A Variant of Heapsort with Almost Optimal Number of Comparisons

@article{Carlsson1987AVO,
  title={A Variant of Heapsort with Almost Optimal Number of Comparisons},
  author={Svante Carlsson},
  journal={Inf. Process. Lett.},
  year={1987},
  volume={24},
  pages={247-250}
}
An algorithm, which asymptotically halves the number of comparisons made by the common HEAPSORT, is presented and analysed in the worst case. The number of comparisons is shown to be (n+ 1)(log(n+ 1) + log log(n+ 1) + 1.82) + O(log n) in the worst case to sort n elements, without using any extra space. QUICKSORT, which usually is referred to as the fastest in-place sorting method, uses 1.38n log n-O(n) in the average case (see Gonnet (1984)). 
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