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 setsthe 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.