Top MCQs on Binary Trees Data Structure with Answers

Question 21

Breadth First Search (BFS) is started on a binary tree beginning from the root vertex. There is a vertex t at a distance four from the root. If t is the n-th vertex in this BFS traversal, then the maximum possible value of n is ________ [This Question was originally a Fill-in-the-blanks Question]

• 15
• 16
• 31
• 32

Question 22

In a binary tree, the number of internal nodes of degree 1 is 5, and the number of internal nodes of degree 2 is 10. The number of leaf nodes in the binary tree is  

• 10
• 11
• 12
• 15

Question 23

The following three are known to be the preorder, inorder and postorder sequences of a binary tree. But it is not known which is which.
MBCAFHPYK
KAMCBYPFH
MABCKYFPH
Pick the true statement from the following.

• I and II are preorder and inorder sequences, respectively
• I and III are preorder and postorder sequences, respectively
• II is the inorder sequence, but nothing more can be said about the other two sequences
• II and III are the preorder and inorder sequences, respectively

Question 24

A binary tree with n > 1 nodes has n₁, n₂ and n₃ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.
n₃ can be expressed as

• n₁ + n₂ - 1
• n₁ - 2
• [((n₁ + n₂)/2)]
• n₂ - 1

Question 25

A binary tree with n > 1 nodes has n₁, n₂ and n₃ nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.
Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?

• 2 * n₁ - 3
• n₂ + 2 * n₁ - 2
• n₃ - n₂
• n₂ + n₁ - 2

Question 26

A binary search tree contains the values 1, 2, 3, 4, 5, 6, 7, 8. The tree is traversed in pre-order and the values are printed out. Which of the following sequences is a valid output?

• 53124786
• 53126487
• 53241678
• 53124768

Question 27

In the balanced binary tree in the below figure, how many nodes will become unbalanced when a node is inserted as a child of the node “g”?

         a
       /   \\
      b     e
     / \\   /
    c  d  f
   /
  g

• 1
• 3
• 7
• 8

Question 28

The number of structurally different possible binary trees with 4 nodes is

• 14

• 12

• 336

• 168

Question 29

A strictly binary tree with 10 leaves

• cannot have more than 19 nodes

• has exactly 19 nodes

• has exactly 17 nodes

• has exactly 20 nodes

Question 30

What is the maximum height of any AVL tree with 7 nodes? Assume that height of tree with single node is 0.

• 2
• 3
• 4
• 5