BST GATE CS PYQ Quiz

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Question 1

A binary search tree T contains n distinct elements. What is the time complexity of picking an element in T that is smaller than the maximum element in T?

  • Θ(nlogn)

  • Θ(n)

  • Θ(logn)

  • Θ(1)

Question 2

The preorder traversal sequence of a binary search tree is 30, 20, 10, 15, 25, 23, 39, 35, 42. Which one of the following is the postorder traversal sequence of the same tree?

  • 10, 20, 15, 23, 25, 35, 42, 39, 30

  • 15, 10, 25, 23, 20, 42, 35, 39, 30

  • 15, 20, 10, 23, 25, 42, 35, 39, 30

  • 15, 10, 23, 25, 20, 35, 42, 39, 30

Question 3

We are given a set of n distinct elements and an unlabeled binary tree with n nodes. In how many ways can we populate the tree with the given set so that it becomes a binary search tree?

  • 0

  • 1

  • n!

  • (1/(n+1)).2nCn

Question 4

How many distinct binary search trees can be created out of 4 distinct keys?

  • 5

  • 14

  • 24

  • 42

Question 5

Postorder traversal of a given binary search tree T produces the following sequence of keys 10, 9, 23, 22, 27, 25, 15, 50, 95, 60, 40, 29 Which one of the following sequences of keys can be the result of an inorder traversal of the tree T?

  • 9, 10, 15, 22, 23, 25, 27, 29, 40, 50, 60, 95

  • 9, 10, 15, 22, 40, 50, 60, 95, 23, 25, 27, 29

  • 29, 15, 9, 10, 25, 22, 23, 27, 40, 60, 50, 95

  • 95, 50, 60, 40, 27, 23, 22, 25, 10, 9, 15, 29

Question 6

The following numbers are inserted into an empty binary search tree in the given order: 10, 1, 3, 5, 15, 12, 16. What is the height of the binary search tree (the height is the maximum distance of a leaf node from the root)?

  • 2

  • 3

  • 4

  • 6

Question 7

Suppose the numbers 7, 5, 1, 8, 3, 6, 0, 9, 4, 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers. What is the in-order traversal sequence of the resultant tree ?

  • 7 5 1 0 3 2 4 6 8 9

  • 0 2 4 3 1 6 5 9 8 7

  • 0 1 2 3 4 5 6 7 8 9

  • 9 8 6 4 2 3 0 1 5 7

Question 8

Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)? 

1. 3, 5, 7, 8, 15, 19, 25
2. 5, 8, 9, 12, 10, 15, 25
3. 2, 7, 10, 8, 14, 16, 20
4. 4, 6, 7, 9, 18, 20, 25

  • 1 and 4 only

  • 2 and 3 only

  • 2 and 4 only

  • 2 only

Question 9

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:

  • 2, 6, 7, 8, 9, 10, 12, 15, 16, 17, 19, 20

  • 2, 7, 6, 10, 9, 8, 15, 17, 20, 19, 16, 12

  • 7, 2, 6, 8, 9, 10, 20, 17, 19, 15, 16, 12

  • 7, 6, 2, 10, 9, 8, 15, 16, 17, 20, 19, 12

Question 10

Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:



Note:

The height of a tree with a single node is 0.

  • 4 and 15 respectively

  • 3 and 14 respectively

  • 4 and 14 respectively

  • 3 and 15 respectively

There are 16 questions to complete.

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