GATE CS 2025 Set 1 — Question 26
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Programming & Data Structures → Trees → Binary Search Trees
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Question
Which of the following statement(s) is/are TRUE for any binary search tree (BST) having distinct integers?
Correct answer
(A) The maximum length of a path from the root node to any other node is (n - 1).; (B) An inorder traversal will always produce a sorted sequence of elements.
Solution
Let's evaluate each statement for a Binary Search Tree (BST) with distinct integers:
- Statement (A) is TRUE: In the worst-case scenario, a BST can be skewed (like a linked list). For a tree with nodes, a skewed structure will have a path from the root to the deepest leaf consisting of edges. Therefore, the maximum length of a path is .
- Statement (B) is TRUE: By definition, a BST is structured such that for any node, all values in the left subtree are smaller and all values in the right subtree are larger. An inorder traversal (Left Root Right) visits nodes in increasing order. Since the integers are distinct, it will always produce a strictly increasing sorted sequence.
- Statement (C) is FALSE: The worst-case time complexity for searching in a BST is , which occurs when the tree is skewed. is the worst-case complexity only for balanced binary search trees (like AVL or Red-Black trees).
- Statement (D) is FALSE: The properties of a BST and a Min-Heap are different. In a BST, the left child is always smaller than the parent. In a Min-Heap, the parent must be smaller than both its children. Thus, a BST node with a left child inherently violates the Min-Heap property.
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