The best algorithms of INSERT and DELETE operations on heap is presented, by which HEAPSORT is improved. Inserting one element into and deleting one element from a heap ofn elements spend at most ⌈log logn⌉ comparisons and ⌊logn⌋ comparisons and transfers of element in the worst cases respectively. The improved HEAPSORT spendsn logn+n log logn+O(n) comparisons and element trnasfers (not swap!) in the worst case. It may be the best HEAPSORT algorithm since the lower bound of sorting algorithm ⌈logn!⌉ ≈n logn+O(n). Especially, in element transfer, this is the best result we known so far.
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Supported by National Natural Science Foundation of China under Grant 6907330.
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Wu, J., Zhu, H. The least basic operations on heap and improved heapsort. J. of Compt. Sci. & Technol. 9, 261–266 (1994). https://doi.org/10.1007/BF02939507
- lower bound
- element transfer