**Minimum Cost Network Problem:** Given some number of cities and,
for each pair of cities, what it would cost to build a power line
between those two cities. It is known that a power generating plant
will be built in one of the given cities (but it does not matter
where). Initially, no power lines have been built. The objective is
to build a lowest-cost, complete network of power lines that connects
all cities to the power plant. A city is connected to the power plant
if, on a 2D map that shows a proposed network (such as the one above
after the "Update" button is clicked), one can place a pencil on the
city and trace a path to the city containing the power plant without
lifting the pencil off the paper and without moving the pencil off a
power line that is contained in the proposed solution.

**Instructions:** First click the "Update" button. You will try to
determine how to find a minimum cost network while restricted to an
environment that is not much different from what a computer program
would operate in. A solution will be obtained iteratively: that is,
there will always be a partial solution of power lines and you will
choose a power line not already in the partial solution by clicking on
the number associated with that power line and then make a test to see
whether it is OK to add it to the partial solution. If it is OK, the
line turns red. If not, the color of the line does not change and the
reason the line is not added to the solution appears in a textfield at
the bottom of the applet. Initially, there are no red lines. A
complete network is achieved when every pair of cities is connected by
a path using only red lines. The cost of the network is shown in a
textfield labeled "Total:". The number of errors made appears in the
textfield labeled "Errors:". New cities can be added by typing a city
name in the textfield to the right of the button labeled "New City:"
and then clicking on the "New City:" button. To have the computer
find an optimal solution click on the "Solve" button. To start over,
click on the "Clear" button.