Comparison With Other Sorts
Heapsort primarily competes with quicksort, another very efficient general purpose nearly-in-place comparison-based sort algorithm.
Quicksort is typically somewhat faster due to better cache behavior and other factors, but the worst-case running time for quicksort is O(n2), which is unacceptable for large data sets and can be deliberately triggered given enough knowledge of the implementation, creating a security risk. See quicksort for a detailed discussion of this problem and possible solutions.
Thus, because of the O(n log n) upper bound on heapsort's running time and constant upper bound on its auxiliary storage, embedded systems with real-time constraints or systems concerned with security often use heapsort.
Heapsort also competes with merge sort, which has the same time bounds. Merge sort requires Ω(n) auxiliary space, but heapsort requires only a constant amount. Heapsort typically runs faster in practice on machines with small or slow data caches. On the other hand, merge sort has several advantages over heapsort:
- Like quicksort, merge sort on arrays has considerably better data cache performance, often outperforming heapsort on modern desktop computers because merge sort frequently accesses contiguous memory locations (good locality of reference); heapsort references are spread throughout the heap.
- Heapsort is not a stable sort; merge sort is stable.
- Merge sort parallelizes well and can achieve close to linear speedup with a trivial implementation; heapsort is not an obvious candidate for a parallel algorithm.
- Merge sort can be adapted to operate on linked lists with O(1) extra space. Heapsort can be adapted to operate on doubly linked lists with only O(1) extra space overhead.
- Merge sort is used in external sorting; heapsort is not. Locality of reference is the issue.
Introsort is an interesting alternative to heapsort that combines quicksort and heapsort to retain advantages of both: worst case speed of heapsort and average speed of quicksort.
Read more about this topic: Heapsort
Famous quotes containing the words comparison with, comparison and/or sorts:
“[Girls] study under the paralyzing idea that their acquirements cannot be brought into practical use. They may subserve the purposes of promoting individual domestic pleasure and social enjoyment in conversation, but what are they in comparison with the grand stimulation of independence and self- reliance, of the capability of contributing to the comfort and happiness of those whom they love as their own souls?”
—Sarah M. Grimke (1792–1873)
“But the best read naturalist who lends an entire and devout attention to truth, will see that there remains much to learn of his relation to the world, and that it is not to be learned by any addition or subtraction or other comparison of known quantities, but is arrived at by untaught sallies of the spirit, by a continual self-recovery, and by entire humility.”
—Ralph Waldo Emerson (1803–1882)
“There are all sorts of ways of murdering a person or at least his soul, and that’s something no police in the world can spot.”
—Max Frisch (1911–1991)