If n elements are sorted in a balanced binary search tree. What would be the asymptotic complexity to search a key in the tree? a. O(n) b. O(1) c. O(logn) d. O(nlogn)

The correct answer is c. O(logn).

Here's why:

A balanced binary search tree is a binary tree in which the depth of the two subtrees of every node never differ by more than 1. This means that the tree is as compact as possible, with the smallest possible maximum depth.

When you search for a key in such a tree, you start at the root and at each step, you go either to the left child or the right child, depending on whether the key you're looking for is smaller or larger than the key of the current node.

This means that in each step, you discard about half of the remaining part of the tree. Therefore, the number of steps you need to find a key is proportional to the logarithm (base 2) of the number of elements in the tree.

Hence, the time complexity of searching in a balanced binary search tree is O(logn).