$20\mathrm{.}12$ Project $4$: Map Coloring

Testing is complete. Please alert me if you encounter problems.

Construct a $4$ coloring of a map such that no two neighboring countries have the same color. For this project you will read in a map encoded as a text file. An example Follows:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~AABBBBBCCDDEFGGG~~HHIHHJJJKK~ ~~ABBBBBCCDDEFGGGGHHHIHHJJJKK~ ~AAAAAALLLLLEMMMMMHHHHHHHHHHH~ ~AAAAA~~LLLLEMMMM~~HHHHHHHHHH~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

~ Are not part of any country and do not have to be colored.

Countries will be marked A though Z$.$

While a $4$ coloring of the map might look like:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~$3311111443341333311131122233$~ ~$3311111443341333311131122233$~ ~$3333332222242222211111111111$~ ~$3333332222242222211111111111$~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You are asked to produce a string in the following format:

Color $1$: B$,$ F$,$ H Color $2$: J$,$ L$,$ M Color $3$: A$,$ D$,$ G$,$ K Color $4$: C$,$ E

The grading engine will parse this string to verify your coloring. Valid colorings are not unique.

You must implement the following function:

std::string colormap$($std:string filename$)$

The input is the name of a file $($eg "map.txt$")$ and you return the coloring described above.