Consider the travelling salesman problem with five cities. The cities are called A, B, C, D, and E. A cycle is a sequence of cities that has the following properties: . The first and last city is the same. . Every other city appears exactly once in the sequence. Therefore, AECBDA is a cycle, while ABDEDCA and ABCED are not. Here is the mileage chart for the cities. A B C D E A 185 119 152 133 B 121 150 200 C 174 120 199 E (a) Complete the chart. (b) Start at city A and use the greedy algorithm to find a cycle. In this context, greedy algorithm means you pick the cheapest link at each step. The length of the cycle should be 773. (c) Start at city B and use the greedy algorithm to find a cycle (722). Explain why this gives a cycle starting at A. (Sketch a picture for Pete's sake!) (d) Repeat the previous question using city C, city D, and city E as starting points. (e) What is the shortest cycle you have found? (It should be 722.) (f) Is shortest cycle 722? If so, explain why. If not, find a shorter cycle