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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 4 is.
- a)16 and 4 respectively.
- b)32 and 4 respectively.
- c)15 and 5 respectively.
- d)31 and 5 respectively.Correct Answer
Correct answer is option 'D'. 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...
Height is defined as path length i.e (height+1) will give number of levels. In a binary tree of height h = 4;
Maximum number of nodes = 2^(h+1)-1
= 31
Minimum number of nodes = 5
Therefore (d) is correct answer.
Most Upvoted Answer
The height of a tree is the length of the longest root to leaf path in...
The height of a binary tree is defined as the length of the longest root-to-leaf path. The minimum number of nodes in a binary tree of height 4 can be calculated using the formula 2^(h+1) - 1, where h is the height of the tree.
To find the minimum number of nodes in a binary tree of height 4, we substitute h = 4 into the formula:
2^(4+1) - 1 = 2^5 - 1 = 32 - 1 = 31
So, the minimum number of nodes in a binary tree of height 4 is 31.
To find the maximum number of nodes in a binary tree of height 4, we consider a complete binary tree. In a complete binary tree, all levels except the last level are completely filled, and the last level is filled from left to right.
In a complete binary tree of height h, the maximum number of nodes can be calculated using the formula 2^(h+1) - 1.
Substituting h = 4 into the formula:
2^(4+1) - 1 = 2^5 - 1 = 32 - 1 = 31
So, the maximum number of nodes in a binary tree of height 4 is also 31.
Therefore, the maximum and minimum number of nodes in a binary tree of height 4 is 31 and 31 respectively.
Option D "31 and 5" is the correct answer.
To find the minimum number of nodes in a binary tree of height 4, we substitute h = 4 into the formula:
2^(4+1) - 1 = 2^5 - 1 = 32 - 1 = 31
So, the minimum number of nodes in a binary tree of height 4 is 31.
To find the maximum number of nodes in a binary tree of height 4, we consider a complete binary tree. In a complete binary tree, all levels except the last level are completely filled, and the last level is filled from left to right.
In a complete binary tree of height h, the maximum number of nodes can be calculated using the formula 2^(h+1) - 1.
Substituting h = 4 into the formula:
2^(4+1) - 1 = 2^5 - 1 = 32 - 1 = 31
So, the maximum number of nodes in a binary tree of height 4 is also 31.
Therefore, the maximum and minimum number of nodes in a binary tree of height 4 is 31 and 31 respectively.
Option D "31 and 5" is the correct 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. Can you explain this answer?.
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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. Can you explain this answer?, a detailed solution 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of 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 4 is.a)16 and 4 respectively.b)32 and 4 respectively.c)15 and 5 respectively.d)31 and 5 respectively.Correct AnswerCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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