Add M-coloring Problem (#4282)

Co-authored-by: BamaCharanChhandogi <b.c.chhandogi@gmailcom>
Co-authored-by: Andrii Siriak <siryaka@gmail.com>
Co-authored-by: Debasish Biswas <debasishbsws.abc@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

src/main/java/com/thealgorithms/backtracking/MColoring.java

@@ -0,0 +1,70 @@
+package com.thealgorithms.backtracking;
+
+import java.io.*;
+import java.util.*;
+
+/**
+ * @author Bama Charan Chhandogi (https://github.com/BamaCharanChhandogi)
+ */
+class Node {
+    int color = 1;
+    Set<Integer> edges = new HashSet<Integer>();
+}
+
+public class MColoring {
+    static int possiblePaint(ArrayList<Node> nodes, int n, int m) {
+
+        // Create a visited array of n nodes
+        ArrayList<Integer> visited = new ArrayList<Integer>();
+        for (int i = 0; i < n + 1; i++) {
+            visited.add(0);
+        }
+
+        // maxColors used till now are 1 as
+        // all nodes are painted color 1
+        int maxColors = 1;
+
+        for (int sv = 1; sv <= n; sv++) {
+            if (visited.get(sv) > 0) {
+                continue;
+            }
+
+            // If the starting point is unvisited,
+            // mark it visited and push it in queue
+            visited.set(sv, 1);
+            Queue<Integer> q = new LinkedList<>();
+            q.add(sv);
+
+            // BFS
+            while (q.size() != 0) {
+                int top = q.peek();
+                q.remove();
+
+                // Checking all adjacent nodes
+                // to "top" edge in our queue
+                for (int it : nodes.get(top).edges) {
+
+                    // If the color of the
+                    // adjacent node is same, increase it by
+                    // 1
+                    if (nodes.get(top).color == nodes.get(it).color) {
+                        nodes.get(it).color += 1;
+                    }
+
+                    // If number of colors used exceeds m,
+                    // return 0
+                    maxColors = Math.max(maxColors, Math.max(nodes.get(top).color, nodes.get(it).color));
+                    if (maxColors > m) return 0;
+
+                    // If the adjacent node is not visited,
+                    // mark it visited and push it in queue
+                    if (visited.get(it) == 0) {
+                        visited.set(it, 1);
+                        q.add(it);
+                    }
+                }
+            }
+        }
+        return 1;
+    }
+}