KMP Pattern Search
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KMP pattern searching allows efficient searching of a pattern within text by taking advantage of prefix matches. It works by pre-processing the pattern to construct a prefix table indicating the length of matching prefix for all prefixes of the pattern. During searching, when a mismatch occurs, it uses the prefix table to "skip" already compared prefix matches, avoiding repeating comparisons and allowing it to run in linear time O(n+m).
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KMP Pattern Search
- 1. KMP Pattern Search QUICK OVERVIEW Created by, Arjun SK arjunsk.com
- 2. 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.
- 4. Naïve Approach The naïve approach is to check whether the pattern matches the string at every possible position in the string. P = Pattern (word) of length m T = Text (document) of length n Naive string matching algorithm takes time O((n-m+1)m)
- 5. Basic Idea of KMP a 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
- 6. 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.
- 7. 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 7 char a b a b a b c a value 0 0 1 2 3 4 0 1 Matching prefix i.e. a Matching prefix i.e. ab Matching prefix i.e. aba Matching prefix i.e. abab No matching prefix
- 8. 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 ] > 1 we may skip ahead partial_match_length - prefix-table[ partial_match_length – 1 ] characters. // Used to skip, already compared prefix match in the pattern.
- 9. Searching 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 This is a partial match length of 1 The value at prefix-table[partial_match_length - 1] (or prefix-table[0]) is 0. so we don’t get to skip ahead any.
- 10. 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
- 11. 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
- 12. 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 5 The 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.
- 13. In KMP we can directly skip comparing “ab” This is a partial match length of 3 The 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.
- 14. 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.