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What is the worst case time complexity for search, insert and delete operations in a general Binary Search Tree?
  • a)
    O(n) for all
  • b)
    O(Logn) for all
  • c)
    O(Logn) for search and insert, and O(n) for delete
  • d)
    O(Logn) for search, and O(n) for insert and delete
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
What is the worst case time complexity for search, insert and delete o...
In skewed Binary Search Tree (BST), all three operations can take O(n). See the following example BST and operations.
    10
  /
20
 /
 30
40
Search 40. 
Delete 40
Insert 50.
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Most Upvoted Answer
What is the worst case time complexity for search, insert and delete o...
Binary Search Tree

A Binary Search Tree (BST) is a binary tree data structure where each node has at most two children, and the value of each node is greater than or equal to the values in its left subtree and less than or equal to the values in its right subtree.

Worst Case Time Complexity

The worst case time complexity for search, insert, and delete operations in a general Binary Search Tree is O(n) for all.

Search Operation: The worst case time complexity for searching an element in a Binary Search Tree occurs when the tree is skewed. In a skewed tree, all the nodes either have only left or right child, and the height of the tree becomes equal to the number of nodes. In this case, the search operation will take O(n) time complexity.

Insert Operation: The worst case time complexity for inserting an element in a Binary Search Tree occurs when the tree is skewed. In a skewed tree, all the nodes either have only left or right child, and the height of the tree becomes equal to the number of nodes. In this case, the insert operation will take O(n) time complexity.

Delete Operation: The worst case time complexity for deleting an element in a Binary Search Tree occurs when the tree is skewed. In a skewed tree, all the nodes either have only left or right child, and the height of the tree becomes equal to the number of nodes. In this case, the delete operation will take O(n) time complexity.

Conclusion

In conclusion, the worst case time complexity for search, insert, and delete operations in a general Binary Search Tree is O(n) for all, which occurs when the tree is skewed. It is essential to balance the tree to avoid the worst case time complexity.
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