Find an element in an infinite length sorted array

Question

Given an infinite length sorted array having both positive and negative integers. Find an element in it.

EDIT
All the elements in the array are

Answer 1

You can apply binary search more or less directly with a small modification. This will roughly correspond to your Approach 2.

Basically, pick some number B and set A to 0, then check if the element you're looking for is between A and B. If it is, perform the usual kind of binary search in these boundaries, otherwise set B=A and A=2*A and repeat. This will take O(log(M)), where M is the position of the element you're looking for in the array.