# What is the quickest sorting method to use?

The answer depends on what you mean by quickest. For most sorting problems, it just doesn’t matter how quick the sort is because it is done infrequently or other operations take significantly more time anyway. Even in cases in which sorting speed is of the essence, there is no one answer. It depends on not only the size and nature of the data, but also the likely order. No algorithm is best in all cases. There are three sorting methods in this author’s “toolbox” that are all very fast and that are useful in different situations. Those methods are quick sort, merge sort, and radix sort.  The Quick Sort The quick sort algorithm is of the “divide and conquer” type. That means it works by reducing a sorting problem into several easier sorting problems and solving each of them. A “dividing” value is chosen from the input data, and the data is partitioned into three sets: elements that belong before the dividing value, the value itself, and elements that come after the dividing value. The partitioning is performed by exchanging elements that are in the first set but belong in the third with elements that are in the third set but belong in the first Elements that are equal to the dividing element can be put in any of the three sets—the algorithm will still work properly.  The Merge Sort The merge sort is a “divide and conquer” sort as well. It works by considering the data to be sorted as a sequence of already-sorted lists (in the worst case, each list is one element long). Adjacent sorted lists are merged into larger sorted lists until there is a single sorted list containing all the elements. The merge sort is good at sorting lists and other data structures that are not in arrays, and it can be used to sort things that don’t fit into memory. It also can be implemented as a stable sort.  The Radix Sort The radix sort takes a list of integers and puts each element on a smaller list, depending on the value of its least significant byte. Then the small lists are concatenated, and the process is repeated for each more significant byte until the list is sorted. The radix sort is simpler to implement on fixed-length data such as ints.

#### agni_suresh896 Profile Answers by agni_suresh896

• Apr 19th, 2007

The algorithms which follows divide and qunquer technique provides fastest implementation.

#### kbjarnason Profile Answers by kbjarnason

• Jul 2nd, 2010

One should point out that quicksort can, on some data sets, degenerate to an O(n^2) sort - meaning the next ice age may arrive before your sort finishes.  There is, kicking around on the net somewhere, a formal proof that Quicksort is susceptible to this no matter what steps you take - other than using a different algorithm.

merge and stable merge tend to be slower than Quicksort in the general case, but they do not degenerate.

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