Boyer Moore Algorithm String Matching Problem Algorithm 3 cases Searching Timing.

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Presentation transcript:

Boyer Moore Algorithm String Matching Problem Algorithm 3 cases Searching Timing

Problem Find if a string is a sub-string of another Brute force approach would be O(mn)

Boyer Moore Algorithm Start matching from the end 3 cases: “Bad characters” Character appears in sub-string Common suffix

Bad Characters Given String ? ? ? ? ? X ? ? ? ? ? ? and sub-string to match a b c d ? ? ? ? ? X ? ? ? ? ? ? a b c d Next possible match: ? ? ? ? ? X ? ? ? ? ? ? a b c d

Semi-Good Character ? ? ? ? ? c ? ? ? ? ? ? a b c d Shift to next occurrence of that character: ? ? ? ? ? c ? ? ? ? ? ? a b c d Need to pre-process to get “shift values” for each character

Common Suffix Need to find shift values for every common suffix E.g.Sub-string to search for: A B C D B C (!B) C6 (!D) B C3 (!C) D B C6 (!B) C D B C6 (!A) B C D B C6

Searching Start:? ? ? ? ? ? ? ? ? ? ? ? a b c d If bad character: shift length of sub-string Else: shift max (semi-good character, good suffix) Semi-good character <= good suffix (good suffix incorporates semi-good character) If (good suffix shift > semi-good character shift) it overrides semi-good character shift (“knows” more)

Timing Usually O(n/m) because of bad character “leaps”