Question

You are given a set \(V\) of distinct integers. A binary search tree \(T\) is created by inserting all elements of \(V\) one by one, starting with an empty tree. The tree \(T\) 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 \(T\), and you do not have access to \(T\). Which one of the following statements is TRUE?

• A. Inorder traversal of \(T\) can be determined from \(V\)
• B. Root node of \(T\) can be determined from \(V\)
• C. Preorder traversal of \(T\) can be determined from \(V\)
• D. Postorder traversal of \(T\) can be determined from \(V\)

Hint:

In a Binary Search Tree (BST), the inorder traversal always gives the sorted order of elements, regardless of the insertion sequence.

Answer 1

The Correct Option is A

In a Binary Search Tree (BST), the inorder traversal of the tree produces the elements in sorted order, regardless of the sequence in which they were inserted. Since \(V\) contains all the elements of \(T\) as a set, sorting \(V\) will give the inorder traversal of \(T\). Hence, Option (A) is correct.
Option (B): The root node of \(T\) depends on the sequence of insertion and cannot be determined solely from \(V\). Hence, Option (B) is incorrect.
Option (C): The preorder traversal depends on the structure of \(T\), which in turn depends on the insertion order. Therefore, it cannot be determined from \(V\). Hence, Option (C) is incorrect.
Option (D): The postorder traversal also depends on the structure of \(T\) and the insertion sequence, and cannot be determined from \(V\). Hence, Option (D) is incorrect. Final Answer: \[ \boxed{\text{(A)}} \]