Finding the Closest Pair of Points Problem: Given n ordered pairs (x_{1} , y_{1}), (x_{2} , y_{2}), ... , (x_{n} , y_{n}), 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 = (n^{2}) distinct pairs of points, it follows that the running time of this algorithm is (n^{2}).