What is the time complexity of inserting an element into a Red-Black tree?

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Question: What is the time complexity of inserting an element into a Red-Black tree?

Options:

Correct Answer: O(log n)

Solution:

The time complexity of inserting an element into a Red-Black tree is O(log n) due to its balanced nature.

What is the time complexity of inserting an element into a Red-Black tree?

What is the time complexity of inserting an element into a Red-Black tree?

Step 1: Understand what a Red-Black tree is. It is a type of binary search tree that keeps itself balanced.
Step 2: Know that a balanced tree means that the height of the tree is kept small, which helps in faster operations.
Step 3: When you insert an element, you first find the correct position for it, which takes time proportional to the height of the tree.
Step 4: In a Red-Black tree, the height is always kept to about log(n), where n is the number of elements in the tree.
Step 5: Therefore, finding the position to insert the new element takes O(log n) time.
Step 6: After finding the position, the tree may need to be rebalanced, but this rebalancing also takes O(log n) time.
Step 7: Combine the time for finding the position and rebalancing, which still results in O(log n) time for the entire insertion process.

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