What is the time complexity of deleting a node from a binary search tree in the

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Question: What is the time complexity of deleting a node from a binary search tree in the average case?

Options:

Correct Answer: O(log n)

Solution:

In the average case, deleting a node from a balanced binary search tree has a time complexity of O(log n).

What is the time complexity of deleting a node from a binary search tree in the average case?

What is the time complexity of deleting a node from a binary search tree in the average case?

Step 1: Understand what a binary search tree (BST) is. A BST is a data structure where each node has at most two children, and the left child is less than the parent node, while the right child is greater.
Step 2: Know that deleting a node from a BST involves finding the node you want to delete first.
Step 3: In a balanced BST, the height of the tree is log(n), where n is the number of nodes. This means that on average, it takes log(n) steps to find a node.
Step 4: After finding the node, there are three cases to consider for deletion: deleting a leaf node, deleting a node with one child, and deleting a node with two children.
Step 5: Each of these cases can be handled in constant time (O(1)) after finding the node, which is already O(log n).
Step 6: Therefore, the overall time complexity for deleting a node in the average case is O(log n).

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