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Can someone explain what "stable" and "unstable" mean in relation to various sorting algorithms> How can one determine whether an algorithm is stable or not, and what applications do unstable sorting algorithms usually have (since they are unstable)?
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Stable sorting algorithms preserve the relative order of equal elements, while unstable sorting algorithms don't. In other words, stable sorting maintains the position of two equals elements relative to one another.
A sorting algorithm is stable if it preserves the order of duplicate keys. OK, fine, but why should this be important? Well, the question of "stability" in a sorting algorithm arises when we wish to sort the same data more than once according to different keys. Sometimes data items have multiple keys.
If a sorting algorithm is said to be "unstable", this means that for any items that rank the same, the order of the tied members is not guaranteed to stay the same with successive sorts of that collection. For a 'stable' sort, the tied entries will always end up in the same order when sorted.
A simple solution would be to use efficient sorting algorithms like Merge Sort, Quicksort, Heapsort, etc., that can solve this problem in O(n. log(n)) time, but those will not take advantage of the fact that there are many duplicated values in the array. A better approach is to use a counting sort.
If a sorting algorithm is said to be "unstable", this means that for any items that rank the same, the order of the tied members is not guaranteed to stay the same with successive sorts of that collection. For a 'stable' sort, the tied entries will always end up in the same order when sorted.
For an example of applications, the quick sort algorithm is not stable. This would work fine for something like sorting actions by priority (if two actions are of equal priority, you would not be likely to care about which elements of a tie are executed first).
A stable sorting algorithm, on the other hand, is good for things like a leaderboard for an online game. If you were to use an unstable sort, sorting by points (for instance), then a user viewing the sorted results on a webpage could experience different results on page refreshes and operations like paging through results would not function correctly.
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