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Question
What is the maximum total number of nodes in a tree that has
N levels? Note that the root is level (zero)
 Question Submitted By :: Data-Structures
I also faced this Question!!     Answer Posted By  
 
Answer
# 1
2^(N+1)-1..

if N=0; it is 2-1=1,1 is the max no of node in the tree
if N=1; it is 4-1=3, 3 is the max no of nodes in the tree
if N=2; it is 8-1=7, 7 is the max

and it goes like that...........
 
Is This Answer Correct ?    97 Yes 5 No
Salmiya Thilsath.a
 
Answer
# 2
(2 pow n)-1,if root level is one and (2 pow n+1)-1, if root
level is zero.
 
Is This Answer Correct ?    24 Yes 9 No
Asharani K P
 
 
 
Answer
# 3
(2^(N+1))-1
Suppose level is 2 then total number of nodes will be
1 root
2 left of root and right of root
2 left and right of left of root
2 left and right of right of root
so total nodes are 1+2+2+2=7

by formula (2^(2+1))-1
8-1=7
 
Is This Answer Correct ?    21 Yes 8 No
Gaurav Gupta
 
Answer
# 4
2^(N+1)-1 
Is This Answer Correct ?    18 Yes 6 No
Deba
 
Answer
# 5
2^N -1 
Is This Answer Correct ?    12 Yes 6 No
Gopala Krishnan
 
Answer
# 6
Infinite

In a tree a node can have any number of nodes independent
of the levels.
 
Is This Answer Correct ?    8 Yes 3 No
S. Sadagopan
 
Answer
# 7
if tree is binary tree then maximum no.of node is 2^(N+1)-1 
Is This Answer Correct ?    4 Yes 0 No
Bipin From Utkal University Mc
 
Answer
# 8
to be more generic this kind of problem is best solved
recursivly.

To point out that 2 ^ N AND 3 ^ N are both wrong,
here's a few examples: (the exponet is the amount of levels)
2^0 = 1, correct
2^1 = 2, incorrect, should be 3
2^2 = 4, incorrect, should be 7

And a tree with three children
3^0 = 1, correct
3^1 = 3, incorrect, should be 4
3^2 = 9, incorrect, should be 13

Looking at that I'm sure you can see the pattern.
Let
C = "Number of Possible Children"
N = Levels

N
Σ C^N
j=0

or in C++ code
int NodeCount(int C, int N)
{
if (N < 0) return 0
return NodeCount(C, N-1) + C^N
}
 
Is This Answer Correct ?    7 Yes 4 No
Hex
 
Answer
# 9
If root is at level 0 then :
Case 0:
When level is 1 max nodes is 1
Case 1:
When level is 1 then max would be 3.
Case 2:
When level is 2 then max nodes would be 7

So formula would be 2^(n+1) -1

2^(0+1)-1=1
2^(1+1)-1=3
2^(2+1)-1=7
 
Is This Answer Correct ?    5 Yes 3 No
Vaishali Naidu
 
Answer
# 10
2^(N+1)-1 
Is This Answer Correct ?    1 Yes 0 No
Saurabh
 

 
 
 
Other Data Structures Interview Questions
 
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Evaluate the following prefix expression " ++ 26 + - 1324" Patni 22
Which data structure is needed to convert infix notations to post fix notations? Fidelity 20
wt is a datastructure CybAge 8
what is atmost complete binary tree?   6
In which data structure, elements can be added or removed at either end, but not in the middle? Wipro 41
Write the programs for Linked List (Insertion and Deletion) operations Persistent 9
How would you sort a linked list?   4
What data structure would you mostly likely see in a non recursive implementation of a recursive algorithm? CTS 3
what is mean by d-queue?   10
How is it possible to insert different type of elements in stack? TCS 7
example of linear and non-linear data structures? Infosys 7
 
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