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The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height h is:
  • a)
    2h−1
  • b)
    2h−1 -1
  • c)
    2h+1-1
  • d)
    2h+1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The height of a binary tree is the maximum number of edges in any root...
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Most Upvoted Answer
The height of a binary tree is the maximum number of edges in any root...
Explanation:

  • A binary tree of height h has at most 2^h leaves (when the tree is a complete binary tree, the tree has 2^h leaves exactly).

  • Therefore, the maximum number of nodes in a binary tree of height h is the sum of the number of nodes in each level from 0 to h, which is:

  • 1 + 2 + 4 + ... + 2^(h-1) + 2^h

  • This is a geometric series with a = 1 and r = 2, so the sum is:

  • 1 + 2 + 4 + ... + 2^(h-1) + 2^h = (2^(h+1) - 1)/(2-1) = 2^(h+1) - 1

  • Therefore, the maximum number of nodes in a binary tree of height h is 2^(h+1) - 1.


Answer: Option C (2^h+1 - 1)
Community Answer
The height of a binary tree is the maximum number of edges in any root...
Considering root it at height 0.
At height 0 , number of nodes 1
At height 1 , number of nodes  3
At height 2 , number of nodes  7
At height 3 , number of nodes 15

Now take a look at the pattern of number of nodes.
1,3,7,15..

You can now the see that , no of nodes at any height is 2ʰ⁺�-1
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