lenKarp

lenKarp is a string searching algorithm that finds all occurrences of a pattern string within a text string. It is a variant of the Rabin-Karp algorithm. The key idea behind lenKarp is to use hashing to quickly compare substrings of the text with the pattern.

The algorithm works by first calculating a hash value for the pattern string. Then, it calculates a hash value for the first substring of the text that has the same length as the pattern. If these hash values match, it performs a character-by-character comparison to confirm a true match. If the hash values do not match, or if the character-by-character comparison fails, the algorithm slides the window one character to the right in the text and efficiently updates the hash value of the new substring using a rolling hash function. This rolling hash allows for quick recalculation without re-hashing the entire substring.

The efficiency of lenKarp depends on the quality of the hash function used. A good hash function minimizes the number of spurious hits (hash collisions where the substrings are not actually identical). In the worst case, if there are many spurious hits, the algorithm's performance can degrade. However, with a well-chosen hash function and modulo, the average time complexity is often linear, making it a practical choice for many string searching tasks. The lenKarp algorithm is named after its developers, Donald Knuth, James H. Morris, and Vaughan Pratt, who introduced the core concepts of string matching with hashing and rolling hashes.