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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

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
1234
Advanced
Filtering by:
#competitive programming
#lazy propagation
#affine update
+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

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

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
🗂️Data StructureAdvanced

Aho-Corasick Automaton

Aho–Corasick is a trie with failure links that finds all occurrences of many patterns in a single pass over the text.

#aho-corasick#multi-pattern matching#trie+12
🗂️Data StructureAdvanced

Suffix Array - LCP Array Applications

The LCP (Longest Common Prefix) array, built alongside a suffix array, unlocks fast solutions to problems like longest repeated substring, number of distinct substrings, and longest common substring.

#suffix array#lcp array#kasai algorithm+12
🗂️Data StructureAdvanced

Euler Tour Tree

An Euler Tour Tree represents each rooted tree as a DFS open/close sequence so that every subtree is a single contiguous interval.

#euler tour tree#implicit treap#dynamic forest+11
🗂️Data StructureAdvanced

Suffix Array

A suffix array stores the starting indices of all suffixes of a string in lexicographic order.

#suffix array#lcp array#kasai algorithm+11
🗂️Data StructureAdvanced

Centroid Decomposition - Distance Queries

Centroid decomposition splits a tree into levels by repeatedly removing a centroid so that each remaining component is at most half the size.

#centroid decomposition#tree distance queries#nearest red node+12