GATE CS 2015 Set 1 — Question 27

MCQ+1 / -0.33EasyTree TraversalsTreesProgramming & Data StructuresBinary Search Trees

Programming & Data Structures → Trees → Binary Search Trees

Last updated 5 September 2026

Question

Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)? I. 3, 5, 7, 8, 15, 19, 25 II. 5, 8, 9, 12, 10, 15, 25 III. 2, 7, 10, 8, 14, 16, 20 IV. 4, 6, 7, 9, 18, 20, 25

Correct answer (A) I and IV only Solution A key property of a Binary Search Tree (BST) is that an inorder traversal of the tree visits the nodes in a sorted (non-decreasing) order of their keys. We need to check which of the given sequences are sorted. Sequence I: 3, 5, 7, 8, 15, 19, 25 This sequence is in strictly increasing order. Therefore, it can be the inorder traversal of a BST. Sequence II: 5, 8, 9, 12, 10, 15, 25 This sequence is not sorted because the element 12 is followed by 10, which is smaller. Therefore, it cannot be the inorder traversal of a BST. Sequence III: 2, 7, 10, 8, 14, 16, 20 This sequence is not sorted because the element 10 is followed by 8, which is smaller. Therefore, it cannot be the inorder traversal of a BST. Sequence IV: 4, 6, 7, 9, 18, 20, 25 This sequence is in strictly increasing order. Therefore, it can be the inorder traversal of a BST. Since only sequences I and IV are sorted, they are the only ones that can be correct inorder traversal sequences of a binary search tree. Thus, option (A) is the correct answer. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

Review answer and solution without JavaScript

Interactive answer checking needs JavaScript. The published solution is available below.

Correct answer (A) I and IV only Solution A key property of a Binary Search Tree (BST) is that an inorder traversal of the tree visits the nodes in a sorted (non-decreasing) order of their keys. We need to check which of the given sequences are sorted. Sequence I: 3, 5, 7, 8, 15, 19, 25 This sequence is in strictly increasing order. Therefore, it can be the inorder traversal of a BST. Sequence II: 5, 8, 9, 12, 10, 15, 25 This sequence is not sorted because the element 12 is followed by 10, which is smaller. Therefore, it cannot be the inorder traversal of a BST. Sequence III: 2, 7, 10, 8, 14, 16, 20 This sequence is not sorted because the element 10 is followed by 8, which is smaller. Therefore, it cannot be the inorder traversal of a BST. Sequence IV: 4, 6, 7, 9, 18, 20, 25 This sequence is in strictly increasing order. Therefore, it can be the inorder traversal of a BST. Since only sequences I and IV are sorted, they are the only ones that can be correct inorder traversal sequences of a binary search tree. Thus, option (A) is the correct answer.

Continue learning with Success Tracker

Use Success Tracker to ask about the reasoning, then try another GATE CS question to check your understanding.

AI-powered practice· Unlimited practice on eligible plans

PYQs with solutions: Attempt available previous-year questions, then compare your reasoning with the worked solution. Coverage varies by stream.
Practice that adapts: Choose a topic, work on weaker areas and bookmark questions to revisit. Your attempts feed your progress tracking.
AI doubt support: Ask follow-up questions about a step or concept while practising, instead of stopping at the final answer.

Unlimited practice is available on eligible plans. Free practice and AI usage have limits; check the current plan allowances before choosing.

This page stays readable without an account. AI responses can be wrong; check them against the solution and source material.