Understanding Red-Black Tree, With Examples

 Understanding Red-Black Tree, With Examples

A red–black tree is a self-balancing binary search tree. Each node of the binary tree is either red or black. These trees satisfy the following properties:

1. Every node is either red or black.
2. The root is black.
3. Every leaf node (NULL) is black.
4. If a node is red, both its children are black.
5. Every simple path from a node to a descendant leaf contains the same number of black nodes.

These properties ensure that the tree is roughly balanced - height of the tree is O(log n) where n is the number of nodes.
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10(B)
/ \
5(R) 15(B)
/ \
2(B) 8(R)

Here 10 is the root node which is black. Nodes 5 and 15 are children of 10. 5 is red and 15 is black.
Nodes 2 and 8 are children of 5. 2 is black and 8 is red.

Operations on red-black trees involve rotations to maintain the balance properties:

• Insertion - When a new node is inserted, it is colored red. Rotations may be needed to fix violations.

• Deletion - When a node is deleted, its child may cause a violation. Recoloring and rotations fix this.

• Search - Searching a key in the tree just follows the left/right pointers like in a regular BST.

• Balancing factors:

  • Height balancing - Max difference between heights of children is 1
  • Size balancing - Size difference between subtrees is atmost 2

Hope this helps! Let me know if you have any other questions.