What is the time complexity of inserting an element into a binary search tree (B

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Question: What is the time complexity of inserting an element into a binary search tree (BST) in the average case?

Options:

Correct Answer: O(log n)

Solution:

Inserting an element into a binary search tree (BST) has an average-case time complexity of O(log n).

What is the time complexity of inserting an element into a binary search tree (BST) in the average case?

What is the time complexity of inserting an element into a binary search tree (BST) 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 when we insert an element into a BST, we start at the root node.
Step 3: Compare the value of the element we want to insert with the value of the current node.
Step 4: If the value is less, we move to the left child; if it's greater, we move to the right child.
Step 5: Repeat steps 3 and 4 until we find an empty spot (null) where we can insert the new element.
Step 6: In a balanced BST, the height of the tree is log(n), where n is the number of nodes. This means we will make about log(n) comparisons to find the right spot for the new element.
Step 7: Therefore, the average-case time complexity for inserting an element into a BST is O(log n).

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