AhoCorasickautomatoner

The Aho-Corasick automaton is a string searching algorithm that finds all occurrences of a finite set of keywords in a text in a single pass. It is an extension of the Knuth-Morris-Pratt algorithm and uses a finite automaton to perform the search. The automaton is built by first constructing a trie (prefix tree) of all the keywords. Then, failure links are added to the trie. These failure links point to the longest proper suffix of the current node's string that is also a prefix of another keyword.

During the search phase, the algorithm traverses the text and the automaton simultaneously. When a character in the text matches a transition in the automaton, the current state is updated. If a character does not match, the automaton follows its failure links until a match is found or it reaches the root. When a state corresponding to the end of a keyword is reached, that keyword is considered found. The automaton efficiently handles overlapping matches by continuing the search from the failure link of the matched state.

The Aho-Corasick algorithm has a time complexity of O(n + m + k), where n is the length of the text, m is the total length of all keywords, and k is the number of matches found. This makes it very efficient for searching multiple patterns in a large text. Applications include spell checkers, intrusion detection systems, and bioinformatics for pattern matching in DNA sequences.