Abstract
We propose a data structure and an online algorithm to report the number of distinct palindromes in any substring of an input string. Assume that the string S of length n arrives symbol-by-symbol and every symbol is followed by zero or more queries of the form “report the number of distinct palindromes in S[i..j]”. We use \(O(n\log n)\) total time to process the string plus \(O(\log n)\) time per query. The required space is \(O(n\log n)\) in general and O(n) in a natural particular case. As a simple application, we describe an algorithm reporting all palindromic rich substrings of an input string in \(O(n\log n)\) time and O(n) space.
This work was Partially supported by the grant 16-01-00795 of the Russian Foundation of Basic Research.
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Notes
- 1.
Unfortunately, there is one more data structure with this name, see, e.g., Wikipedia.
- 2.
By Fact 1, only \(l_1\) can be undefined; if so, we assume that \(\mathsf{add}(l_1,-1)\) is ignored.
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Rubinchik, M., Shur, A.M. (2017). Counting Palindromes in Substrings. In: Fici, G., Sciortino, M., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2017. Lecture Notes in Computer Science(), vol 10508. Springer, Cham. https://doi.org/10.1007/978-3-319-67428-5_25
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