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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
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The height of a tree is the length of the longest root-to-leaf path in...
Number of nodes is maximum for a perfect binary tree. A perfect binary tree of height h has 2h+1 - 1 nodes
Number of nodes is minimum for a skewed binary tree. A perfect binary tree of height h has h+1 nodes.
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The height of a tree is the length of the longest root-to-leaf path in...
Solution:

Maximum number of nodes in a binary tree of height 5
To find the maximum number of nodes in a binary tree of height 5, we can use the formula:

Max Nodes = 2^(h+1) - 1
where h is the height of the binary tree.

So, for a binary tree of height 5, the maximum number of nodes would be:
Max Nodes = 2^(5+1) - 1
Max Nodes = 63

Therefore, option 'A' is correct.

Minimum number of nodes in a binary tree of height 5
To find the minimum number of nodes in a binary tree of height 5, we can use the fact that a binary tree of height h can have a minimum of h+1 nodes.

So, for a binary tree of height 5, the minimum number of nodes would be:
Min Nodes = 5+1
Min Nodes = 6

Therefore, option 'A' is correct.

Conclusion:

The maximum number of nodes in a binary tree of height 5 is 63, and the minimum number of nodes is 6.
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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 area)63 and 6, respectivelyb)64 and 5, respectivelyc)32 and 6, respectivelyd)31 and 5, respectivelyCorrect answer is option 'A'. Can you explain this answer?
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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 area)63 and 6, respectivelyb)64 and 5, respectivelyc)32 and 6, respectivelyd)31 and 5, respectivelyCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about 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 area)63 and 6, respectivelyb)64 and 5, respectivelyc)32 and 6, respectivelyd)31 and 5, respectivelyCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 area)63 and 6, respectivelyb)64 and 5, respectivelyc)32 and 6, respectivelyd)31 and 5, respectivelyCorrect answer is option 'A'. Can you explain this answer?.
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