A characterization of heaps and its applications

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In this paper we present a new view of a classical data structure, the heap. We view a heap on n elements as an ordered collection of {top left corner}log2(n + 1){top right corner} substructures of sizes 2i with i in {0, ..., ⌈log2(n)⌉}. We use the new view in the design of an algorithm for splitting a heap on n elements into two heaps on k and n - k elements, respectively. The algorithm requires O(log2(n)) comparisons, improving the previous bound of O(k) comparisons for all but small values of k, i.e., for k log2(n). We also present a new and conceptually simple algorithm for merging heaps of sizes n and k into one heap of size n + k in O(log(n) * log(k)) comparisons. © 1990.




Sack, J. R., & Strothotte, T. (1990). A characterization of heaps and its applications. Information and Computation, 86(1), 69–86. https://doi.org/10.1016/0890-5401(90)90026-E

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