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/test/java/com/thealgorithms/backtracking/MColoringTest.java

@@ -0,0 +1,57 @@
+package com.thealgorithms.backtracking;
+
+import static org.junit.jupiter.api.Assertions.*;
+
+import java.util.*;
+import org.junit.jupiter.api.Test;
+
+/**
+ * @author Bama Charan Chhandogi (https://github.com/BamaCharanChhandogi)
+ */
+class MColoringTest {
+
+    @Test
+    void testGraphColoring1() {
+        int n = 4;
+        int[][] graph = {{0, 1, 1, 1}, {1, 0, 1, 0}, {1, 1, 0, 1}, {1, 0, 1, 0}};
+        int m = 3; // Number of colors
+
+        assertEquals(1, MColoring.possiblePaint(createGraph(graph), n, m));
+    }
+
+    @Test
+    void testGraphColoring2() {
+        int n = 5;
+        int[][] graph = {{0, 1, 1, 1, 0}, {1, 0, 0, 1, 0}, {1, 0, 0, 1, 1}, {1, 1, 1, 0, 1}, {0, 0, 1, 1, 0}};
+        int m = 2; // Number of colors
+
+        assertEquals(0, MColoring.possiblePaint(createGraph(graph), n, m));
+    }
+
+    @Test
+    void testGraphColoring3() {
+        int n = 3;
+        int[][] graph = {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}};
+        int m = 2; // Number of colors
+
+        assertEquals(0, MColoring.possiblePaint(createGraph(graph), n, m));
+    }
+
+    private ArrayList<Node> createGraph(int[][] graph) {
+        int n = graph.length;
+        ArrayList<Node> nodes = new ArrayList<>(n + 1);
+        for (int i = 0; i <= n; i++) {
+            nodes.add(new Node());
+        }
+
+        for (int i = 0; i < n; i++) {
+            for (int j = i + 1; j < n; j++) { // Use j = i + 1 to avoid setting edges twice
+                if (graph[i][j] > 0) {
+                    nodes.get(i + 1).edges.add(j + 1);
+                    nodes.get(j + 1).edges.add(i + 1);
+                }
+            }
+        }
+        return nodes;
+    }
+}