title: Finding the smallest positive number in O(nlogn) and O(logn) additional space
body: <p>This is a slightly modified version of a well known problem, but I can't seem to figure this one out.</p>
  
  <blockquote>
    <p>We are given an array of size n that contains unsorted sequence of positive numbers with no duplicates. I'm trying to find the smallest positive number that is not contained in the array, but I can't sort or edit the array in any way. The whole thing should be in O(nlogn) time and O(logn) space complexity.</p>
  </blockquote>
  
  <p>All the solutions I can think of are in polynomial time complexity.</p>