Explain the time complexity of exponential search.

Exponential search is a searching algorithm that is used to find a specific element in a sorted array. It is an improvement over binary search, especially when the size of the array is unknown or unbounded.

The time complexity of exponential search can be explained as follows:

1. First, we need to determine the range in which the target element may exist. To do this, we start with an index, typically 0, and keep doubling it until we find an index that is either out of bounds or contains an element greater than the target element. This step takes O(log n) time, where n is the size of the array.

2. Once we have determined the range, we perform a binary search within that range to find the target element. Binary search takes O(log n) time as well.

3. Therefore, the overall time complexity of exponential search is O(log n + log n), which simplifies to O(log n).

It is important to note that exponential search is efficient when the target element is closer to the beginning of the array. This is because the range is determined by doubling the index, which means the range grows exponentially. As a result, the time complexity of exponential search can be significantly better than binary search in certain scenarios.

However, exponential search may not be the best choice when the target element is located towards the end of the array. In such cases, the time complexity can approach O(n), as the range may cover a large portion of the array.

In conclusion, the time complexity of exponential search is O(log n), making it an efficient searching algorithm for sorted arrays, especially when the target element is closer to the beginning.