title: Closest pair of points brute-force; Why O(n^2)?
body: <p>I feel stupid for asking this question, but...</p>
  
  <p>For the "closest pair of points" problem (see <a href="https://en.wikipedia.org/wiki/Closest_pair_of_points_problem" rel="nofollow noreferrer">this</a> if unfamiliar with it), why is the worst-case running time of the brute-force algorithm O(n^2)?</p>
  
  <p>If say n = 4, then there would only be 12 possible pair of points to compare in the search space, if we also consider comparing two points from either direction. If we don't compare two points twice, then it's going to be 6.</p>
  
  <p>O(n^2) doesn't add up to me.</p>