KMP Pattern SearchQUICK OVERVIEW

Created by,Arjun SKarjunsk.com

What is Patter Searching ?

o Suppose you are reading a text document.o You want to search for a word.o You click CTRL + F and search for that word. o The word processor scans the document and shows the position

of occurrence.

What exactly happens is that, word i.e. pattern is searched inside the text document.

Implementation

Naïve ApproachThe naïve approach is to check whether the pattern matches the string at every possible position in the string.

P = Pattern (word) of length mT = Text (document) of length n

Naive string matching algorithm takes time O((n-m+1)m)

Basic Idea of KMPa b c d a b c a a a b c b a b

a b c d a b c d

Text

Pattern

Text

Pattern

We can find the next position for comparison, by looking at the pattern.

a b c d a b c a a a b c b a b

a b c d a b c d

KMP (Knuth-Morris-Prattern String Matching Algorithm)

Why KMP?Best known for linear time for exact pattern matching.

How is it implemented?

o We find patterns within the search pattern.

o When a pattern comparison partially fails, we can skip to next occurrence of prefix pattern.

o In this way, we can skip trivial comparisons.

Pre-processing

Let’s say we’re matching the pattern “abababca” against the text “bacbababaabcbab”.

Here’s our prefix match table : i.e. prefix-table[i]index 0 1 2 3 4 5 6 7char a b a b a b c avalue 0 0 1 2 3 4 0 1

Matching prefix i.e. aMatching prefix i.e. ab

Matching prefix i.e. abaMatching prefix i.e. abab

No matching prefix

Pre-processing - cont.

• partial_match_length = length of the matched pattern in a step.

• prefix-table = pre-processed prefix table

• If prefix-table[ partial_match_length ] > 1we may skip ahead

partial_match_length - prefix-table[ partial_match_length – 1 ] characters.

// Used to skip, already compared prefix match in the pattern.

Searchingb a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

This is a partial match length of 1The value at prefix-table[partial_match_length - 1] (or prefix-table[0]) is 0.so we don’t get to skip ahead any.

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

In naïve approach we shift right and compare again:

Step 2

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

Step 1

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

But in KMP approach, we can directly skip Step 1

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern X X

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

This is a partial match length of 5The value at prefix-table[partial_match_length - 1] (or prefix-table[4]) is 3.

That means we get to skip ahead partial_match_length – prefix-table[partial_match_length - 1] (or 5 - table[4] = 5 - 3 = 2) characters:

We skip comparing “b”. The next comparison starts at next “ab” i.e. the prefix match.

In KMP we can directly skip comparing “ab”

This is a partial match length of 3The value at prefix-table[partial_match_length - 1] (or prefix-table[2]) is 1.

That means we get to skip ahead partial_match_length – prefix-table[partial_match_length - 1] (or 3 - table[2] = 3 - 1 = 2) characters:

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern

b a c b a b a b a a b c b a b

a b a b a b c a

Text

Pattern X X

We skip comparing “b”. The next comparison starts at next “a” i.e. the prefix match.

Complexity

O(m) - It is to compute the prefix function values. O(n) - It is to compare the pattern to the text. Total of O(n + m) run time.