Pattern searching is an important problem in computer science. When we do search for a string in notepad/word file or browser or database, pattern searching algorithms are used to show the search results. A typical problem statement would be-
Given a text txt[0..n-1] and a pattern pat[0..m-1], write a function search(char pat, char txt) that prints all occurrences of pat in txt. You may assume that n > m.
Input: txt = "THIS IS A TEST TEXT" pat = "TEST" Output: Pattern found at index 10 Input: txt = "AABAACAADAABAABA" pat = "AABA" Output: Pattern found at index 0 Pattern found at index 9 Pattern found at index 12
In this post, we will discuss Boyer Moore pattern searching algorithm. Like KMP and Finite Automata algorithms, Boyer Moore algorithm also preprocesses the pattern.
Boyer Moore is a combination of following two approaches.
1) Bad Character Heuristic
2) Good Suffix Heuristic
Both of the above heuristics can also be used independently to search a pattern in a text. Let us first understand how two independent approaches work together in the Boyer Moore algorithm. If we take a look at the Naive algorithm, it slides the pattern over the text one by one. KMP algorithm does preprocessing over the pattern so that the pattern can be shifted by more than one. The Boyer Moore algorithm does preprocessing for the same reason. It processes the pattern and creates different arrays for both heuristics. At every step, it slides the pattern by the max of the slides suggested by the two heuristics. So it uses best of the two heuristics at every step.
Unlike the previous pattern searching algorithms, Boyer Moore algorithm starts matching from the last character of the pattern.
In this post, we will discuss bad character heuristic, and discuss Good Suffix heuristic in the next post.
Bad Character Heuristic
The idea of bad character heuristic is simple. The character of the text which doesn’t match with the current character of the pattern is called the Bad Character. Upon mismatch, we shift the pattern until –
1) The mismatch becomes a match
2) Pattern P move past the mismatched character.
Case 1 – Mismatch become match
We will lookup the position of last occurrence of mismatching character in pattern and if mismatching character exist in pattern then we’ll shift the pattern such that it get aligned to the mismatching character in text T.
Explanation: In the above example, we got a mismatch at position 3. Here our mismatching character is “A”. Now we will search for last occurrence of “A” in pattern. We got “A” at position 1 in pattern (displayed in Blue) and this is the last occurrence of it. Now we will shift pattern 2 times so that “A” in pattern get aligned with “A” in text.
Case 2 – Pattern move past the mismatch character
We’ll lookup the position of last occurrence of mismatching character in pattern and if character does not exist we will shift pattern past the mismatching character.
Explanation: Here we have a mismatch at position 7. The mismatching character “C” does not exist in pattern before position 7 so we’ll shift pattern past to the position 7 and eventually in above example we have got a perfect match of pattern (displayed in Green). We are doing this because, “C” do not exist in pattern so at every shift before position 7 we will get mismatch and our search will be fruitless.
In the following implementation, we preprocess the pattern and store the last occurrence of every possible character in an array of size equal to alphabet size. If the character is not present at all, then it may result in a shift by m (length of pattern). Therefore, the bad character heuristic takes time in the best case.
pattern occurs at shift = 4
The Bad Character Heuristic may take time in worst case. The worst case occurs when all characters of the text and pattern are same. For example, txt = “AAAAAAAAAAAAAAAAAA” and pat = “AAAAA”.
This article is co-authored by Atul Kumar. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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