Unit SS, Part B: String Matching, Naive Algorithm

• O(mn) since can try entire pattern at each position in text string
• Definitions
  • i = index over text where a match might start(1<=i<=n)
  • j = index over pattern (1<=j<=m)
  • k= index over text as try to match

Example of Matching Pattern Against Text

ababaxabracabracadabratcadabrax
abracadabra
^(match)
ababaxabracabracadabratcadabrax
abracadabra
 ^(match)
ababaxabracabracadabratcadabrax
abracadabra
  ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
 abracadabra
 ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
  abracadabra
  ^(match)
ababaxabracabracadabratcadabrax
  abracadabra
   ^(match)
ababaxabracabracadabratcadabrax
  abracadabra
    ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
   abracadabra
   ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
    abracadabra
    ^(match)
ababaxabracabracadabratcadabrax
    abracadabra
     ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
     abracadabra
     ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
      abracadabra
      ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
       ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
        ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
         ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
          ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
           ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
            ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
       abracadabra
       ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
        abracadabra
        ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
         abracadabra
         ^(match)
ababaxabracabracadabratcadabrax
         abracadabra
          ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
          abracadabra
          ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
           abracadabra
           ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
            ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
             ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
              ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
               ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
                ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
                 ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
                  ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
                   ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
                    ^(match)
ababaxabracabracadabratcadabrax
           abracadabra
                     ^(match,full-match,advance-pattern-1)
ababaxabracabracadabratcadabrax
            abracadabra
            ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
             abracadabra
             ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
              abracadabra
              ^(match)
ababaxabracabracadabratcadabrax
              abracadabra
               ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
               abracadabra
               ^(no-match, advance-pattern-1)
                abracadabra
                ^(match)
ababaxabracabracadabratcadabrax
                abracadabra
                 ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
                 abracadabra
                 ^(no-match, advance-pattern-1)
ababaxabracabracadabratcadabrax
                  abracadabra
                  ^(match)
...