Bicoloring

The Problem
In 1976 the “Four Color Map Theorem" was proven with the assistance of a computer. This theorem states that every map can be colored using only four colors, in such a way that no region is colored using the same color as a neighbor region.

Here you are asked to solve a simpler similar problem. You have to decide whether a given arbitrary connected graph can be bi-colored. That is, if one can assign colors (from a palette of two) to the nodes in such a way that no two adjacent nodes have the same color. To simplify the problem you can assume:

  • No node will have an edge to itself.
  • The graph is non-directed. That is, if a node a, is said to be connected to a node b, then you must assume that b is connected to a.
  • The graph will be strongly connected. That is, there will be at least one path from any node to any other node.

Input 

The input consists of several test cases. Each test case starts with a line containing the number n ( 1 < n < 200) of different nodes. The second line contains the number of edges l. After this, l lines will follow, each containing two numbers that specify an edge between the two nodes that they represent. A node in the graph will be labeled using a number a ( ). An input with n = 0 will mark the end of the input and is not to be processed.

 

Output 

You have to decide whether the input graph can be bi-colored or not, and print it as shown below.

 

Sample Input

3
3
0 1
1 2
2 0
9
8
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0

 

Sample Output

NOT BICOLORABLE.
BICOLORABLE.

 

using System;

using System.Collections.Generic;

using System.Text;

using System.IO;

using System.Collections;

using System.Text.RegularExpressions;

 

namespace ConsoleApplication1

{

    class Edge

    {

        public int a = 0;

        public int b = 0;

    }

    class Program

    {

        static void Main(string[] args)

        {

            Console.Write("Enter number of nodes: ");

            int numberOfNodes = int.Parse(Console.ReadLine().ToString());

            int[] node = new int[numberOfNodes];

            //Initializing the node array to -1

            for (int i = 0; i < numberOfNodes; i++)

            {

                node[i] = -1;

            }

            Console.Write("Enter number of edges: ");

            int numberOfEdges = int.Parse(Console.ReadLine().ToString());

            Edge[] edg = new Edge[numberOfEdges];

            Console.WriteLine("Enter pairs of node connected separated by a space:");

            for (int i = 0; i < numberOfEdges; i++)

            {

                edg[i] = new Edge();

                Console.Write("");

                string inputStr = Console.ReadLine();

                Regex reg = new Regex(" ");

                int flag = 0;

                foreach (string val in reg.Split(inputStr))

                {

                    if (flag == 0)

                    {

                        edg[i].a = int.Parse(val);

                        flag = 1;

                    }

                    else

                    {

                        edg[i].b = int.Parse(val);

                    }

                }

            }

            bool check = true;

            //Processing the edges for bi-coloring

            for (int i = 0; i < numberOfEdges; i++)

            {

                if (node[edg[i].a] == -1 && node[edg[i].b] == -1)

                {

                    node[edg[i].a] = 0;

                    node[edg[i].b] = 1;

                }

                else if (node[edg[i].a] == -1 && node[edg[i].b] > -1)

                {

                    if (node[edg[i].b] == 0)

                    {

                        node[edg[i].a] = 1;

                    }

                    else

                    {

                        node[edg[i].a] = 0;

                    }

                }

                else if (node[edg[i].a] > -1 && node[edg[i].b] == -1)

                {

                    if (node[edg[i].a] == 0)

                    {

                        node[edg[i].b] = 1;

                    }

                    else

                    {

                        node[edg[i].b] = 0;

                    }

                }

                else if (node[edg[i].a] > -1 && node[edg[i].b] > -1)

                {

                    if (node[edg[i].a] == 0 && node[edg[i].b] == 1)

                    {

                        continue;

                    }

                    else if (node[edg[i].a] == 1 && node[edg[i].b] == 0)

                    {

                        continue;

                    }

                    else

                    {

                        Console.WriteLine("NOT BICOLORABLE.");

                        check = false;

                        break;

                    }

                }

            }

            if (check)

            {

                Console.WriteLine("BICOLORABLE.");

            }

        }

    }

}

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