Solution 

This task can be solved by dynamic programming. Let us root the tree by choosing one of the
leaves as a root. Then we can process the tree in a bottom-up order. For each vertex we should
compute two solutions for a sub-tree rooted in the given vertex:
 	- the optimal solution, together with the gems g used for the given vertex;
 	- the optimal solution, assuming, that the given vertex is modelled by a gem 
 	  different from g.