Added M-coloring solution

Author: Akshat-Pandey16

Programs/Backtracking/Mcolor.java

@@ -0,0 +1,99 @@
+// Java program for m coloring problem
+ 
+public class Mcolor {
+ 
+ // Number of vertices in the graph
+ static int V = 4;
+ 
+ /* A utility function to print solution */
+ static void printSolution(int[] color)
+ {
+ System.out.println(
+ "Solution Exists:"
+ + " Following are the assigned colors ");
+ for (int i = 0; i < V; i++)
+ System.out.print(" " + color[i]);
+ System.out.println();
+ }
+ 
+ // check if the colored
+ // graph is safe or not
+ static boolean isSafe(boolean[][] graph, int[] color)
+ {
+ // check for every edge
+ for (int i = 0; i < V; i++)
+ for (int j = i + 1; j < V; j++)
+ if (graph[i][j] && color[j] == color[i])
+ return false;
+ return true;
+ }
+ 
+ /* This function solves the m Coloring
+ problem using recursion. It returns
+ false if the m colours cannot be assigned,
+ otherwise, return true and prints
+ assignments of colours to all vertices.
+ Please note that there may be more than
+ one solutions, this function prints one
+ of the feasible solutions.*/
+ static boolean graphColoring(boolean[][] graph, int m,
+ int i, int[] color)
+ {
+ // if current index reached end
+ if (i == V) {
+ 
+ // if coloring is safe
+ if (isSafe(graph, color)) {
+ 
+ // Print the solution
+ printSolution(color);
+ return true;
+ }
+ return false;
+ }
+ 
+ // Assign each color from 1 to m
+ for (int j = 1; j <= m; j++) {
+ color[i] = j;
+ 
+ // Recur of the rest vertices
+ if (graphColoring(graph, m, i + 1, color))
+ return true;
+ color[i] = 0;
+ }
+ return false;
+ }
+ 
+ // Driver code
+ public static void main(String[] args)
+ {
+ 
+ /* Create following graph and
+ test whether it is 3 colorable
+ (3)---(2)
+ | / |
+ | / |
+ | / |
+ (0)---(1)
+ */
+ boolean[][] graph = {
+ { false, true, true, true },
+ { true, false, true, false },
+ { true, true, false, true },
+ { true, false, true, false },
+ };
+ int m = 3; // Number of colors
+ 
+ // Initialize all color values as 0.
+ // This initialization is needed
+ // correct functioning of isSafe()
+ int[] color = new int[V];
+ for (int i = 0; i < V; i++)
+ color[i] = 0;
+ 
+ // Function call
+ if (!graphColoring(graph, m, 0, color))
+ System.out.println("Solution does not exist");
+ }
+}
+