Consider the problem of finding the closest pair of points out of a set of points in a 2 dimensional space. This problem is discussed at a high level in Section 5.5 of the text. This description can be imprecise at omit important details. In this problem you will fill in the details omitted and add precision. 1. (I point) Express this problem formally with input and output conditions. 2. (3 points) The algorithm in the text divides the problem into halves around the median point according to x-coordinate. Recursion occurs on the left and right halves but we must still consider that the closest points cross the dividing line. Let be the distance between the closest points in the left partition and let r be the distance between the closest points in the right partition. Then let = min{ , Prove this theorem: Theorem 1. If u = (Xu,Yu) and v = (xu, yu) are the closest points such that u is on the left side of the partition and v is on the right side of the partition then both u and v are within of the partitioning line where is the minimum distance betueen points in the left half and points in the right half