Question

I am reading about string algorithms in Cormen’s book “Introduction to Algorithms”. For Transition which is shown below.

My question: why are we doing min(m+1, q+2) and why are we incrementing m by 1 and q by 2.

Following link has back ground to above question.

http://people.scs.carleton.ca/~maheshwa/courses/5703COMP/Fall2009/StringMatching.pdf

Kindly help here with a simple example.

Algorithm Compute-Transition-Function(P, Sigma)
m = length(P);
for  q = 0 through m  do
   for each character  x  in Sigma
       k = min(m+1, q+2);
       repeat  k = k-1  // work backwards from q+1
       until  Pk 'is-suffix-of' Pqx;
       d(q, x) = k; // assign transition table
   end for;
end for;

return  d;
End algorithm.

Answer 1

• It is m + 1 because in the next repeat loop k is decreased first.
• It is q + 2 because in the repeat you start then with q + 1 so have at least 1 char.
  

  ---

The following code might have a boundary problem (q == m is missing),
but wants to make the indexing a bit clearer.

m = length(P);
for  q = 0 through m - 1 do // Loop through substrings [0, q+1]
   for each character  x  in Sigma
       k = q+1;
       // work backwards from q+1
       while not Pk 'is-suffix-of' Pqx;
       do k = k-1; end do;
       d(q, x) = k; // assign transition table
   end for;
end for;

return  d;