Worst case efficiency of binary search is

The worst case efficiency of binary search is O(log n).

Here's the step by step explanation:

1. Binary search is an algorithm that is used to find the position of a specific value within a sorted array. It does this by repeatedly dividing the array in half.

2. If the value of the search key is less than the item in the middle of the interval, narrow the interval to the lower half. Otherwise, narrow it to the upper half.

3. Repeatedly check until the value is found or the interval is empty.

4. The worst case scenario for a binary search is when the desired value is not in the array, or is the last possible match in the array.

5. In this case, the algorithm has to go through all the levels of the binary tree to find the value.

6. The number of levels in the binary tree is log(n) (base 2), where n is the number of elements in the array.

7. Therefore, the worst case time complexity of binary search is O(log n).

8. This means that in the worst case, the binary search algorithm would take log(n) steps to run to completion.