Question

How can I tell whether an algorithm is stable or not?..

Also, how does this algorithm Bucketsort compare to Mergesort, Quicksort, Bubblesort, and Insertionsort
?

Answer 1

At first glance it would seem that if your queues are FIFO then it is stable. However I think there some context from class or other homework that would help you make a more solid determination.

From wikipedia:

Stability
Stable sorting algorithms maintain the relative order of records with equal keys. If all keys are different then this distinction is not necessary. But if there are equal keys, then a sorting algorithm is stable if whenever there are two records (let’s say R and S) with the same key, and R appears before S in the original list, then R will always appear before S in the sorted list. When equal elements are indistinguishable, such as with integers, or more generally, any data where the entire element is the key, stability is not an issue. However, assume that the following pairs of numbers are to be sorted by their first component:

http://en.wikipedia.org/wiki/Sorting_algorithm#Stability

As far as comparing to other algorithms. Wikipedia has a concise entry on it:

http://en.wikipedia.org/wiki/Bucket_sort#Comparison_with_other_sorting_algorithms

Also: https://stackoverflow.com/a/7341355/1416221