Knuth-Morris-Pratt Algorithm

 Knuth-Morris-Pratt Algorithm

             Knuth Morris Pratt (KMP) is an algorithm, which checks the characters from left to right. When a pattern has a sub-pattern appears more than one in the sub-pattern, it uses that property to improve the time complexity, also for in the worst case.

           The KMP matching algorithm uses degenerating property (pattern having same sub-patterns appearing more than once in the pattern) of the pattern and improves the worst case complexity to O(n). The basic idea behind KMP’s algorithm is: whenever we detect a mismatch (after some matches), we already know some of the characters in the text of the next window. We take advantage of this information to avoid matching the characters that we know will anyway match. 

Algorithm:

findPrefix(pattern, m, prefArray)

Begin
   length := 0
   prefArray[0] := 0

   for all character index ‘i’ of pattern, do
      if pattern[i] = pattern[length], then
         increase length by 1
         prefArray[i] := length
      else
         if length ≠ 0 then
            length := prefArray[length - 1]
            decrease i by 1
         else
            prefArray[i] := 0
   done
End

kmpAlgorithm(text, pattern)

Begin
   n := size of text
   m := size of pattern
   call findPrefix(pattern, m, prefArray)

   while i < n, do
      if text[i] = pattern[j], then
         increase i and j by 1
      if j = m, then
         print the location (i-j) as there is the pattern
         j := prefArray[j-1]
      else if i < n AND pattern[j] ≠ text[i] then
         if j ≠ 0 then
            j := prefArray[j - 1]
         else
            increase i by 1
   done
End

Example:


#include<iostream>
using namespace std;

void findPrefix(string pattern, int m, int prefArray[]) {
   int length = 0;
   prefArray[0] = 0;     //first place is always 0 as no prefix

   for(int i = 1; i<m; i++) {
      if(pattern[i] == pattern[length]) {
         length++;
         prefArray[i] = length;    
      }else {
         if(length != 0) {
            length = prefArray[length - 1];
            i--;     //decrease i to avoid effect of increasing after iteration
         }else
            prefArray[i] = 0;
      }
   }
}

void kmpPattSearch(string mainString, string pattern, int *locArray, int &loc) {
   int n, m, i = 0, j = 0;
   n = mainString.size();
   m = pattern.size();
   int prefixArray[m];    //prefix array as same size of pattern
   findPrefix(pattern, m, prefixArray);
   loc = 0;

   while(i < n) {
      if(mainString[i] == pattern[j]) {
         i++; j++;
      }

      if(j == m) {
         locArray[loc] = i-j;      //item found at i-j position.
         loc++;
         j = prefixArray[j-1];    //get the prefix length from array
      }else if(i < n && pattern[j] != mainString[i]) {
         if(j != 0)
            j = prefixArray[j-1];
         else
            i++;
      }
   }
}

int main() {
   string str = "AAAABAAAAABBBAAAAB";
   string patt = "AAAB";
   int locationArray[str.size()];
   int index;
   kmpPattSearch(str, patt, locationArray, index);

   for(int i = 0; i<index; i++) {
      cout << "Pattern found at location: " <<locationArray[i] << endl;
   }
}

 

 

 

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