A binary search tree \( T \) contains \( n \) distinct elements. What is the time complexity of picking an element in \( T \) that is smaller than the maximum element in \( T \)?
Show Hint
- \( \Theta(n \log n) \)
- \( \Theta(n) \)
- \( \Theta(\log n) \)
- \( \Theta(1) \)
The Correct Option is D
Solution and Explanation
Step 1: Understanding the question.
The question asks for the time required to pick any element that is smaller than the maximum element in a binary search tree.
Step 2: Key observation.
In a BST with distinct elements, the maximum element is the rightmost node. Any other node in the tree automatically satisfies the condition of being smaller than the maximum.
Step 3: Time complexity.
We can simply pick the root (or any arbitrary node other than the maximum) without performing any traversal or comparison. This operation takes constant time.
Step 4: Conclusion.
Thus, the time complexity is \( \Theta(1) \).
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