/**
 * Homework 9.
 *
 * #2. Construct a Sudograph solver.
 *
 * Sudograph is a generalization of the popular sudoku puzzles.
 *
 * A single puzzle specifies
 *     a list of nodes, represented by logical variables,
 *     a list of constraints, represented as lists of those same local variables,
 *     a list of colors, which are atomic (atoms or numbers).
 *
 * The objective is to find a solution of the puzzle, which is defined to be
 * an assignment of a color to each node, such that no two nodes in any
 * constraint are assigned the same color.
 * 
 * You should write a predicate called sudograph( Nodes, Constraints, Colors ) to achieve this goal.
 * Be sure to give it exactly this name or the test code below will not work.  The names of the arguments
 * do not matter, just the name of the predicate, i.e., "sudograph".
 */


 /* Here is some code that will help make testing your predicate easier. */
testSudoGraph(1) :-
   Nodes = [A, B, C, D, E, F, G],
   Constraints = [[A, B, C], [B, C, D], [C, D, E], [D, E, F], [E, F, G], [G, A, B]],
   Colors = [red, blue, green, yellow],
   testSudoGraph(Nodes, Constraints, Colors).

/* Sample output:

?- testSudoGraph(1).
Colors: [red, blue, green, yellow]
Nodes:  [red, blue, green, red, blue, green, yellow]
Constraints:
      [red, blue, green]
      [blue, green, red]
      [green, red, blue]
      [red, blue, green]
      [blue, green, yellow]
      [yellow, red, blue]
*/

testSudoGraph(Nodes, Constraints, Colors) :-
   sudograph(
       Nodes,
       Constraints,
       Colors),
   write('Colors: '), write(Colors), nl,
   write('Nodes:  '), write(Nodes), nl,
   write('Constraints: '), nl,
   showConstraints(Constraints).

showConstraints([]).
showConstraints([Constraint | Constraints]) :-
   write('       '), write(Constraint), nl,
   showConstraints(Constraints).