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You are given the postorder traversal, P, of a binary search tree on the n elements 1, 2,..., n. You have to determine the unique binary search tree that has P as its postorder traversal. What is the time complexity of the most efficient algorithm for doing this?

1. Θ(log n)
2. Θ(n)
3. Θ(n log n)
4. none of the above, as the tree cannot be uniquely determined.

Correct answer: Θ(n)

Solution

The correct option is Θ(n) because reconstructing a binary search tree from its postorder traversal involves processing each of the n elements exactly once to determine their positions in the tree, leading to a linear time complexity.

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