Trees

Question 1

Consider the following 2-3-4 tree (i.e., B-tree with a minimum degree of two) in which each data item is a letter. The usual alphabetical ordering of letters is used in constructing the tree.

What is the result of inserting G in the above tree?

A
B
C
D
None of the above
Question 1 Explanation: 
Given Tree is

Insert G at root level:
Question 2

A 2-3 tree is tree such that

    (a) all internal nodes have either 2 or 3 children
    (b) all paths from root to the leaves have the same length

The number of internal nodes of a 2-3 tree having 9 leaves could be

A
4
B
5
C
6
D
7
E
Both A and D
Question 2 Explanation: 
Case 1:

Where L is leaf node.
So, no. of internal node is 4.
Case 2:

Where L is leaf node.
So, no. of internal node is 7.
Question 3

The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are

A
63 and 6, respectively
B
64 and 5, respectively
C
32 and 6, respectively
D
31 and 5, respectively
Question 3 Explanation: 
Maximum number of nodes in a binary tree of height h is,
2h+1 - 1 = 25+1 - 1 = 63
Minimum number of nodes in a binary tree of height h is
h + 1 = 5 + 1 = 6
Question 4

The number of ways in which the numbers 1, 2, 3, 4, 5, 6, 7 can be inserted in an empty binary search tree, such that the resulting tree has height 6, is _________.

Note: The height of a tree with a single node is 0.
A
64
B
65
C
66
D
67
Question 4 Explanation: 
To get the tree of height 6, every level should contain only 1 node.
So to get such tree at each level we should have either maximum or minimum element from remaining numbers till that level. So no. of binary search tree possible is,
1st level - 2 (maximum or minimum)

2nd level - 2

3rd level - 2

4th level - 2

5th level - 2

6th level - 2

7th level - 2
= 2 × 2 × 2 × 2 × 2 × 2 × 1
= 26
= 64
Question 5

Let T be a tree with 10 vertices. The sum of the degrees of all the vertices in T is _________.

A
18
B
19
C
20
D
21
Question 5 Explanation: 
Sum of degrees of all vertices is double the number of edges.
A tree, with 10 vertices, consists n - 1, i.e. 10 - 1 = 9 edges.
Sum of degrees of all vertices = 2(#edges)
= 2(9)
= 18
Question 6

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 _______.

A
1
B
2
C
3
D
4
Question 6 Explanation: 
Post – 8 9 6 7 4 5 2 3 1
In – 8 6 9 4 7 2 5 1 3
Post: 8 9 6 7 4 5 2 3 1→(root)
In: 8 6 9 4 7 2 5→(left subtree) 13→(right subtree)



Question 7
Which of the following is a nonlinear data structure?
A
Stack
B
Queue
C
Tree
D
All the above
Question 7 Explanation: 
Stack and queue are linear data structure, but tree is a non linear data structure.
Question 8
The maximum depth that a tree of N nodes can have is
A
N/2
B
N
C
Log N
D
1
Question 8 Explanation: 
The maximum depth that a tree of N nodes can have is N,when the tree is skewed.
There are 8 questions to complete.

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