Top MCQs on Binary Trees Data Structure with Answers

Question 31

Which one of the following property is correct for a red-black tree?

• Every simple path from a node to a descendant leaf contains the same number of black nodes
• If a node is red, then one children is red and another is black
• If a node is red, then both its children are red
• Every leaf node (sentinel node) is red

Question 32

Consider a full binary tree with n internal nodes, internal path length i, and external path length e. The internal path length of a full binary tree is the sum, taken over all nodes of the tree, of the depth of each node. Similarly, the external path length is the sum, taken over all leaves of the tree, of the depth of each leaf. Which of the following is correct for the full binary tree?

• e = i+n
• e = i+2n
• e = 2i+n
• e = 2ⁿ+i

Question 33

The order of a leaf node in a B⁺ tree is the maximum number of children it can have. Suppose that block size is 1 kilobytes, the child pointer takes 7 bytes long and search field value takes 14 bytes long. The order of the leaf node is ________.

• 16
• 63
• 64
• 68

Question 34

A complete binary tree with n non-leaf nodes contains

• log₂ n nodes
• n+1 nodes
• 2n nodes
• 2n+1 nodes

Question 35

Suppose you are given a binary tree with n nodes, such that each node has exactly either zero or two children. The maximum height of the tree will be

• n / 2 - 1
• n / 2 + 1
• (n – 1) / 2
• (n + 1) / 2

Question 36

The number of different binary trees with 6 nodes is ______.

• 6
• 42
• 132
• 256

Question 37

Which of the following number of nodes can form a full binary tree?

• 8

• 15

• 14

• 13

Question 38

A complete binary tree with the property that the value at each node is as least as large as the values at its children is known as

• Binary search tree

• AVL tree

• Completely balanced tree

• Heap

Question 39

A full binary tree with n leaves contains

• n nodes
• log ₂ n nodes
• 2n –1 node
• 2 ⁿ nodes

Question 40

Any decision tree that sorts n elements has height

• Ω(n)

• Ω(lgn)

• Ω(nlgn)

• Ω(n²)