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Postorder traversal of a given binary search tree T produces following sequence of keys: 3, 5, 7, 9, 4, 17, 16, 20, 18, 15, 14 Which one of the following sequences of keys can be the result of an in-order traversal of the tree T?

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UGC NET Computer Science (Paper 2) Nov 2017 Official Paper
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  1. 3, 4, 5, 7, 9, 14, 20, 18, 17, 16, 15
  2. 20, 18, 17, 16, 15, 14, 3, 4, 5, 7, 9
  3. 20, 18, 17, 16, 15, 14, 9, 7, 5, 4, 3
  4. 3, 4, 5, 7, 9, 14, 15, 16, 17, 18, 20

Answer (Detailed Solution Below)

Option 4 : 3, 4, 5, 7, 9, 14, 15, 16, 17, 18, 20
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The correct answer is "option 4".

CONCEPT:

The in-order traversal of the Binary Search Tree(BST) always gives elements in ascending or increasing order.

So, in-order traversal of the sequence of keys given in post-order traversal is sorted ascending order of that keys.

Hence, the sequence of keys in an in-order traversal of BST are : 3, 4, 5, 7, 9, 14, 15, 16, 17, 18, 20

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Q7.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The AVL trees are more balanced as compared to Red Black trees, but they may cause more rotations during insertion and deletion Reason R: A Red Black tree with n nodes has height that is greater than 2 log2 (n + 1) and the AVL tree with n nodes has height less than logΦ (√5 (n+2)) -2 (where Φ is golden ratio) In the light of the above statements, choose the correct answer from the options given below. 
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