A stable sorting algorithm is any sorting algorithm that preserves the relative ordering of items with equal values. For instance, consider a list of ordered pairs

Some examples of stable sorting algorithms are bubblesort and mergesort (although the stability of mergesort is dependent upon how it is implemented). Some examples of unstable sorting algorithms are heapsort and quicksort (quicksort could be made stable, but then it wouldn't be quick any more). Stability is a useful property when the total ordering relation is dependent upon initial position. Using a stable sorting algorithm means that sorting by ascending position for equal keys is built-in, and need not be implemented explicitly in the comparison operator.