Recursion greatly minimizes the effort sometimes, like here in this question (on topcoder):- Thepalindrome
instead of any DP (although on the statistics page it was written to be dp ) a simple recursive approach can be applied :- algorithm/code

//header files
//class declarations
int find(string s) 
{
 int ret=rec(s);
 return (s.size()-ret)+s.size();
}
int rec(string s)
{
 string k=s;
 std::reverse(k.begin(),k.end());
 if(k==s)
 {
  return s.size();
 }
 else
 {
  s.erase(s.begin());
  return rec(s);
 }
}
and about the endsem  of discrete maths i am not sure :P anyways gotta sleep now  :)