Finding the Closest Pair of Points Problem: Given n ordered pairs (x1 , y1), (x2 , y2), ... , (xn , yn), find the distance between the two points in the set that are closest together. The brute force algorithm is as follows: Iterate through all possible pairs of points, calculating the distance between each of these pairs. Any time you see a distance shorter than the shortest distance seen, update the shortest distance seen. Since computing the distance between two points takes O(1) time, and there are a total of = (n2) distinct pairs of points, it follows that the running time of this algorithm is (n2).
