Adding WHERE part to the extend expression

   While considering the expression, I just consider the case without WHERE template. Then the algorithm is base on without WHERE condition. 

   However, in order to prove the correctness of the algorithm, it must be CORRECT firstly. A counter-example was given to consider the case that WHERE is used. My later tasks is to add the WHERE part to the approach.

   There are a lot of things to do before getting to write something. It's really interesting to get over and complete the algorithm step by step, little by little. Anyway, whether there is any thing to publish or not, it's not much a problem to me, the most important thing is that I could learn something new, and have a good algorithm for the problem, then I can write something, again and again.