What are Red Black trees? Write down the properties of Red Black trees.

Red-Black Trees

Red-black trees are a type of self-balancing binary search tree, a data structure used to organize and store data efficiently. They were invented by Rudolf Bayer in 1972. Red-black trees have many useful properties that make them efficient for various applications, including:

1. Self-Balancing: Red-black trees automatically maintain a balanced structure. After every insertion or deletion operation, the tree rebalances itself to ensure that the height of the tree remains roughly logarithmic in the number of nodes. This property guarantees efficient search, insertion, and deletion operations.

2. Properties:

   • Each node is either red or black.
   • The root is always black.
   • Every red node must have two black child nodes.
   • Every path from a node to any of its descendant leaves contains the same number of black nodes.
   • No two adjacent nodes can be red.

3. Operations:

   • Insertion: When a new node is inserted into the tree, it is initially colored red. The tree is then rebalanced by applying a series of rotations and color changes to maintain the properties mentioned above.
   • Deletion: When a node is deleted from the tree, the tree is rebalanced by applying a series of rotations and color changes to maintain the properties.
   • Search: Searching for a specific key in a red-black tree is similar to searching in a binary search tree. The algorithm starts at the root and recursively traverses the tree, comparing the key with each node's key until the desired node is found.

4. Time Complexity: The time complexity of basic operations in a red-black tree is as follows:

   • Search: O(log n)
   • Insertion: O(log n)
   • Deletion: O(log n)

5. Applications: Red-black trees are used in various applications where balanced binary search trees are required, including:

   • Implementing sets and maps
   • C++ Standard Template Library (STL)
   • File systems
   • Database indexing
   • Network routing

In conclusion, red-black trees are a type of self-balancing binary search tree that maintains certain properties to ensure efficient search, insertion, and deletion operations. They are widely used in various applications where balanced binary search trees are required.