# Data Structures: Question Set – 25

#### How does the AVL tree deletion algorithm differ from the binary search tree deletion algorithm?

The AVL tree deletion algorithm differs from the binary search tree deletion algorithm in that it performs additional operations to maintain the AVL property after deleting a node. Specifically, it replaces the deleted node with its successor or predecessor (depending on whether it has a left child or a right child), and then rebalances the tree by performing rotations on the affected nodes and their ancestors until the AVL property is restored.

#### What is the AVL tree successor of a node?

The AVL tree successor of a node is the node with the smallest key that is greater than the key of the given node. It can be found by traversing the right subtree of the given node and then the left subtree of its right child until a leaf node is reached.

#### What is the AVL tree predecessor of a node?

The AVL tree predecessor of a node is the node with the largest key that is smaller than the key of the given node. It can be found by traversing the left subtree of the given node and then the right subtree of its left child until a leaf node is reached.

#### What is a red-black tree?

A red-black tree is a type of self-balancing binary search tree where each node has a color either red or black. The color of a node represents its balance status, with the property that every path from the root to a leaf node contains the same number of black nodes.

#### What are the properties of a red-black tree?

The properties of a red-black tree are:

Every node is either red or black.

The root node is black.

Every leaf node (NIL node) is black.

If a node is red, then both its children are black.

For each node, all paths from the node to its descendant leaves contain the same number of black nodes.

#### What is the time complexity of basic operations on a red-black tree?

The time complexity of basic operations on a red-black tree, such as search, insertion, and deletion, is O(log n), where n is the number of nodes in the tree.

#### How is a red-black tree different from a binary search tree?

A red-black tree is a type of self-balancing binary search tree where each node has a color either red or black, whereas a binary search tree does not have any balancing mechanism. In a red-black tree, the color of a node represents its balance status, with the property that every path from the root to a leaf node contains the same number of black nodes, whereas a binary search tree does not have any such property.

#### How is the balance of a red-black tree maintained during insertion and deletion operations?

The balance of a red-black tree is maintained during insertion and deletion operations by performing a series of rotations and color flips on the affected nodes. The specific rotation and color flip operations depend on the position and color of the nodes involved in the operation. The goal of these operations is to ensure that the tree maintains the properties of a red-black tree even after the insertion or deletion operation.

#### Can a red-black tree have a node with both children being red?

No, a red-black tree cannot have a node with both children being red. This violates property 4 of a red-black tree, which states that if a node is red, then both its children must be black.

#### What is the advantage of using a red-black tree over a binary search tree?

The advantage of using a red-black tree over a binary search tree is that the red-black tree is self-balancing, which ensures that the worst-case time complexity of basic operations such as search, insertion, and deletion is O(log n). In contrast, the worst-case time complexity of these operations on a binary search tree can be O(n), which can occur if the tree is highly unbalanced.