How does a Red-Black tree ensure balance after deletion?

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Question: How does a Red-Black tree ensure balance after deletion?

Options:

Correct Answer: By performing rotations and recoloring.

Solution:

After deletion in a Red-Black tree, balance is restored through a combination of rotations and recoloring.

How does a Red-Black tree ensure balance after deletion?

How does a Red-Black tree ensure balance after deletion?

Step 1: Identify the node that has been deleted and its properties (color and position).
Step 2: If the deleted node was red, the tree remains balanced because removing a red node does not violate the Red-Black tree properties.
Step 3: If the deleted node was black, it creates a double black situation, which needs to be resolved.
Step 4: Check the sibling of the deleted node. If the sibling is red, perform a rotation to make it black and move the blackness up.
Step 5: If the sibling is black, check the color of its children. If at least one child is red, perform rotations and recoloring to balance the tree.
Step 6: If the sibling and its children are black, move the double black up to the parent and repeat the process until the tree is balanced.

Red-Black Tree Properties – Understanding the properties of Red-Black trees, including node color, balance, and the rules that govern them.
Tree Rotations – Knowledge of how rotations (left and right) are used to maintain tree balance after operations.
Recoloring – Understanding how changing the color of nodes can help restore the properties of the Red-Black tree after deletions.