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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?
Most Upvoted Answer
The height of a tree is the length of the longest root-to-leaf path in...
Introduction:
In a binary tree, the height is defined as the length of the longest path from the root to a leaf node. The maximum and minimum number of nodes in a binary tree of height 5 can be determined by analyzing the structure of the tree.

Understanding the problem:
To find the maximum and minimum number of nodes in a binary tree of height 5, we need to consider the characteristics of a binary tree and the relationship between the height and the number of nodes.

Minimum number of nodes:
The minimum number of nodes in a binary tree of height 5 can be determined by considering a balanced binary tree. In a balanced binary tree, each level is completely filled except for the bottom level, which is filled from left to right. Since the height of the tree is 5, the number of nodes in the bottom level will be 2^5 = 32. Therefore, the minimum number of nodes in a binary tree of height 5 is 32.

Maximum number of nodes:
The maximum number of nodes in a binary tree of height 5 can be determined by considering a skewed binary tree. In a skewed binary tree, all the nodes are either left-skewed or right-skewed. In the case of a left-skewed binary tree, each node has only a left child, and in the case of a right-skewed binary tree, each node has only a right child. The height of the tree will be equal to the number of nodes in the longest path.

For a binary tree of height 5, the maximum number of nodes can be achieved by a left-skewed or right-skewed tree. In this case, the number of nodes in the longest path will be equal to the height of the tree. Since the height is 5, the maximum number of nodes will be 5+1 = 6.

Conclusion:
Therefore, the minimum number of nodes in a binary tree of height 5 is 32 and the maximum number of nodes is 6. Hence, the correct answer is option A) 63 and 6, respectively.
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Community 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 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?
Question Description
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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