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What is the time complexity of searching for an element in a binary search tree?
- a)O(1)
- b)O(n)
- c)O(log n)
- d)O(n log n)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the time complexity of searching for an element in a binary se...
The time complexity of searching for an element in a binary search tree is O(log n) in the average case, where n is the number of nodes in the tree.
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What is the time complexity of searching for an element in a binary se...
Time Complexity of Searching in a Binary Search Tree
Introduction:
In a binary search tree (BST), searching for an element involves comparing the target value with the value of the current node and then deciding whether to search the left subtree, the right subtree, or if the current node is the target element.
Time Complexity Analysis:
- The time complexity of searching in a binary search tree is determined by the height of the tree.
- In the best-case scenario, when the tree is balanced, the time complexity is O(log n), where n is the number of nodes in the tree.
- In the worst-case scenario, when the tree is skewed, the time complexity can be O(n), where n is the number of nodes in the tree.
Explanation:
- The reason for the time complexity being O(log n) in the best-case scenario is that at each step of the search, we are eliminating half of the nodes based on the comparison of the target value with the current node's value.
- This results in a logarithmic time complexity as the height of the tree increases at a slower rate compared to the number of nodes.
- On the other hand, in the worst-case scenario where the tree is skewed, the search may have to traverse through all the nodes in a linear fashion, resulting in a time complexity of O(n).
Conclusion:
- The time complexity of searching in a binary search tree is typically O(log n) in the best case and O(n) in the worst case, depending on the balance of the tree.
Introduction:
In a binary search tree (BST), searching for an element involves comparing the target value with the value of the current node and then deciding whether to search the left subtree, the right subtree, or if the current node is the target element.
Time Complexity Analysis:
- The time complexity of searching in a binary search tree is determined by the height of the tree.
- In the best-case scenario, when the tree is balanced, the time complexity is O(log n), where n is the number of nodes in the tree.
- In the worst-case scenario, when the tree is skewed, the time complexity can be O(n), where n is the number of nodes in the tree.
Explanation:
- The reason for the time complexity being O(log n) in the best-case scenario is that at each step of the search, we are eliminating half of the nodes based on the comparison of the target value with the current node's value.
- This results in a logarithmic time complexity as the height of the tree increases at a slower rate compared to the number of nodes.
- On the other hand, in the worst-case scenario where the tree is skewed, the search may have to traverse through all the nodes in a linear fashion, resulting in a time complexity of O(n).
Conclusion:
- The time complexity of searching in a binary search tree is typically O(log n) in the best case and O(n) in the worst case, depending on the balance of the tree.
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What is the time complexity of searching for an element in a binary search tree?a)O(1)b)O(n)c)O(log n)d)O(n log n)Correct answer is option 'C'. Can you explain this answer?
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