Classical

Data Structures - Trees

16:  

The maximum number of nodes on level i of a binary tree is

A.

2i-1

B.

3i-1

C.

i+1

D.

2i+2

 
 

Option: A

Explanation :


17:   The smallest number of key that will force a B-tree of order 3 to have a height 3 is
A. 12
B. 10
C. 7
D. None of these
 
 

Option: C

Explanation :


18:   A binary tree in which every non-leaf node has non-empty left and right subtrees is called a strictly binary tree. Such a tree with 10 leaves
A. Cannot have more than 19 nodes
B. Has exactly 19 nodes
C. Has exactly 17 nodes
D. Cannot have more than 19 nodes
 
 

Option: B

Explanation :
A strictly binary tree with 'n' leaves must have (2n 1) nodes. Verify for some small 'n'. This can be proved by the principle of mathematical induction.


19:  

Number of possible binary trees with 3 nodes is

A.

12

B.

9

C.

14

D.

5

 
 

Option: D

Explanation :


20:   A-2-3 tree is a tree such that
1. All internal nodes have either 2 or 3 children.
2. 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. 8
D. 7
 
 

Option: A

Explanation :




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