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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  
# 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
# 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
# 3
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
Is This Answer Correct ?    21 Yes 8 No
Gaurav Gupta
# 4
Is This Answer Correct ?    18 Yes 6 No
# 5
2^N -1 
Is This Answer Correct ?    12 Yes 6 No
Gopala Krishnan
# 6

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
# 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
# 8
to be more generic this kind of problem is best solved

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.
C = "Number of Possible Children"
N = Levels


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
# 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

Is This Answer Correct ?    5 Yes 3 No
Vaishali Naidu
# 10

because root is at level 0. and there are n levels only.
so last level i.e level of leaves should be n-1. for maximum
we will consider complete binary tree which is full at level

for 0 level -> 2^0 i.e 1 element
for 1 level -> 2^1
so on

for n-1 levle ->2^(n-1) nodes
sum = 2^n-1
Is This Answer Correct ?    2 Yes 1 No

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