Assume that you are given n white and n black dots, lying on a line, equally spaced The dots appear in any order of black and white, see the example picture below. We need an algorithm which connects each black dot with a (different) white dot, so that the total length of wires used to form such connected pairs is minimal. The length of wire used to connect two dots is equal to their distance along the line. (a) Someone has proposed the following algorithm: start by connecting the closest pair of a black and a white dot. Repeat. Give an example where such an algorithm fails to produce an optimal solution. (b) Design an algorithm which produces an optimal solution