Dr. Carter, a scientist, is aiming to sequence a set of genes. The set is represented by a sequence of natural numbers gi, where gi takes the values 1,...,n, i {1...n}, and where n denotes the length of the sequence. Dr. Carter seeks the most efficient order to read the DNA fragments, minimizing redundancy and optimizing sequencing efforts. Given a sequence G = [g1,g2,...,gn], there is a cost associated with processing every pair (gi,gj) for 1 i,j n of genes. The pairwise cost between the genes is represented as a symmetric matrix C Rnn >0 where the entries in the main diagonal are set to . Let C(i, j) denote the cost associated with the pair (gi,gj). Given a sequence of natural numbers, s P(n), where P(n) denotes the set of all permutations of the first n natural numbers, let the cost associated with s be denoted by cost(s). Then cost(s) can be computed by