GATE CS 2018 Set 1 — Question 30

NAT+1 / -0MediumTree TraversalsTreesProgramming & Data StructuresBinary Tree Properties

Programming & Data Structures → Trees → Binary Tree Properties

Last updated 5 September 2026

Question

The postorder traversal of a binary tree is 8, 9, 6, 7, 4, 5, 2, 3, 1. The inorder traversal of the same tree is 8, 6, 9, 4, 7, 2, 5, 1, 3. The height of a tree is the length of the longest path from the root to any leaf. The height of the binary tree above is______.

Correct answer 4 to 4 Solution We can reconstruct the binary tree using the given traversals: Postorder: 8, 9, 6, 7, 4, 5, 2, 3, 1 (Root is the last element: 1) Inorder: 8, 6, 9, 4, 7, 2, 5, 1, 3 1. Root is 1. From Inorder, Left Subtree is {8, 6, 9, 4, 7, 2, 5} and Right Subtree is {3}. 2. For the Left Subtree, the last element in Postorder is 2, so 2 is the root. From Inorder, Left of 2 is {8, 6, 9, 4, 7} and Right of 2 is {5}. 3. For the subtree {8, 6, 9, 4, 7}, the root is 4. Left of 4 is {8, 6, 9} and Right of 4 is {7}. 4. For the subtree {8, 6, 9}, the root is 6. Left of 6 is {8} and Right of 6 is {9}. The tree structure is: Level 0: 1 Level 1: 2 (Left), 3 (Right) Level 2: 4 (Left of 2), 5 (Right of 2) Level 3: 6 (Left of 4), 7 (Right of 4) Level 4: 8 (Left of 6), 9 (Right of 6) The longest path from the root (1) to a leaf (8 or 9) is 1-2-4-6-8 or 1-2-4-6-9. The length of this path (number of edges) is 4. Therefore, the height of the tree is 4. Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer 4 to 4 Solution We can reconstruct the binary tree using the given traversals: Postorder: 8, 9, 6, 7, 4, 5, 2, 3, 1 (Root is the last element: 1) Inorder: 8, 6, 9, 4, 7, 2, 5, 1, 3 1. Root is 1. From Inorder, Left Subtree is {8, 6, 9, 4, 7, 2, 5} and Right Subtree is {3}. 2. For the Left Subtree, the last element in Postorder is 2, so 2 is the root. From Inorder, Left of 2 is {8, 6, 9, 4, 7} and Right of 2 is {5}. 3. For the subtree {8, 6, 9, 4, 7}, the root is 4. Left of 4 is {8, 6, 9} and Right of 4 is {7}. 4. For the subtree {8, 6, 9}, the root is 6. Left of 6 is {8} and Right of 6 is {9}. The tree structure is: Level 0: 1 Level 1: 2 (Left), 3 (Right) Level 2: 4 (Left of 2), 5 (Right of 2) Level 3: 6 (Left of 4), 7 (Right of 4) Level 4: 8 (Left of 6), 9 (Right of 6) The longest path from the root (1) to a leaf (8 or 9) is 1-2-4-6-8 or 1-2-4-6-9. The length of this path (number of edges) is 4. Therefore, the height of the tree is 4.

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