structure that answers range queries in O(1) time after O(n \log \log n) preprocessing.

#sqrt tree#range query#associative operation+11
🗂️Data StructureAdvanced

Dominator Tree

A dominator tree summarizes “must-pass” relationships in a directed graph from a chosen root r: u dominates v if every path from r to v goes through u.

#dominator tree
12345
Advanced
#lengauer tarjan
#semidominator
+10
🗂️Data StructureAdvanced

Chtholly Tree (ODT - Old Driver Tree)

Chtholly Tree (ODT) stores an array as a set of non-overlapping value-constant intervals and updates by cutting and replacing whole ranges.

#odt#chtholly tree#range assign+9
🗂️Data StructureAdvanced

Segment Tree with Range Affine Transformation

A segment tree with lazy propagation can support range updates of the form x → a·x + b (affine transformations) and range-sum queries in O(log n) per operation.

#segment tree#lazy propagation#affine update+12
🗂️Data StructureAdvanced

Persistent DSU (Fully Persistent Union-Find)

A persistent DSU (Union-Find) keeps all historical versions so you can query connectivity at any past version and even branch new futures from old states.

#persistent dsu#fully persistent union-find#union by rank+12
🗂️Data StructureAdvanced

Top Tree

Top trees are dynamic tree data structures that represent a forest as a hierarchy of clusters, allowing O(log n) amortized time for link, cut, path queries/updates, and many subtree queries.

#top tree#dynamic tree#link cut+12
🗂️Data StructureAdvanced

Kinetic Tournament Tree

A kinetic tournament tree maintains the minimum (or maximum) of moving values whose pairwise order can change over time.

#kinetic data structure#tournament tree#certificate+12
🗂️Data StructureAdvanced

Aho-Corasick - DP Applications

Aho–Corasick (AC) turns a set of forbidden patterns into a finite automaton that lets you process or generate strings while tracking whether any pattern appears.

#aho-corasick#automaton dp#forbidden substrings+12
🗂️Data StructureAdvanced

Li Chao Tree

A Li Chao tree maintains a set of lines y = m x + b and answers minimum (or maximum) value queries at a given x in O(log C) time, where C is the numeric range of x.

#li chao tree#dynamic convex hull#segment tree lines+12
🗂️Data StructureAdvanced

Palindromic Tree (Eertree)

A Palindromic Tree (Eertree) stores every distinct palindromic substring of a string as a node and can be built online in linear time.

#palindromic tree#eertree#palindromic substrings+12
🗂️Data StructureAdvanced

Suffix Automaton - Advanced Usage

A suffix automaton (SAM) is a compact DFA that captures all distinct substrings of a string and supports many advanced queries in linear time.

#suffix automaton#endpos#suffix link+12
🗂️Data StructureAdvanced

Suffix Automaton

A suffix automaton (SAM) is the minimal deterministic finite automaton that recognizes all substrings of a string, built online in O(n) time and space.

#suffix automaton#endpos equivalence#suffix link+12