What is the maximum height of a Red-Black tree with n nodes?

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Question: What is the maximum height of a Red-Black tree with n nodes?

Options:

Correct Answer: 2 log(n)

Solution:

The maximum height of a Red-Black tree is 2 log(n), which ensures that the tree remains balanced.

What is the maximum height of a Red-Black tree with n nodes?

What is the maximum height of a Red-Black tree with n nodes?

Step 1: Understand what a Red-Black tree is. It is a type of binary search tree that maintains balance through specific properties.
Step 2: Know that the height of a tree is the number of edges on the longest path from the root to a leaf.
Step 3: Recognize that Red-Black trees have properties that limit their height to ensure they remain balanced.
Step 4: Learn that for a Red-Black tree with n nodes, the maximum height is defined as 2 times the logarithm (base 2) of n.
Step 5: The formula for maximum height is: Height = 2 * log2(n). This means as the number of nodes increases, the height grows slowly.
Step 6: Conclude that this height limit helps keep the tree operations efficient, like searching and inserting.

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