Concepts158
Binary Search
Binary search quickly finds targets or boundaries in sorted or monotonic data by halving the search interval each step.
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.
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.
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
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.
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.
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.
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.
Suffix Array
A suffix array stores the starting indices of all suffixes of a string in lexicographic order.
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
Centroid decomposition splits a tree around a special node (centroid) so that every remaining component has at most half the nodes.
HLD - Path Queries and Updates
Heavy-Light Decomposition (HLD) breaks a tree into a small number of vertical chains so any path (u,v) becomes O(log n) contiguous segments in an array.