kthtree problem: Given a directed tree T, each vertex u in the tree T has a weight w(u); each edge (u,v) of the tree also has a non-negative edge length d(u,v). Each vertex u of the directed tree T can be regarded as a customer, and its service demand is w(u). The edge length d(u,v) of each edge (u,v) can be regarded as the transportation cost. If there is no service agency at vertex u, the service transfer cost to transfer the service demand at vertex u along the edge (u,v) of the directed tree to the service agency at vertex v is w(u)*d(u,v). A service agency has been set up at the root of the tree. Now we need to add k service agencies in the tree T to minimize the service transfer cost of the entire tree T.
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