title: Algorithm to determine if array contains n...n+m?
body: <p>I saw this question on Reddit, and there were no positive solutions presented, and I thought it would be a perfect question to ask here. This was in a thread about interview questions:</p>
  <blockquote>
  <p>Write a method that takes an int array of size m, and returns (True/False) if the array consists of the numbers n...n+m-1, all numbers in that range and only numbers in that range. The array is not guaranteed to be sorted. (For instance, {2,3,4} would return true. {1,3,1} would return false, {1,2,4} would return false.</p>
  <p>The problem I had with this one is that my interviewer kept asking me to optimize (faster O(n), less memory, etc), to the point where he claimed you could do it in one pass of the array using a constant amount of memory. Never figured that one out.</p>
  </blockquote>
  <p>Along with your solutions please indicate if they assume that the array contains unique items. Also indicate if your solution assumes the sequence starts at 1. (I've modified the question slightly to allow cases where it goes 2, 3, 4...)</p>
  <p><strong>edit:</strong> I am now of the opinion that there does not exist a linear in time and constant in space algorithm that handles duplicates. Can anyone verify this?</p>
  <p>The duplicate problem boils down to testing to see if the array contains duplicates in O(n) time, O(1) space. If this can be done you can simply test first and if there are no duplicates run the algorithms posted. So can you test for dupes in O(n) time O(1) space?</p>