15.4 Closest Pair

Divide and conquer approach for finding the distance between the two closest points.

• Sort the points along the x-axis,
• Partition the region into two parts R_left and R_right having equal number of points, and recursively apply the algorithm on the sub-regions
• Derive the minimal distance in the original region.

  The closest pair resides in the left region, the right region, or across the borderline.

• For the borderline case, consider the points at distance = min(_left,_right) from the dividing line, where _left and _right are the minimal distances for the left and right regions, respectively.
• Compare each point along the border with neighbors at distance y = ± (at most 6 neighbors)