Given an array part is sorted part is not, How to find a particular element?

Question

To be honest this was an interview question. I know if the array is totally sorted then I could use binary search which is O(logN). But now the condition is:

1. Some part is sorted while others are not.
2. We don't know which is part is sorted nor how long this part is.

I could only think of a full array scan solution which is O(N). But interviewer said there is a O(logN) solution. Please help.

Answer 1

Either you are not telling the full question, or your the interviewer is totally wrong. Here is an example that fits your description.

[1, 2, 3, 4, 5, 9, -1, 8, 0, 8, -2, 4, 7, 6]

As you see the first 5 elements are sorted. But it does not help you at al to locate where the 6 is in my array. You will still need O(n) to find an element.

Putting your question to an extreme, what if the sorted part consists of 2 elements and unsorted part is n-2 elements? Can he still search it in O(log n ) ?

Just an advise to you. Once you hear something that you can't actually believe, ask a person to explain you an idea and think of a counter example that makes this idea useless.

Answer 2

The interviewer is wrong. Without knowing where the sorted part begins, and its size, you cannot search it in O(logN).