**Which Data Structure Is Used in Set STL?**

In the C++ Standard Template Library (STL), the __set__ container is implemented using a self-balancing binary search tree called a __red-black tree__. A red-black tree is a type of binary search tree that ensures that the height of the tree is always balanced, providing efficient insertion, deletion, and search operations.

## Red-Black Trees

A red-black tree is a binary search tree that has the following properties:

**Color Property:**Each node in the tree is either red or black.**Root Property:**The root of the tree is always black.**Leaf Property:**The leaves (NULL nodes) are considered black.**Red Property:**If a node is red, both its children are black.**Black Depth Property:**For any node, all paths from that node to its descendant leaves contain an equal number of black nodes.

### The Advantages of Red-Black Trees

The use of red-black trees as the underlying data structure for sets in STL provides several advantages. Some key advantages include:

**Balanced Height:**Red-black trees ensure that the height of the tree remains balanced. This guarantees optimal time complexity for insertion, deletion, and search operations, which have an average time complexity of O(log n).**Duplicate Elements:**Red-black trees allow duplicate elements to be stored.Each element in the set is unique but can have multiple instances.

**Ordered Elements:**Red-black trees maintain the elements in a specific order. The elements are sorted in ascending order by default, but you can also specify a custom sorting criterion.

### The Complexity of Operations

The time complexity of various operations on the set container implemented using red-black trees are as follows:

**Insertion:**O(log n)**Deletion:**O(log n)**Search:**O(log n)**Traversal:**O(n)

Note that these complexities are for average cases, not considering worst-case scenarios.

## In Conclusion

The set container in the C++ STL uses a red-black tree as its underlying data structure. Red-black trees provide efficient operations, balanced height, the ability to store duplicate elements, and maintain elements in a specific order. Understanding the data structure used in set STL helps us make informed decisions when choosing an appropriate container for our needs.