THE KNUTH - MORRIS-PRATT ALGOTITHM - AOA MODULES 6

Knuth-Morris-Pratt (KMP) Algorithm

Knuth-Morris-Pratt (KMP) Algorithm

Definition

The Knuth-Morris-Pratt (KMP) algorithm is a pattern matching algorithm that improves upon the brute-force method by preprocessing the pattern to determine the longest prefix which is also a suffix. This allows skipping unnecessary comparisons.

Steps

Step 1: Construct the prefix table (LPS Array) for the pattern.
Step 2: Start the matching process by comparing the text and pattern characters.
Step 3: If a mismatch occurs, use the LPS array to determine the next shift.
Step 4: Continue until the entire text is scanned.
Step 5: If q reaches m (length of pattern), a match is found.

Example

Let's consider the following example:

Text (T): abcabababcbc

Pattern (P): bababcb

Prefix Table (LPS)

q1234567
P[q]bababcb
Prefix0012311

Matching Process

i = 1, q = 0 → Compare T[1] = a with P[1] = b (Mismatch) i = 2, q = 0 → Compare T[2] = b with P[1] = b (Match) i = 3, q = 1 → Compare T[3] = c with P[2] = a (Mismatch) i = 5, q = 0 → Compare T[5] = b with P[1] = b (Match) i = 6, q = 1 → Compare T[6] = a with P[2] = a (Match) i = 7, q = 2 → Compare T[7] = b with P[3] = b (Match) i = 8, q = 3 → Compare T[8] = a with P[4] = a (Match) i = 9, q = 4 → Compare T[9] = b with P[5] = b (Match) i = 10, q = 5 → Compare T[10] = c with P[6] = c (Match) i = 11, q = 6 → Compare T[11] = b with P[7] = b (Match) Pattern found at shift 4

Conclusion

The KMP algorithm efficiently finds pattern matches in a text with a time complexity of O(n + m), where n is the length of the text and m is the length of the pattern.

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