What is the benefit for a sort algorithm to be stable?

Question

A sort is said to be stable if it maintains the relative order of elements with equal keys. I guess my question is really, what is the benefit of maintaining this relative o

Answer 1

Not all sorting is based upon the entire value. Consider a list of people. I may only want to sort them by their names, rather than all of their information. With a stable sorting algorithm, I know that if I have two people named "John Smith", then their relative order is going to be preserved.

Last     First       Phone
-----------------------------
Wilson   Peter       555-1212
Smith    John        123-4567
Smith    John        012-3456
Adams    Gabriel     533-5574

Since the two "John Smith"s are already "sorted" (they're in the order I want them), I won't want them to change positions. If I sort these items by last, then first with an unstable sorting algorithm, I could end up either with this:

Last     First       Phone
-----------------------------
Adams    Gabriel     533-5574
Smith    John        123-4567
Smith    John        012-3456
Wilson   Peter       555-1212

Which is what I want, or I could end up with this:

Last     First       Phone
-----------------------------
Adams    Gabriel     533-5574
Smith    John        012-3456
Smith    John        123-4567
Wilson   Peter       555-1212

(You see the two "John Smith"s have switched places). This is NOT what I want.

If I used a stable sorting algorithm, I would be guaranteed to get the first option, which is what I'm after.