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Linear time probabilistic pattern matching and the Rabin-Karp algorithm

Output of a multi-patterns string searching algorithmMost linear-time string searching algorithms are tricky to implement, and require heavy preprocessing of the pattern before running the search. This article presents the Rabin-Karp algorithm, a simple probabilistic string searching algorithm based on hashing and polynomial equality testing, along with a Python implementation. A streaming variant of the algorithm and a generalization to searching for multiple patterns in one pass over the input are also described, and performance aspects are discussed.

The algorithm is probabilistic in that it doesn’t always return correct results; more precisely, it returns all valid matches and (with reasonably small probability) a few incorrect matches (algorithms such as this one that tend to be over-optimistic in reporting their results are usually said to be true-biased).

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