How many rotations are required in the worst case when inserting a node in a Red

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Question: How many rotations are required in the worst case when inserting a node in a Red-Black Tree?

Options:

Correct Answer: 2

Solution:

In the worst case, up to 2 rotations may be required to maintain the properties of a Red-Black Tree after insertion.

How many rotations are required in the worst case when inserting a node in a Red-Black Tree?

How many rotations are required in the worst case when inserting a node in a Red-Black Tree?

Step 1: Understand what a Red-Black Tree is. It is a type of binary search tree that has specific properties to keep it balanced.
Step 2: Know the properties of a Red-Black Tree. These include: each node is either red or black, the root is always black, red nodes cannot have red children, and every path from a node to its descendant leaves must have the same number of black nodes.
Step 3: When you insert a new node, it is initially colored red. This can sometimes violate the Red-Black Tree properties.
Step 4: If the properties are violated after insertion, you need to fix the tree. This is done through rotations and recoloring.
Step 5: In the worst case, you may need to perform up to 2 rotations to restore the properties of the tree after inserting a node.

Red-Black Tree Properties – Understanding the balancing properties of Red-Black Trees, including the rules that dictate node color and structure.
Tree Rotations – Knowledge of how rotations are used to maintain tree balance during insertions and deletions.