kmp algorithm

Explanation of the Knuth-Morris-Pratt (KMP) Algorithm in C++

The Knuth-Morris-Pratt (KMP) algorithm is used to search for occurrences of a "word" W within a main "text" T. It works by precomputing a "failure" function to efficiently skip ahead in the text when a mismatch occurs.

Step 1: Preprocessing the Pattern - Initialize an array L[] of the same length as the pattern, where L[i] stores the length of the longest proper prefix which is also a suffix of the pattern ending at position i.

Step 2: Building the Failure Function - Using the L[] array, build a failure function F[] to determine the number of characters to be skipped when a mismatch occurs at position i in the pattern.

Step 3: Searching for the Pattern in the Text - Compare the characters of the pattern with the text using the failure function F[] to efficiently skip ahead when a mismatch occurs.

Step 4: Handling Mismatch - When a mismatch occurs at position i in the pattern, use the failure function F[] to determine the new position to compare characters in the pattern.

Step 5: Handling Match - If a match is found, record the position in the text and continue searching for subsequent occurrences.

The KMP algorithm efficiently searches for a pattern within a text by utilizing the precomputed failure function to skip unnecessary comparisons.