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Which operation is guaranteed to be O(log n) in a Red-Black tree?

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Question: Which operation is guaranteed to be O(log n) in a Red-Black tree?

Options:

  1. Insertion
  2. Deletion
  3. Searching
  4. All of the above

Correct Answer: All of the above

Solution: 

All fundamental operations (insertion, deletion, and searching) in a Red-Black tree are guaranteed to be O(log n) due to the tree\'s balanced structure.

Which operation is guaranteed to be O(log n) in a Red-Black tree?

Practice Questions

Q1
Which operation is guaranteed to be O(log n) in a Red-Black tree?
  1. Insertion
  2. Deletion
  3. Searching
  4. All of the above

Questions & Step-by-Step Solutions

Which operation is guaranteed to be O(log n) in a Red-Black tree?
  • Step 1: Understand what a Red-Black tree is. It is a type of self-balancing binary search tree.
  • Step 2: Know that in a binary search tree, the left child is less than the parent, and the right child is greater.
  • Step 3: Learn that Red-Black trees maintain balance through specific rules, which helps keep the tree height low.
  • Step 4: Recognize that the height of a Red-Black tree is always O(log n), where n is the number of nodes in the tree.
  • Step 5: Understand that operations like insertion, deletion, and searching involve traversing the tree from the root to a leaf node.
  • Step 6: Since the height of the tree is O(log n), the time taken to perform these operations is also O(log n).
  • Step 7: Conclude that all fundamental operations (insertion, deletion, and searching) in a Red-Black tree are guaranteed to be O(log n).
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