string matching

KMP matches a pattern in linear time by precomputing a failure function that skips redundant comparisons rather than backtracking the text. The signal is what the prefix function actually holds and why the text pointer never moves backward. Here is the answer.

Rabin-Karp slides a fixed-width hash across the text so each window costs O(1) to update, which makes it ideal for matching many patterns at once. The signal is the polynomial rolling hash, modular arithmetic, and why you still verify on a hash hit. Here is the answer.