Trees

Question 1

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
       Data-Structures       Trees       Gate 2018
Question 1 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 3①⏟root In: 8 6 9 4 7 2 5⏟left subtree 13⏟right subtree


Question 2
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
       Data-Structures       Trees       Gate 2017 set-01
Question 2 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 3
A
64
B
65
C
66
D
67
       Data-Structures       Trees       GATE 2016 set-2
Question 3 Explanation: 
The number of ways in which the number 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:
Given the height of a tree with a single node is 0.
The root must be either 1 or 7, so with 1, 7 we can form 2 ways (left & right skew) each.

For each height we have 2 choices, except the leaf node.
Hence T(n) = 2 * T (n – 1)
∵ Total number of ways will be 2(n-1)=2(7-1)=26=64
Question 4
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
       Data-Structures       Trees       GATE 2015 (Set-01)
Question 4 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 5
   
A
B
C
D
None of the above
       Data-Structures       Trees       Gate-2003
Question 5 Explanation: 
Given Tree is

Insert G at root level:
Question 6
A binary tree T has n leaf nodes. The number of nodes of degree 2 in T is:
A
log2 n
B
n - 1
C
n
D
2n
       Data-Structures       Trees       Gate-1995
Question 6 Explanation: 
A binary tree is a tree data structure in which each node has atmost two child nodes.
The no. of subtrees of a node is called the degree of the node. In a binary tree, all nodes have degree 0, 1 and 2.
The degree of a tree is the maximum degree of a node in the tree. A binary tree is of degree 2.
The number of nodes of degree 2 in T is "n - 1".
Question 7
 
A
4
B
5
C
6
D
7
E
Both A and D
       Data-Structures       Trees       Gate-1992
Question 7 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.
There are 7 questions to complete.