Pattern Searching | Set 7 (Boyer Moore Algorithm – Bad Character Heuristic)

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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.

Examples:

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
pattern-searching

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 preporcesses the pattern and creates different arrays for both heuristics. At every step, it slides the pattern by 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 pattern is called the Bad Character. Upon mismatch we shift the pattern until –
1) The mismatch become a match
2) Pattern P move past the mismatch character.

Case 1 – Mismatch become match
We will lookup the position of last occurence 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.

case 1

case 1


Explanation: In the above example, we got a mismatch at position 3. Here our mismatching character is “A”. Now we will search for last occurence of “A” in pattern. We got “A” at position 1 in pattern (displayed in Blue) and this is the last occurence 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 occurence of mismatching character in pattern and if character does not exist we will shift pattern past the mismatching character.

case2

case2


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 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 O(n/m) time in the best case.

C

/* Program for Bad Character Heuristic of Boyer 
   Moore String Matching Algorithm */
# include <limits.h>
# include <string.h>
# include <stdio.h>

# define NO_OF_CHARS 256

// A utility function to get maximum of two integers
int max (int a, int b) { return (a > b)? a: b; }

// The preprocessing function for Boyer Moore's
// bad character heuristic
void badCharHeuristic( char *str, int size, 
                        int badchar[NO_OF_CHARS])
{
    int i;

    // Initialize all occurrences as -1
    for (i = 0; i < NO_OF_CHARS; i++)
         badchar[i] = -1;

    // Fill the actual value of last occurrence 
    // of a character
    for (i = 0; i < size; i++)
         badchar[(int) str[i]] = i;
}

/* A pattern searching function that uses Bad
   Character Heuristic of Boyer Moore Algorithm */
void search( char *txt,  char *pat)
{
    int m = strlen(pat);
    int n = strlen(txt);

    int badchar[NO_OF_CHARS];

    /* Fill the bad character array by calling 
       the preprocessing function badCharHeuristic() 
       for given pattern */
    badCharHeuristic(pat, m, badchar);

    int s = 0;  // s is shift of the pattern with 
                // respect to text
    while(s <= (n - m))
    {
        int j = m-1;

        /* Keep reducing index j of pattern while 
           characters of pattern and text are 
           matching at this shift s */
        while(j >= 0 && pat[j] == txt[s+j])
            j--;

        /* If the pattern is present at current
           shift, then index j will become -1 after
           the above loop */
        if (j < 0)
        {
            printf("\n pattern occurs at shift = %d", s);

            /* Shift the pattern so that the next 
               character in text aligns with the last 
               occurrence of it in pattern.
               The condition s+m < n is necessary for 
               the case when pattern occurs at the end 
               of text */
            s += (s+m < n)? m-badchar[txt[s+m]] : 1;

        }

        else
            /* Shift the pattern so that the bad character
               in text aligns with the last occurrence of
               it in pattern. The max function is used to
               make sure that we get a positive shift. 
               We may get a negative shift if the last 
               occurrence  of bad character in pattern
               is on the right side of the current 
               character. */
            s += max(1, j - badchar[txt[s+j]]);
    }
}

/* Driver program to test above funtion */
int main()
{
    char txt[] = "ABAAABCD";
    char pat[] = "ABC";
    search(txt, pat);
    return 0;
}

Python

# Python3 Program for Bad Character Heuristic
# of Boyer Moore String Matching Algorithm 

NO_OF_CHARS = 256

def badCharHeuristic(string, size):
    '''
    The preprocessing function for
    Boyer Moore's bad character heuristic
    '''

    # Initialize all occurence as -1
    badChar = [-1]*NO_OF_CHARS

    # Fill the actual value of last occurence
    for i in range(size):
        badChar[ord(string[i])] = i;

    # retun initialized list
    return badChar

def search(txt, pat):
    '''
    A pattern searching function that uses Bad Character
    Heuristic of Boyer Moore Algorithm
    '''
    m = len(pat)
    n = len(txt)

    # create the bad character list by calling 
    # the preprocessing function badCharHeuristic()
    # for given pattern
    badChar = badCharHeuristic(pat, m) 

    # s is shift of the pattern with respect to text
    s = 0
    while(s <= n-m):
        j = m-1

        # Keep reducing index j of pattern while 
        # characters of pattern and text are matching
        # at this shift s
        while j>=0 and pat[j] == txt[s+j]:
            j -= 1

        # If the pattern is present at current shift, 
        # then index j will become -1 after the above loop
        if j<0:
            print("Pattern occur at shift = {}".format(s))

            '''    
                Shift the pattern so that the next character in text
                      aligns with the last occurrence of it in pattern.
                The condition s+m < n is necessary for the case when
                   pattern occurs at the end of text
               '''
            s += (m-badChar[ord(txt[s+m])] if s+m<n else 1)
        else:
            '''
               Shift the pattern so that the bad character in text
               aligns with the last occurrence of it in pattern. The
               max function is used to make sure that we get a positive
               shift. We may get a negative shift if the last occurrence
               of bad character in pattern is on the right side of the
               current character.
            '''
            s += max(1, j-badChar[ord(txt[s+j])])


# Driver program to test above funtion
def main():
    txt = "ABAAABCD"
    pat = "ABC"
    search(txt, pat)

if __name__ == '__main__':
    main()

# This code is contributed by Atul Kumar
# (www.facebook.com/atul.kr.007)


Output:
 pattern occurs at shift = 4

The Bad Character Heuristic may take O(mn) 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”.

Boyer Moore Algorithm | Good Suffix heuristic

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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