GATE CS 2024 Set 2 — Question 39
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Programming & Data Structures → Trees → Binary Search Trees
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Question
You are given a set of distinct integers. A binary search tree is created by inserting all elements of one by one, starting with an empty tree. The tree follows the convention that, at each node, all values stored in the left subtree of the node are smaller than the value stored at the node. You are not aware of the sequence in which these values were inserted into , and you do not have access to .Which one of the following statements is TRUE?
Correct answer
(A) Inorder traversal of T can be determined from V
Solution
A fundamental property of a Binary Search Tree (BST) is that its inorder traversal yields the keys in sorted (non-decreasing) order.Since we are given the set of distinct integers, we can simply sort the elements of in ascending order. This sorted sequence corresponds exactly to the inorder traversal of the BST , regardless of the insertion order or the resulting structure of the tree.The root node, preorder traversal, and postorder traversal all depend on the specific structure of the tree, which is determined by the order in which elements are inserted. Since the insertion sequence is unknown, these cannot be determined uniquely from the set alone.
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