Unit SS, Part B: String Matching, Knuth-Morris-Pratt

• Algorithm in Fig. 10.2
  • k advances in text, j in pattern
  • if pattern mismatch occurs, then use "next" position in pattern
• Explanation of "next" table example
  • mismatch pat[j] => try pat[next[j]]
  • a/0 b/1 r/1 a/0 c/2 a/0 d/2 a/0 b/1 r/1 a/0 X/5 (for X not in text)
• Explanation of "next" table example by tracing pattern pre-processing
• i=1, j=next[1]=0 **
• j==0 => i=2, j=1 (restart w. pat) pat[2]!=pat[1] => next[2]=1 ** "b" failed so backup and try "a"
• j!=0, pat[2]!=pat[1] => j=next[1]=0
• j==0 => i=3, j=1 (restart w. pat) pat[3]!=pat[1] => next[3]=1 ** "r" failed so backup and try "a"
• j!=0, pat[3]!=pat[1] => j=next[1]=0
• j==0 => i=4, j=1 (restart w. pat) pat[4]==pat[1] => next[4]=next[1]=0 ** "a" failed => advance pat
• j!=0, pat[4]==pat[1] => i=5, j=2 pat[5]!=pat[2] => next[5]=2 ** "c" failed but had "a" before so should see if text has "ab" so later would check position 2: "b"

Example of Searching for Pattern in Text

KMP ALGORITHM (never decrease k)
ababaxabracabracadabratcadabrax
abracadabra
^(match)
ababaxabracabracadabratcadabrax
abracadabra
 ^(match)
ababaxabracabracadabratcadabrax
abracadabra
  ^(no-match, next[r]=1)
ababaxabracabracadabratcadabrax
  abracadabra
  ^(match)
ababaxabracabracadabratcadabrax
  abracadabra
   ^(match)
ababaxabracabracadabratcadabrax
  abracadabra
    ^(no-match, next[r]=1)
ababaxabracabracadabratcadabrax
    abracadabra
    ^(match)
ababaxabracabracadabratcadabrax
    abracadabra
     ^(no-match, next[b]=1)
ababaxabracabracadabratcadabrax
     abracadabra
     ^(no-match, next[a]=0)
ababaxabracabracadabratcadabrax
      abracadabra
      ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
       ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
        ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
         ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
          ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
           ^(match)
ababaxabracabracadabratcadabrax
      abracadabra
            ^(no-match, next[d]=2)
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,j=resume=5)
ababaxabracabracadabratcadabrax
                  abracadabra
                      ^(no-match, next[c]=2)
ababaxabracabracadabratcadabrax
                     abracadabra
                      ^(no-match, next[b]=1)
ababaxabracabracadabratcadabrax
                      abracadabra
                      ^(no-match, next[a]=0)
ababaxabracabracadabratcadabrax
                       abracadabra
                       ^(no-match, next[a]=0)
ababaxabracabracadabratcadabrax
                        abracadabra
                        ^(match)
ababaxabracabracadabratcadabrax
                        abracadabra
                         ^(no-match, next[b]=1)
ababaxabracabracadabratcadabrax
                         abracadabra
                         ^(no-match, next[a]=0)
...