我在一次面试中被问到这个问题。它们都是O(nlogn),但大多数人使用快速排序而不是归并排序。为什么呢?


当前回答

维基百科上关于快速排序的词条:

Quicksort also competes with mergesort, another recursive sort algorithm but with the benefit of worst-case Θ(nlogn) running time. Mergesort is a stable sort, unlike quicksort and heapsort, and can be easily adapted to operate on linked lists and very large lists stored on slow-to-access media such as disk storage or network attached storage. Although quicksort can be written to operate on linked lists, it will often suffer from poor pivot choices without random access. The main disadvantage of mergesort is that, when operating on arrays, it requires Θ(n) auxiliary space in the best case, whereas the variant of quicksort with in-place partitioning and tail recursion uses only Θ(logn) space. (Note that when operating on linked lists, mergesort only requires a small, constant amount of auxiliary storage.)

其他回答

当我试验这两种排序算法时,通过计算递归调用的次数, 快速排序始终比归并排序具有更少的递归调用。 这是因为快速排序有枢轴,而在下一个递归调用中不包括枢轴。这样快速排序可以比归并排序更快地达到递归基本情况。

我想补充的是,到目前为止提到的三种算法(归并排序,快速排序和堆排序)只有归并排序是稳定的。也就是说,对于那些具有相同键的值,顺序不会改变。在某些情况下,这是可取的。

但是,说实话,在实际情况下,大多数人只需要良好的平均性能和快速排序…快速=)

所有排序算法都有其起伏。有关排序算法的概述,请参阅维基百科的文章。

维基百科上关于快速排序的词条:

Quicksort also competes with mergesort, another recursive sort algorithm but with the benefit of worst-case Θ(nlogn) running time. Mergesort is a stable sort, unlike quicksort and heapsort, and can be easily adapted to operate on linked lists and very large lists stored on slow-to-access media such as disk storage or network attached storage. Although quicksort can be written to operate on linked lists, it will often suffer from poor pivot choices without random access. The main disadvantage of mergesort is that, when operating on arrays, it requires Θ(n) auxiliary space in the best case, whereas the variant of quicksort with in-place partitioning and tail recursion uses only Θ(logn) space. (Note that when operating on linked lists, mergesort only requires a small, constant amount of auxiliary storage.)

快速排序具有更好的平均情况复杂度,但在某些应用中它是错误的选择。快速排序容易受到拒绝服务攻击。如果攻击者可以选择要排序的输入,他可以很容易地构造一个时间复杂度为o(n^2)的最坏情况的集合。

归并排序的平均情况复杂性和最坏情况复杂性是相同的,因此不会遇到相同的问题。归并排序的这一特性也使它成为实时系统的最佳选择——确切地说,因为没有导致它运行得非常非常慢的病理情况。

由于这些原因,我更喜欢归并排序,而不是快速排序。

维基百科的解释是:

通常,快速排序在实践中比其他Θ(nlogn)算法要快得多,因为它的内部循环可以在大多数架构上有效地实现,并且在大多数现实数据中,可以做出设计选择,使需要二次时间的概率最小化。

快速排序

Mergesort

我认为归并排序(即Ω(n))所需要的存储量也存在快速排序实现所不具备的问题。在最坏的情况下,它们的算法时间是相同的,但归并排序需要更多的存储空间。