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Consider a binary tree with the following more conditions :
Condition 1: The elements present in the left sub-tree of a specific node are smaller than that node and elements present in the right sub-tree of a specific node are greater than that node.
Condition 2: The tree is always balanced i.e. the height of the left subtree and right sub-tree is approximately the same. (maximum differ by 1)
What is the worst-case time complexity to run a membership test for an element on this tree?
- a)O(n)
- b)O(logn)
- c)O(n2)
- d)O(nlogn)
Correct answer is option 'B'. Can you explain this answer?
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Consider a binary tree with the following more conditions :Condition ...
The tree is nothing but a balanced BST where the worst case time to find an element = O(logn)
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Consider a binary tree with the following more conditions :Condition ...
Explanation:
Binary Search Tree (BST):
- In a balanced BST, the height of the left subtree and right subtree is approximately the same, with a maximum difference of 1.
- This property helps in reducing the time complexity of search operations.
Worst-case Time Complexity:
- In a balanced BST, the worst-case time complexity to run a membership test for an element is O(logn).
- This is because at each step of the search process, we are able to discard half of the remaining nodes in the tree.
- As a result, the height of the tree plays a crucial role in determining the time complexity of the search operation.
Comparison with Other Options:
- Option 'A' (O(n)) would be the time complexity if the tree was unbalanced, as in the worst case scenario, we would have to traverse through all n nodes.
- Option 'C' (O(n^2)) and Option 'D' (O(nlogn)) are not applicable for a balanced BST, as the time complexity would be much lower due to the balanced nature of the tree.
Therefore, the correct answer is option 'B' (O(logn) ).
Binary Search Tree (BST):
- In a balanced BST, the height of the left subtree and right subtree is approximately the same, with a maximum difference of 1.
- This property helps in reducing the time complexity of search operations.
Worst-case Time Complexity:
- In a balanced BST, the worst-case time complexity to run a membership test for an element is O(logn).
- This is because at each step of the search process, we are able to discard half of the remaining nodes in the tree.
- As a result, the height of the tree plays a crucial role in determining the time complexity of the search operation.
Comparison with Other Options:
- Option 'A' (O(n)) would be the time complexity if the tree was unbalanced, as in the worst case scenario, we would have to traverse through all n nodes.
- Option 'C' (O(n^2)) and Option 'D' (O(nlogn)) are not applicable for a balanced BST, as the time complexity would be much lower due to the balanced nature of the tree.
Therefore, the correct answer is option 'B' (O(logn) ).
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Consider a binary tree with the following more conditions :Condition 1: The elements present in the left sub-tree of a specific node are smaller than that node and elements present in the right sub-tree of a specific node are greater than that node.Condition 2: The tree is always balanced i.e. the height of the left subtree and right sub-tree is approximately the same. (maximum differ by 1)What is the worst-case time complexity to run a membership test for an element on this tree?a)O(n)b)O(logn)c)O(n2)d)O(nlogn)Correct answer is option 'B'. Can you explain this answer?
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Consider a binary tree with the following more conditions :Condition 1: The elements present in the left sub-tree of a specific node are smaller than that node and elements present in the right sub-tree of a specific node are greater than that node.Condition 2: The tree is always balanced i.e. the height of the left subtree and right sub-tree is approximately the same. (maximum differ by 1)What is the worst-case time complexity to run a membership test for an element on this tree?a)O(n)b)O(logn)c)O(n2)d)O(nlogn)Correct answer is option 'B'. 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 binary tree with the following more conditions :Condition 1: The elements present in the left sub-tree of a specific node are smaller than that node and elements present in the right sub-tree of a specific node are greater than that node.Condition 2: The tree is always balanced i.e. the height of the left subtree and right sub-tree is approximately the same. (maximum differ by 1)What is the worst-case time complexity to run a membership test for an element on this tree?a)O(n)b)O(logn)c)O(n2)d)O(nlogn)Correct answer is option 'B'. 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 binary tree with the following more conditions :Condition 1: The elements present in the left sub-tree of a specific node are smaller than that node and elements present in the right sub-tree of a specific node are greater than that node.Condition 2: The tree is always balanced i.e. the height of the left subtree and right sub-tree is approximately the same. (maximum differ by 1)What is the worst-case time complexity to run a membership test for an element on this tree?a)O(n)b)O(logn)c)O(n2)d)O(nlogn)Correct answer is option 'B'. Can you explain this answer?.
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