Question

I have an Array (linear field)
with pre sorted numbers

 [1, 2, 3, 4, 5, 6],

but these arra y is shift to the right (k times),

now its

[5,6,1,2,3,4], k = 2

But I don´t know k. Only the array A.

Now I need an Algorithm to find the max in A (with runtime O(logn))

I think its something with binary search, can anyone help me??

Answer 1

The question can be re-stated in terms of finding the “point of discontinuity”, i.e the index of the 6, 1 spot in the array. You can do it iteratively using an approach similar to that of a binary search, like this:

Take an array A and two indexes, low and high, initially set to 0 and A.Length-1. The spot of discontinuity is between low and high.

Divide (low, high) in half. Call the midpoint mid. Compare A[low] to A[mid] and A[mid] to A[high]. If only one pair is ordered correctly, adjust the endpoint: if it’s the low-mid pair that’s ordered, assign low = mid, otherwise assign high = mid. If both intervals are ordered, the answer is A[high].

This runs in O(LogN) because each step reduces the size of the problem in half.