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Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:
Note: The height of a tree with a single node is 0.
Note: The height of a tree with a single node is 0.
- a)4 and 15 respectively
- b)3 and 14 respectively
- c)4 and 14 respectively
- d)3 and 15 respectively
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Let T be a binary search tree with 15 nodes. The minimum and maximum p...
The minimum height of a binary search tree will be when tree is full complete tree:
Now, let h be the height of the binary tree, then, 2^{0}+2^{1}+2^{2}+2^{3}+...+2^{h}=2^{h+1}-1 <= n
So, Min height of a binary search tree = log2(n+1) - 1 = log2(15+1) - 1 = 4 - 1 = 3
So, Min height of a binary search tree = log2(n+1) - 1 = log2(15+1) - 1 = 4 - 1 = 3
The maximum height of a binary search tree will be when the tree is fully skewed: (like below)
Max height of the binary search tree = n-1 = 15 - 1 = 14, where the tree is Skewed tree
Therefore, option B
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Let T be a binary search tree with 15 nodes. The minimum and maximum p...
Explanation:
To find the minimum and maximum possible heights of a binary search tree with 15 nodes, we need to understand the properties of a binary search tree. In a binary search tree, the left subtree of a node contains only nodes with values less than the node's value, and the right subtree contains only nodes with values greater than the node's value.
Minimum Height:
A binary search tree with minimum height is a balanced binary search tree. A balanced binary search tree is a tree in which the height of the left and right subtrees of any node differ by at most 1. To minimize the height of the tree, we need to balance the tree as much as possible.
The minimum height of a binary search tree with 15 nodes can be achieved by arranging the nodes in a balanced way. A balanced binary search tree with 15 nodes will have a height of 3.
Maximum Height:
A binary search tree with maximum height is a skewed binary search tree. A skewed binary search tree is a tree in which all the nodes are in one straight line. The maximum height of a binary search tree with 15 nodes can be achieved by arranging the nodes in a skewed way.
A skewed binary search tree with 15 nodes can be either in left-skewed or right-skewed form. In a left-skewed binary search tree, all the nodes are arranged in a straight line going towards the left. In a right-skewed binary search tree, all the nodes are arranged in a straight line going towards the right.
The maximum height of a binary search tree with 15 nodes can be achieved by arranging the nodes in a right-skewed binary search tree. A right-skewed binary search tree with 15 nodes will have a height of 14.
Therefore, the minimum and maximum possible heights of T are 3 and 14 respectively. Hence, option B is the correct answer.
To find the minimum and maximum possible heights of a binary search tree with 15 nodes, we need to understand the properties of a binary search tree. In a binary search tree, the left subtree of a node contains only nodes with values less than the node's value, and the right subtree contains only nodes with values greater than the node's value.
Minimum Height:
A binary search tree with minimum height is a balanced binary search tree. A balanced binary search tree is a tree in which the height of the left and right subtrees of any node differ by at most 1. To minimize the height of the tree, we need to balance the tree as much as possible.
The minimum height of a binary search tree with 15 nodes can be achieved by arranging the nodes in a balanced way. A balanced binary search tree with 15 nodes will have a height of 3.
Maximum Height:
A binary search tree with maximum height is a skewed binary search tree. A skewed binary search tree is a tree in which all the nodes are in one straight line. The maximum height of a binary search tree with 15 nodes can be achieved by arranging the nodes in a skewed way.
A skewed binary search tree with 15 nodes can be either in left-skewed or right-skewed form. In a left-skewed binary search tree, all the nodes are arranged in a straight line going towards the left. In a right-skewed binary search tree, all the nodes are arranged in a straight line going towards the right.
The maximum height of a binary search tree with 15 nodes can be achieved by arranging the nodes in a right-skewed binary search tree. A right-skewed binary search tree with 15 nodes will have a height of 14.
Therefore, the minimum and maximum possible heights of T are 3 and 14 respectively. Hence, option B is the correct answer.
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Let T be a binary search tree with 15 nodes. The minimum and maximum p...
Maximum height will be wen it skewed so (n-1)=14
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Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. Can you explain this answer?
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Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. 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 Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. 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 Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. Can you explain this answer?.
Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. 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 Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. 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 Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. Can you explain this answer?.
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Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are:Note:The height of a tree with a single node is 0.a)4 and 15 respectivelyb)3 and 14 respectivelyc)4 and 14 respectivelyd)3 and 15 respectivelyCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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