Counting Distinct Palindromic Substrings

Question

Given a string S, I want to count the number of distinct palindromic substrings of S. I know the basic O(n^2) approach to do so. But I want to find a better approach for strings that can be very large (of the order of 10^5).

So I want a more efficient algorithm.

Example:

Say S=xyx, then the palindromic counter must return 3 as answer, as S has three palindromic substrings: {x,xyx,y}.

My code :

int countPalindrome(char *str)
{
int i,j,k,count=0;
for(i=0;str[i];i++)
{
    k=i-1;j=i+1;  //count odd length palindromes
    while(k>=0 && str[j] && str[k]==str[j])
    {
        ++count;
        k--;j++;
    }

    k=i;j=i+1; //count even length palindrome
    while(k>=0 && str[j] && str[k]==str[j])
    {
        ++count;
        k--;j++;
    }
}
return count;
}

Clearly its O(n^2) and even does not provide distinct but all palindromes .Can someone provide a better algorithm to count Distinct Palindromic Substrings

Possible duplicate http://stackoverflow.com/questions/20473485/number-of-distinct-palindromic-substrings/20473566 — Abhishek Bansal, Dec 10 '13 at 11:53
@AbhishekBansal How to find the number of palindromic substrings in linear time using Manacher's algorithm.? — user3086701, Dec 10 '13 at 11:55
You can google for the exact algorithm. It basically builds the substrings from their centre. — Abhishek Bansal, Dec 10 '13 at 11:57
Ya. i knew.Actually suppose b is center of a palindrome substring aabaa then will it take into consideration both the substrings that are aabaa and aba? — user3086701, Dec 10 '13 at 11:59
The array maintains just only the length of longest palindromic substring of string S, centered at i — user3086701, Dec 10 '13 at 12:01
You can adapt the algorithm for your need as explained in the link I gave. — Abhishek Bansal, Dec 10 '13 at 12:02
It does not contain implementation of Manacher's Algorithm.In the link its assumed that user had implemented it by using the algorithm. That is not the case with me — user3086701, Dec 10 '13 at 12:05
@user3086701 seems like online contest problem where u need to optimize. — Vikram Bhat, Dec 10 '13 at 12:07
have a look at http://algs4.cs.princeton.edu/53substring/Manacher.java.html . Adapt it to your need as @Abhishek pointed. — Srini, Dec 10 '13 at 12:25
@srini I dont want to find longest palindromic substring in linear time but the count of palindromic substrings.How to get it from this algorithm.Please help — user3086701, Dec 10 '13 at 12:28
I don't see a way to get this below O(n^2). For each starting index, you *have* to look all the way to the ends of the string, since that could be one. — Geobits, Dec 10 '13 at 14:03

Counting Distinct Palindromic Substrings

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