GATE | GATE CS 2008 | Question 46

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?
(A) O(Logn)
(B) O(n)
(C) O(nLogn)
(D) none of the above, as the tree cannot be uniquely determined.


Answer: (B)

Explanation: One important thing to note is, it is Binary Search Tree, not Binary Tree. In BST, inorder traversal can always be obtained by sorting all keys.

See method 2 of https://www.geeksforgeeks.org/construct-bst-from-given-preorder-traversa/ for details.

Same technique can be used for postorder traversal.

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