I have an array of Sorted integers. We can use binary search to find an element . Now if one element of sorted array is interchanged with another element. What would be the best way to find the interchanged element?

It appears that the only method to find such element is regular linear search. You cannot do faster because you basically not searching particular element, you are searching the position when some property is violated (in this case the ordering). As you don't know anything that can help you skip checking some positions you basically need to check all of them. So it will be O(n) — regular linear search.

I am not sure I totally understand the question, anyway If you don't know the both elements, and as the interchange has no "rule". it seems you need at least o(n) to find the interchanged element. (by a simple loop).

If you do know one element (one of the pair) and want to find the other pair. simply binary search the one pair you know, you will find the other in his place.

You do need to do linear search, and worst-case time is linear. But best case time could be log n.

Once you find the first displaced element, you'll know that integer. Therefore, you can do a binary descent to find the position that it should be in. So basically, if one of the two mismatches occurs early, you will save time

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