string matching

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

Rabin-Karp slides a fixed-width hash over the text so each window costs O(1) to update, making 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.