GATE CS 2017 Set 2 — Question 36

MCQ+2 / -0.67EasyTree TraversalsTreesProgramming & Data StructuresBinary Search Trees

Programming & Data Structures → Trees → Binary Search Trees

Last updated 5 September 2026

Question

The pre-order traversal of a binary search tree is given by 12, 8, 6, 2, 7, 9, 10, 16, 15, 19, 17, 20. Then the post-order traversal of this tree is:

Correct answer (B) 2, 7, 6, 10, 9, 8, 15, 17, 20, 19, 16, 12 Solution 1. Determine In-order Traversal: For a Binary Search Tree (BST), the in-order traversal is the sorted sequence of its elements. In-order: 2, 6, 7, 8, 9, 10, 12, 15, 16, 17, 19, 20 2. Construct the Tree using Pre-order and In-order: Root is the first element of pre-order: 12 . Left subtree elements (from in-order): 2, 6, 7, 8, 9, 10. Pre-order for these: 8, 6, 2, 7, 9, 10. Right subtree elements (from in-order): 15, 16, 17, 19, 20. Pre-order for these: 16, 15, 19, 17, 20. Recursively applying this, the tree structure is: Root 12 Left child 8; 8's left is 6 (with children 2, 7), 8's right is 9 (with right child 10). Right child 16; 16's left is 15, 16's right is 19 (with children 17, 20). 3. Determine Post-order Traversal (Left, Right, Root): Post-order of left subtree (rooted at 8): 2, 7, 6, 10, 9, 8 Post-order of right subtree (rooted at 16): 15, 17, 20, 19, 16 Full post-order: 2, 7, 6, 10, 9, 8, 15, 17, 20, 19, 16, 12. This matches option (B). Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (B) 2, 7, 6, 10, 9, 8, 15, 17, 20, 19, 16, 12 Solution 1. Determine In-order Traversal: For a Binary Search Tree (BST), the in-order traversal is the sorted sequence of its elements. In-order: 2, 6, 7, 8, 9, 10, 12, 15, 16, 17, 19, 20 2. Construct the Tree using Pre-order and In-order: Root is the first element of pre-order: 12 . Left subtree elements (from in-order): 2, 6, 7, 8, 9, 10. Pre-order for these: 8, 6, 2, 7, 9, 10. Right subtree elements (from in-order): 15, 16, 17, 19, 20. Pre-order for these: 16, 15, 19, 17, 20. Recursively applying this, the tree structure is: Root 12 Left child 8; 8's left is 6 (with children 2, 7), 8's right is 9 (with right child 10). Right child 16; 16's left is 15, 16's right is 19 (with children 17, 20). 3. Determine Post-order Traversal (Left, Right, Root): Post-order of left subtree (rooted at 8): 2, 7, 6, 10, 9, 8 Post-order of right subtree (rooted at 16): 15, 17, 20, 19, 16 Full post-order: 2, 7, 6, 10, 9, 8, 15, 17, 20, 19, 16, 12. This matches option (B).

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