Penka Borukova Student at Telerik Academy

1. Boyer Moore String Search Algorithm 2. The bad character rule 3. The good suffix rule 4. The algorithm itself 2

 Finds pattern in text  Useful for very large text  Space and time are expensive!  Some definitions  S[i…n] – suffix  S[1…i] – prefix  P – Pattern  T – Text 4

 Boyer-Moore uses information gained by preprocessing P to skip as many alignments as possible  The strings are matched from the end and toward the beginning of P  The comparisons continue until either a mismatch occurs or the beginning of P is reached (which means of P is reached (which means there is a match) there is a match) 5

 When mismatch is found Bad Character Rule Good Suffix Rule Bad Character Rule Good Suffix Rule 6

 The idea of bad character rule is to shift P by more than one characters when possible  R(x): The right-most occurrence of character x in P  R(x)=0 if x does not occur in the pattern  When mismatch is found shift is found shift it over underneath it over underneath 8

Pattern -> ABBABAA R(‘A’) = 1; R(‘B’)= 2; R(x) = 0; x >=0 && x =0 && x < 256 && x != ‘A’ && x != ‘B’ 9ABCABCBBCAABBABAA ABCABCBBCAABBABAA

 Bad character rule focuses on characters  Work well in practice with large alphabets like the English alphabet  Work less well with small alphabets like DNA  Space required: O(|  ) for the number of characters in the alphabet 10

 2D table indexed first by the index of the character c in the Alphabet and second by the index i in the Pattern  Return the occurrence of c in P with the next- highest index j < i or -1 if there is no such occurrence  The proposed shift will then be i - j  Space required: O(n|  |) 11

 Good suffix rule focuses on substrings  L’(i): For each i, L’(i) is the largest position less than n such that substring P[i,…,n] matches a suffix of P[1,…, ’(i) ]  with the additional requirement that the character preceding that suffix is not equal to character P[i-1]  If there is no such a position, L’(i) =0. 13

 Example: 14ABCABCABCAAABCAACA ABCABCABCAAABCAACA

 l’(i) : the length of the largest suffix of P[i,…,n], that is also a prefix of P  If none exists, then l’(i)=0. 15ABCABCABCAACACA ABCABCABCAACACA

 Example: Indexes of P: Pattern: Pattern: l’(i) : l’(i) : L’(i) : L’(i) : CCACBCCBACC

 Precompute L’(i), l’(i) for each position in P  Precompute R(x) or R(x,i) for each character x in   Align P to T  Compare right to left  On mismatch, shift by the max possible from (extended) bad character rule and good suffix rule and return to compare 17

 O(m + n) - if the pattern does not appear in the text  O(nm) - when the pattern occurs in the text  This is the worst case 18

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 3Moore_string_search_algorithm 3Moore_string_search_algorithm 3Moore_string_search_algorithm  flensburg.de/lang/algorithmen/pattern/bmen. htm flensburg.de/lang/algorithmen/pattern/bmen. htm flensburg.de/lang/algorithmen/pattern/bmen. htm  bnotes.pdf bnotes.pdf bnotes.pdf  mlv.fr/~lecroq/string/node14.html mlv.fr/~lecroq/string/node14.html mlv.fr/~lecroq/string/node14.html 21

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