Stable sort

A sorting algorithm is called stable if it keeps elements with equal keys in the same relative order in the output as they were in the input.

For example, in the following input the two 4's are indistinguishable:
 * 1,4a,3,4b,2

And so the output of a stable sorting algorithm must be:
 * 1,2,3,4a,4b

Bubble sort, selection sort, merge sort, counting sort are stable sorting methods. Most implementations of quicksort are not stable sorts.

Radix sorting is an important application of stable sorting: the observation is that if we want to sort elements by a composite key, such as (year, month, day), we may as well do three stable sorting passes on separate keys day, month and year (in that order), and get the same result.