Improve comments in Mcoloring.java (#5484)

Author: Hardvan

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

@@ -7,71 +7,90 @@
 import java.util.Set;
 
 /**
+ * Node class represents a graph node. Each node is associated with a color
+ * (initially 1) and contains a set of edges representing its adjacent nodes.
+ *
  * @author Bama Charan Chhandogi (https://github.com/BamaCharanChhandogi)
  */
 class Node {
-    int color = 1;
-    Set<Integer> edges = new HashSet<Integer>();
+    int color = 1; // Initial color for each node
+    Set<Integer> edges = new HashSet<Integer>(); // Set of edges representing adjacent nodes
 }
 
+/**
+ * MColoring class solves the M-Coloring problem where the goal is to determine
+ * if it's possible to color a graph using at most M colors such that no two
+ * adjacent nodes have the same color.
+ */
 public final class MColoring {
+
     private MColoring() {
-    }
-    static int possiblePaint(ArrayList<Node> nodes, int n, int m) {
+    } // Prevent instantiation of utility class
 
-        // Create a visited array of n nodes
+    /**
+     * Determines whether it is possible to color the graph using at most M colors.
+     *
+     * @param nodes List of nodes representing the graph.
+     * @param n     The total number of nodes in the graph.
+     * @param m     The maximum number of allowed colors.
+     * @return true if the graph can be colored using M colors, false otherwise.
+     */
+    static boolean isColoringPossible(ArrayList<Node> nodes, int n, int m) {
+
+        // Visited array keeps track of whether each node has been processed.
         ArrayList<Integer> visited = new ArrayList<Integer>();
         for (int i = 0; i < n + 1; i++) {
-            visited.add(0);
+            visited.add(0); // Initialize all nodes as unvisited (0)
         }
 
-        // maxColors used till now are 1 as
-        // all nodes are painted color 1
+        // The number of colors used so far (initially set to 1, since all nodes
+        // start with color 1).
         int maxColors = 1;
 
+        // Loop through all the nodes to ensure every node is visited, in case the
+        // graph is disconnected.
         for (int sv = 1; sv <= n; sv++) {
             if (visited.get(sv) > 0) {
-                continue;
+                continue; // Skip nodes that are already visited
             }
 
-            // If the starting point is unvisited,
-            // mark it visited and push it in queue
+            // If the node is unvisited, mark it as visited and add it to the queue for BFS.
             visited.set(sv, 1);
             Queue<Integer> q = new LinkedList<>();
             q.add(sv);
 
-            // BFS
+            // Perform BFS to process all nodes and their adjacent nodes
             while (q.size() != 0) {
-                int top = q.peek();
+                int top = q.peek(); // Get the current node from the queue
                 q.remove();
 
-                // Checking all adjacent nodes
-                // to "top" edge in our queue
+                // Check all adjacent nodes of the current node
                 for (int it : nodes.get(top).edges) {
 
-                    // If the color of the
-                    // adjacent node is same, increase it by
-                    // 1
+                    // If the adjacent node has the same color as the current node, increment its
+                    // color to avoid conflict.
                     if (nodes.get(top).color == nodes.get(it).color) {
                         nodes.get(it).color += 1;
                     }
 
-                    // If number of colors used exceeds m,
-                    // return 0
+                    // Keep track of the maximum number of colors used so far
                     maxColors = Math.max(maxColors, Math.max(nodes.get(top).color, nodes.get(it).color));
+
+                    // If the number of colors used exceeds the allowed limit M, return false.
                     if (maxColors > m) {
-                        return 0;
+                        return false;
                     }
 
-                    // If the adjacent node is not visited,
-                    // mark it visited and push it in queue
+                    // If the adjacent node hasn't been visited yet, mark it as visited and add it
+                    // to the queue for further processing.
                     if (visited.get(it) == 0) {
                         visited.set(it, 1);
                         q.add(it);
                     }
                 }
             }
         }
-        return 1;
+
+        return true; // Possible to color the entire graph with M or fewer colors.
     }
 }

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

@@ -1,6 +1,7 @@
 package com.thealgorithms.backtracking;
 
-import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertFalse;
+import static org.junit.jupiter.api.Assertions.assertTrue;
 
 import java.util.ArrayList;
 import org.junit.jupiter.api.Test;
@@ -16,7 +17,7 @@ void testGraphColoring1() {
         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));
+        assertTrue(MColoring.isColoringPossible(createGraph(graph), n, m));
     }
 
     @Test
@@ -25,7 +26,7 @@ void testGraphColoring2() {
         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));
+        assertFalse(MColoring.isColoringPossible(createGraph(graph), n, m));
     }
 
     @Test
@@ -34,7 +35,7 @@ void testGraphColoring3() {
         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));
+        assertFalse(MColoring.isColoringPossible(createGraph(graph), n, m));
     }
 
     private ArrayList<Node> createGraph(int[][] graph) {