Here's an instance of the topcoder problem.
10 51 93 52 13 51 94 52 51 52 12 52 10 52 15 51 92 51 93 52 19 51 91 51 92 52 12 51 95 52 11
Hint: This is a great time to use your shell and vi tools: What are the unique nodes? How best to represent notes that Bob must sing and that Alice must sing? What's the best way to calculate the weights of the edges?