Create code for determining the smallest possible federation

[joewledger]

Given:

• There is a map that contains the hexagons, planets, and buildings.

When:

• The a set of planets that could compose a federation are provided.

Then:

• One of the smallest possible federations (most importantly the included hexagons) is returned, along with its size

Notes:

• If there are multiple federations that are tied for the smallest, only one needs to be returned
• No validation on the federation needs to be done (this includes checking to see if the player has enough power, and that all the provided planets are owned by the same player).
• Validation should be done to make sure that the provided federation does not intersect with any federations already owned by the same player.

[gretchenwright]

The problem of finding the minimal spanning tree for a provided set of nodes in a graph is the Steiner tree problem. There is a thread in Stack Overflow about approximation algorithms, which includes references to several papers.

https://stackoverflow.com/questions/7685291/construct-a-minimum-spanning-tree-covering-a-specific-subset-of-the-vertices