using System;
using System.Threading.Tasks;

class GraphColoringProblem
{
    // Number of vertices in the graph
    const int V = 4;

    // A utility function to check if the current color assignment is safe for vertex v
    static bool IsSafe(int v, bool[,] graph, int[] color, int c)
    {
        for (int i = 0; i < V; i++)
        {
            if (graph[v, i] && c == color[i])
                return false;
        }
        return true;
    }

    // A parallel utility function to solve m coloring problem
    static bool GraphColoringUtilParallel(bool[,] graph, int m, int[] color, int v)
    {
        if (v == V)
            return true;

        bool result = false;

        Parallel.For(1, m + 1, (c, state) =>
        {
            if (IsSafe(v, graph, color, c))
            {
                color[v] = c;

                if (GraphColoringUtilParallel(graph, m, color, v + 1))
                {
                    result = true;
                    state.Break(); // Exit parallel loop as a solution is found
                }
                if (result == false)
                    color[v] = 0; // Backtrack
            }
        });

        return result;
    }

    // This function solves the m Coloring problem using parallelism
    static bool SolveGraphColoring(bool[,] graph, int m)
    {
        int[] color = new int[V];
        for (int i = 0; i < V; i++)
            color[i] = 0;

        if (!GraphColoringUtilParallel(graph, m, color, 0))
        {
            Console.WriteLine("Solution does not exist");
            return false;
        }

        PrintSolution(color);
        return true;
    }

    // A utility function to print solution
    static void PrintSolution(int[] color)
    {
        Console.WriteLine("Solution Exists: Following are the assigned colors");
        for (int i = 0; i < V; i++)
            Console.Write(" " + color[i] + " ");
        Console.WriteLine();
    }

    // Driver code
    static void Main(string[] args)
    {
        /* Create following graph and test whether it is 3 colorable
           (3)---(2)
            |   / |
            |  /  |
            | /   |
           (0)---(1)
        */
        bool[,] graph = {
            { false, true, true, true },
            { true, false, true, false },
            { true, true, false, true },
            { true, false, true, false }
        };

        // Number of colors
        int m = 3;

        // Function call
        SolveGraphColoring(graph, m);
    }
}