Hi , I was trying to solve this problem , which is about finding number of **unique** palindromic substrings in string of size n . As n can be large(10^5) ,only feasible is nlogn algorithm for this problem.Can you help me ? ( I was trying to solve with suffix array but don't succeed )

The problem is just a simple application of eertree (palindromic tree).

I have known about this algorithm , but problem is one should't study every(and not so useful ) data structure for solving problems . It's better to know few and know it well.

You don't need palindromic tree. This problem existed before palindromic trees became well-known. You only need to be familiar with Manacher's algorithm and maybe not even that, if O(N log N) passes .

how?

Let's call the array that you're supposed to output V. Think about how much V[i] can differ from V[i — 1] in general.

There are my very old code for this problem, that using hashes: http://pastebin.com/SZmQFEL2