title: In the closest pair of points divide and conquer algorithm, what is the significance of sorting the "strip" by the points' y values?
body: <p>I believe I understand the algorithm quite clearly, except for the step where you look to see if there's any points that are close by looking across the division and create a strip where points within the strip are candidates.</p>
  
  <p>But then the algorithm states to sort the points by their y coordinates and then check each other point in the strip to find if there is a smaller distance than the one previously found. It basically sounds like you brute force within the strip.</p>
  
  <p>For example, here's what <em>Introduction to Algorithms</em> states:</p>
  
  <p><img src="https://i.stack.imgur.com/Wpkum.png" alt="enter image description here"></p>
  
  <p>So it seems you just take each point and compare it against all the others to find the closest points? Why is it necessary to sort by y value then? You already have them sorted by x, why not brute force with that?</p>