Consider a sequence of real numbers (assume is even). We are interested in partitioning the numbers into pairs (that is, each of the numbers appears in exactly one of the pairs) in the following way. For each pair in the partition, compute the sum of its numbers. Denote by the sums. The goal is to find the partition that minimizes the maximum sum. (a) Describe concisely in English the idea of a brute-force algorithm for solving this problem, and provide, using big- notation, the worst-case running time of your algorithm. (b) Establish a mathematical result that will allow you to design a worst-case polynomial-time algorithm for the problem, and prove the result. (c) Describe the polynomial-time algorithm and provide, using big- notation, its worst-case running time.