Water For Everyone

Here's another problem we can model with graphs:

• We've got a set of nodes representing campus buildings. One of them is a pumping station.
• We've got edges between them representing possible places for building water pipes.
• We need to create a network of pipes that link all the buildings together, so we can supply all of them with water.
• Because of differences in the ground and distances, etc., there are different costs associated with digging pipes between different pairs of buildings: w(u,v) is the cost for constructing a pipe between buildings u and v.

Our task is to dig a set of pipes so that:

• All buildings get water.
• Cost is minimized.

Answer?