Build a tree from differences

You will write the three parts of a program that builds a tree from a table of differences, the UPGMA method of the lesson.

The idea. Join the closest pair of groups. The new group is at half their distance. Its distance to every other group is the average of the two old distances, weighted by the size of the groups. Repeat until one group is left.

Your tasks.

1. Finish closest. It gives the pair of groups with the smallest difference.
2. Finish average_distance. It gives the distance from a new group to another group.
3. Finish build_tree. It gives the list of joins as (group, group, height).