We are given an array of n points in the plane, and the problem is to find out the closest pair of points in the array. This problem arises in a number of applications. For example, in air-traffic control, you may want to monitor planes that come too close together, since this may indicate a possible collision. Recall the following formula for distance between two points p and q.

\left \|pq \right \| = \sqrt{(p_{x}-q_{x})^{2}+ (p_{y}-q_{y})^{2}}       
The Brute force solution is O(n^2), compute the distance between each pair and return the smallest. We can calculate the smallest distance in O(nLogn) time using Divide and Conquer strategy. In this post, a O(n x (Logn)^2) approach is discussed. We will be discussing a O(nLogn) approach in a separate post.

Closest Pair of Points : https://www.geeksforgeeks.org/closest-pair-of-points-using-divide-and-conquer-algorithm/