Why would anyone use set instead of unordered set

Question

C++0x introduces unordered set, which can be found in boost and many other places.

According to my understanding, unordered set is a hash table with an O(1) lookup complexity.

Set, on the other hand, is nothing more than a tree with log(n) lookup complexity.

Why would anyone use set rather than unordered set?

Is there still a need for set?

Answer 1

Unordered sets must compensate for their O(1) average access time in several ways:

To store the same number of elements, set uses less memory than unordered set.

Lookups in a set may be faster than lookups in an unordered set for a small number of elements.

Even though unordered set is faster in the average case, set is almost always guaranteed to have lower worst-case complexities (for example insert).

If you want to access the elements in order, that set sorts them.

Different sets can be lexicographically compared using <,<=, >, and >=.

These operations do not require unordered sets to be supported.