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Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:
• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node
• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.
Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.
Correct answer is '94'. Can you explain this answer?
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Consider a new data structure which is named as A- tree. Consider the...
Let h(n) be the minimum no. of nodes required by AVL tree of height n.
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for height (O) h(n) = 1 (root node)
height (l) h(n) = 2 height (2) h(2) 4
Also, h(n) = h(n-1) + h(N-2) + 1
for height 6.
h(3) = h(1) + h(2) + 1 = 7
h(4) = h(3) + h(2) + 1 = 12
h(5) = h(4) + h(3) + 1 = 20
h(6) = h(5) + h(4) + 1 = 20 + 12 + 1 = 33
value of a = 33
Also, no. of Nodes will be maximum when tree is a complete binary tree
No. of Nodes in a complete tree with height (n) = 2n+1 - 1
= 27 – 1 = 127
value of b = 127
|a-b| = 127 – 33 = 94
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Consider a new data structure which is named as A- tree. Consider the...
Introduction:
The A-tree is a new data structure with specific properties. It ensures that all nodes in the left subtree of a particular node are smaller than that node, and all nodes in the right subtree are larger. Additionally, the height of the tree is balanced, meaning the height of the left and right subtrees differ by almost one.
Determining the minimum number of nodes:
To determine the minimum number of nodes required to generate an A-tree of height 6, we need to consider the properties of the tree. The height of the tree is 6, which means there are 6 levels from the root to the deepest leaf.
Calculating the minimum number of nodes:
To calculate the minimum number of nodes, we can use the formula: 2^(h+1) - 1, where h is the height of the tree. Plugging in the value of h=6, we get:
2^(6+1) - 1 = 2^7 - 1 = 128 - 1 = 127
So, the minimum number of nodes required to generate an A-tree of height 6 is 127.
Determining the maximum number of nodes:
To determine the maximum number of nodes that can be in an A-tree of height 6, we need to consider the balanced property of the tree. Since the height of the left and right subtrees differ by almost one, the maximum number of nodes can be achieved when the tree is perfectly balanced.
Calculating the maximum number of nodes:
To calculate the maximum number of nodes in a perfectly balanced tree, we can use the formula: 2^(h+1) - 1, where h is the height of the tree. Plugging in the value of h=6, we get:
2^(6+1) - 1 = 2^7 - 1 = 128 - 1 = 127
So, the maximum number of nodes that can be in an A-tree of height 6 is 127.
Calculating the difference:
To find the difference between the minimum and maximum number of nodes, we subtract the minimum from the maximum:
127 - 127 = 0
Therefore, the difference between the minimum and maximum number of nodes in an A-tree of height 6 is 0.
Conclusion:
The minimum number of nodes required to generate an A-tree of height 6 is 127, and the maximum number of nodes that can be in an A-tree of height 6 is also 127. Therefore, the difference between the minimum and maximum number of nodes is 0.
The A-tree is a new data structure with specific properties. It ensures that all nodes in the left subtree of a particular node are smaller than that node, and all nodes in the right subtree are larger. Additionally, the height of the tree is balanced, meaning the height of the left and right subtrees differ by almost one.
Determining the minimum number of nodes:
To determine the minimum number of nodes required to generate an A-tree of height 6, we need to consider the properties of the tree. The height of the tree is 6, which means there are 6 levels from the root to the deepest leaf.
Calculating the minimum number of nodes:
To calculate the minimum number of nodes, we can use the formula: 2^(h+1) - 1, where h is the height of the tree. Plugging in the value of h=6, we get:
2^(6+1) - 1 = 2^7 - 1 = 128 - 1 = 127
So, the minimum number of nodes required to generate an A-tree of height 6 is 127.
Determining the maximum number of nodes:
To determine the maximum number of nodes that can be in an A-tree of height 6, we need to consider the balanced property of the tree. Since the height of the left and right subtrees differ by almost one, the maximum number of nodes can be achieved when the tree is perfectly balanced.
Calculating the maximum number of nodes:
To calculate the maximum number of nodes in a perfectly balanced tree, we can use the formula: 2^(h+1) - 1, where h is the height of the tree. Plugging in the value of h=6, we get:
2^(6+1) - 1 = 2^7 - 1 = 128 - 1 = 127
So, the maximum number of nodes that can be in an A-tree of height 6 is 127.
Calculating the difference:
To find the difference between the minimum and maximum number of nodes, we subtract the minimum from the maximum:
127 - 127 = 0
Therefore, the difference between the minimum and maximum number of nodes in an A-tree of height 6 is 0.
Conclusion:
The minimum number of nodes required to generate an A-tree of height 6 is 127, and the maximum number of nodes that can be in an A-tree of height 6 is also 127. Therefore, the difference between the minimum and maximum number of nodes is 0.
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Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer?
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Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. 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 Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer?.
Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. 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 Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer?.
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Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer?, a detailed solution for Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer? has been provided alongside types of Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider a new data structure which is named as A- tree. Consider the properties of new discovered A-tree:• The nodes are inserted in such a way that all the nodes in the left subtree of a particular node are smaller than that node. Also, all the nodes in the right subtree of a particular node are larger than that node• The height of the tree is balanced in such a way that the height of the left subtree and height of the right subtree differ by almost one.Let the minimum number of nodes required to generate an A- tree of height 6 = 'a' and the maximum number of nodes which can be there in A- tree of height 6 = 'b' , find |a-b| = ________.Correct answer is '94'. Can you explain this answer? tests, examples and also practice GATE tests.
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