Consider a sequence of n real numbers (assume n is even). Partition the n numbers into n/2 pairs (each of the n numbers appears in exactly one of the n/2 pairs) in the following way. For each pair in the partition, compute the sum of its numbers. Denote by the n/2 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-O 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-O notation, its worst-case running time

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