Abstract
In this paper a well-known algorithm is studied which accomplishes the insertion of a new element into a heap. Under the assumption of uniformly distributed heaps and new elements, respectively, an explicit expression for the expected number of comparisons in terms of the binary representation of the number of elements in the heap is derived. From this, higher moments are calculated and asymptotically evaluated. Some numerical evidence is given that the mathematically derived results agree with results obtained in a simulation.
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Some results of this paper have been presented at the 1981 Conference on Information Sciences and Systems, Johns Hopkins University, Baltimore.
Sponsored in part by the Institute of Educational Informatics, Forschungs- und Entwicklungszentrum für objektivierte Lehr- und Lernverfahren, Paderborn.
(on leave to the Dept. of Mathematics and Computer Science, Clarkson College of Technology, Potsdam, N.Y. 13676, U.S.A.)
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Doberkat, EE. Inserting a new element into a heap. BIT 21, 255–269 (1981). https://doi.org/10.1007/BF01941462
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DOI: https://doi.org/10.1007/BF01941462