suffixautomaton

The suffix automaton is a data structure in computer science that represents all substrings of a given string. It is a minimal finite automaton, meaning it has the smallest possible number of states, that accepts precisely the set of all substrings of a string. The suffix automaton is a directed acyclic graph where each edge is labeled with a single character. The states in the automaton represent sets of substrings, and paths from the initial state to any other state spell out substrings.

Constructing a suffix automaton for a string of length n can be done in linear time, O(n). This efficiency makes it a powerful tool for various string processing tasks. For instance, it can be used to count the number of distinct substrings of a string in linear time. It can also efficiently answer queries about whether a given pattern is a substring of the text, or to find all occurrences of a pattern.

The suffix automaton is closely related to other string data structures like suffix trees and suffix arrays. While a suffix tree for a string of length n has O(n) states and O(n) edges, its construction can be more complex. Suffix arrays, which are sorted arrays of all suffixes of a string, also offer efficient substring searching but typically require a slightly larger constant factor in their time complexity for some operations compared to suffix automata. The suffix automaton's strength lies in its compact representation and fast query capabilities, making it a valuable asset for algorithmic problems involving string analysis.