String Matching Algorithms

Status: draft · Confidence: medium (0.635) · Basis: verified_sources

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## TL;DR

String matching finds occurrences of a pattern in text. Naive: O(nm). KMP (Knuth-Morris-Pratt): O(n+m) using prefix function. Boyer-Moore: O(n/m) average, O(nm) worst. Rabin-Karp: O(n+m) average using rolling hash. Real-world text search uses hybrid algorithms.

## Core Explanation

KMP precomputes failure function (longest proper prefix that is also suffix). Boyer-Moore scans pattern right-to-left, skipping characters — fastest in practice for English text. Aho-Corasick extends KMP for multiple pattern matching (used in fgrep, intrusion detection). Suffix arrays/trees enable O(m) substring search with O(n) preprocessing.

## Further Reading

- [Introduction to Algorithms (CLRS)](undefined)

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