What is the time complexity (worst case) of a binary search in an array of size n?

The worst-case time complexity of a binary search in an array of size n is O(log n).

Here's a step-by-step explanation:

1. Binary search begins by comparing the middle element of the array with the target value.

2. If the target value matches the middle element, its position in the array is returned.

3. If the target value is less or more than the middle element, the search continues on the lower or upper half of the array respectively, ignoring the other half.

4. This process continues, eliminating half of the elements, and comparing the target value with the middle element of the remaining elements until the target value is either found or until the remaining half is empty.

5. This continual halving of the search space makes the time complexity of binary search logarithmic, hence O(log n).