 String-searching algorithm

A string-searching algorithm locates occurrences of a pattern in a text, typically requiring a contiguous substring match. For text ababa and pattern aba, zero-based matches start at zero and two; overlaps count unless excluded by the specification. The direct algorithm compares the pattern at each start and can require $O(nm)$ character comparisons. The Knuth-Morris-Pratt algorithm reuses prefix information for linear total scanning work. State the alphabet, case handling and empty-pattern convention: matching bytes, Unicode code points and user-perceived characters can describe different tasks.