Abstract
We describe a sorting algorithm that is optimally adaptive with respect to several important measures of presortedness. In particular, the algorithm requires O(nlog(k/n)) time on sequences with k inversions; O(n+ k log k) time on sequences X that have a longest ascending subsequence of length n−k and for which Rem(X)=k; and O(n log k) time on sequences that can be decomposed into k monotone shuffles. The algorithm makes use of an adaptive merging operation implemented using finger search trees.
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© 1992 Springer-Verlag Berlin Heidelberg
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Moffat, A., Petersson, O., Wormald, N.C. (1992). Sorting and/by merging finger trees. In: Ibaraki, T., Inagaki, Y., Iwama, K., Nishizeki, T., Yamashita, M. (eds) Algorithms and Computation. ISAAC 1992. Lecture Notes in Computer Science, vol 650. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56279-6_102
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DOI: https://doi.org/10.1007/3-540-56279-6_102
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