Abstract
A square is an immediately repeated nonempty string, e.g., aa, abab, abcabc. This paper presents a new O(n log n) algorithm to determine whether a string of length n has a substring which is a square. The algorithm is not as general as some previous algorithms for finding all squares [1,7,8,13], but it does have a simplicity which the others lack. Also, for a fixed alphabet of size k, the algorithm can be improved by a factor of log k (n), yielding an O(n) algorithm for determining whether a string contains a square.
Research supported by the University of Colorado Council on Research and Creative Work.
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Main, M.G., Lorentz, R.J. (1985). Linear Time Recognition of Squarefree Strings. In: Apostolico, A., Galil, Z. (eds) Combinatorial Algorithms on Words. NATO ASI Series, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82456-2_18
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DOI: https://doi.org/10.1007/978-3-642-82456-2_18
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