Fast sort algorithms for arrays with mostly duplicated elements?

Question

What are efficient ways to sort arrays that have mostly a small set of duplicated elements? That is, a list like:

{ 10, 10, 55, 10, 999, 8851243, 10, 55, 55, 55, 10

Answer 1

Not the best algorithm, but simple:
You can put everything in a trie, and have the leaves be counters. That should take O(n*m) where n is the number of elements and m is the size of the biggest element (typically that would be a constant, but not necessarily). Then pre-order traverse the tie, outputting counter elements of the current key when you hit a leaf. That should take only O(n+p) where p is the size of the trie, which should be tiny compared to n.