title: Given list of 2d points, find the point closest to all other points
body: <pre><code>Input: list of 2d points (x,y) where x and y are integers.
  
  Distance: distance is defined as the Manhattan distance. 
      ie:
      def dist(p1,p2) 
           return abs(p1.x-p2.x) + abs(p1.y - p2.y)
  </code></pre>
  
  <p>What is an efficient algorithm to find the point that is closest to all other points. </p>
  
  <p>I can only think of a brute force O(n^2) solution:</p>
  
  <pre><code>minDist=inf
  bestPoint = null
  for p1 in points:
      dist = 0
      for p2 in points:
          dist+=distance(p1,p2)
      minDist = min(dist,minDist)
      bestPoint = argmin(p1, bestPoint)
  </code></pre>
  
  <p>basically look at every pair of points.</p>