soulecho wrote:
Wrong, the most efficient search/sort mechanism is a hash/key pair, which is O(1). Heapsort is O(nLog(n))

You can't sort in constant time. You can use a hash table for constant time lookup (assuming there are no collisions), but hashes are not useful for sorting.
Edit: well there are bucket-type sorts but those are linear time at best and need big data structures.
Yes, you are correct. But in my defense, I was thinking purely about the search aspect when I posted my response.