refactor: Enhance docs, add more tests in WelshPowell

src/main/java/com/thealgorithms/datastructures/graphs/WelshPowell.java

@@ -5,21 +5,41 @@
 import java.util.HashSet;
 import java.util.stream.IntStream;
 
-/*
- *  The Welsh-Powell algorithm is a graph coloring algorithm
- *  used for coloring a graph with the minimum number of colors.
- *  https://en.wikipedia.org/wiki/Graph_coloring
+/**
+ * The Welsh-Powell algorithm is a graph coloring algorithm that aims to color a graph
+ * using the minimum number of colors such that no two adjacent vertices share the same color.
+ *
+ * <p>
+ * The algorithm works by:
+ * <ol>
+ * <li>Sorting the vertices in descending order based on their degrees (number of edges connected).</li>
+ * <li>Iterating through each vertex and assigning it the smallest available color that has not been used by its adjacent vertices.</li>
+ * <li>Coloring adjacent vertices with the same color is avoided.</li>
+ * </ol>
+ * </p>
+ *
+ * <p>
+ * For more information, see <a href="https://en.wikipedia.org/wiki/Graph_coloring">Graph Coloring</a>.
+ * </p>
  */
-
 public final class WelshPowell {
-    private static final int BLANK_COLOR = -1; // Representing uncolored state
+    private static final int BLANK_COLOR = -1; // Constant representing an uncolored state
 
     private WelshPowell() {
     }
 
+    /**
+     * Represents a graph using an adjacency list.
+     */
     static final class Graph {
-        private HashSet<Integer>[] adjacencyLists;
-
+        private final HashSet<Integer>[] adjacencyLists;
+
+        /**
+         * Initializes a graph with a specified number of vertices.
+         *
+         * @param vertices the number of vertices in the graph
+         * @throws IllegalArgumentException if the number of vertices is negative
+         */
         private Graph(int vertices) {
             if (vertices < 0) {
                 throw new IllegalArgumentException("Number of vertices cannot be negative");
@@ -29,6 +49,13 @@ private Graph(int vertices) {
             Arrays.setAll(adjacencyLists, i -> new HashSet<>());
         }
 
+        /**
+         * Adds an edge between two vertices in the graph.
+         *
+         * @param nodeA one end of the edge
+         * @param nodeB the other end of the edge
+         * @throws IllegalArgumentException if the vertices are out of bounds or if a self-loop is attempted
+         */
         private void addEdge(int nodeA, int nodeB) {
             validateVertex(nodeA);
             validateVertex(nodeB);
@@ -39,21 +66,46 @@ private void addEdge(int nodeA, int nodeB) {
             adjacencyLists[nodeB].add(nodeA);
         }
 
+        /**
+         * Validates that the vertex index is within the bounds of the graph.
+         *
+         * @param vertex the index of the vertex to validate
+         * @throws IllegalArgumentException if the vertex is out of bounds
+         */
         private void validateVertex(int vertex) {
             if (vertex < 0 || vertex >= getNumVertices()) {
                 throw new IllegalArgumentException("Vertex " + vertex + " is out of bounds");
             }
         }
 
+        /**
+         * Returns the adjacency list for a specific vertex.
+         *
+         * @param vertex the index of the vertex
+         * @return the set of adjacent vertices
+         */
         HashSet<Integer> getAdjacencyList(int vertex) {
             return adjacencyLists[vertex];
         }
 
+        /**
+         * Returns the number of vertices in the graph.
+         *
+         * @return the number of vertices
+         */
         int getNumVertices() {
             return adjacencyLists.length;
         }
     }
 
+    /**
+     * Creates a graph with the specified number of vertices and edges.
+     *
+     * @param numberOfVertices the total number of vertices
+     * @param listOfEdges a 2D array representing edges where each inner array contains two vertex indices
+     * @return a Graph object representing the created graph
+     * @throws IllegalArgumentException if the edge array is invalid or vertices are out of bounds
+     */
     public static Graph makeGraph(int numberOfVertices, int[][] listOfEdges) {
         Graph graph = new Graph(numberOfVertices);
         for (int[] edge : listOfEdges) {
@@ -65,6 +117,12 @@ public static Graph makeGraph(int numberOfVertices, int[][] listOfEdges) {
         return graph;
     }
 
+    /**
+     * Finds the coloring of the given graph using the Welsh-Powell algorithm.
+     *
+     * @param graph the input graph to color
+     * @return an array of integers where each index represents a vertex and the value represents the color assigned
+     */
     public static int[] findColoring(Graph graph) {
         int[] colors = initializeColors(graph.getNumVertices());
         Integer[] sortedVertices = getSortedNodes(graph);
@@ -83,30 +141,70 @@ public static int[] findColoring(Graph graph) {
         return colors;
     }
 
+    /**
+     * Helper method to check if a color is unassigned
+     *
+     * @param color the color to check
+     * @return {@code true} if the color is unassigned, {@code false} otherwise
+     */
     private static boolean isBlank(int color) {
         return color == BLANK_COLOR;
     }
 
+    /**
+     * Checks if a vertex has adjacent colored vertices
+     *
+     * @param graph the input graph
+     * @param vertex the vertex to check
+     * @param colors the array of colors assigned to the vertices
+     * @return {@code true} if the vertex has adjacent colored vertices, {@code false} otherwise
+     */
     private static boolean isAdjacentToColored(Graph graph, int vertex, int[] colors) {
         return graph.getAdjacencyList(vertex).stream().anyMatch(otherVertex -> !isBlank(colors[otherVertex]));
     }
 
+    /**
+     * Initializes the colors array with blank color
+     *
+     * @param numberOfVertices the number of vertices in the graph
+     * @return an array of integers representing the colors assigned to the vertices
+     */
     private static int[] initializeColors(int numberOfVertices) {
         int[] colors = new int[numberOfVertices];
         Arrays.fill(colors, BLANK_COLOR);
         return colors;
     }
 
+    /**
+     * Sorts the vertices by their degree in descending order
+     *
+     * @param graph the input graph
+     * @return an array of integers representing the vertices sorted by degree
+     */
     private static Integer[] getSortedNodes(final Graph graph) {
         return IntStream.range(0, graph.getNumVertices()).boxed().sorted(Comparator.comparingInt(v -> - graph.getAdjacencyList(v).size())).toArray(Integer[] ::new);
     }
 
+    /**
+     * Computes the colors already used by the adjacent vertices
+     *
+     * @param graph the input graph
+     * @param vertex the vertex to check
+     * @param colors the array of colors assigned to the vertices
+     * @return an array of booleans representing the colors used by the adjacent vertices
+     */
     private static boolean[] computeUsedColors(final Graph graph, final int vertex, final int[] colors) {
         boolean[] usedColors = new boolean[graph.getNumVertices()];
         graph.getAdjacencyList(vertex).stream().map(neighbor -> colors[neighbor]).filter(color -> !isBlank(color)).forEach(color -> usedColors[color] = true);
         return usedColors;
     }
 
+    /**
+     * Finds the first unused color
+     *
+     * @param usedColors the array of colors used by the adjacent vertices
+     * @return the first unused color
+     */
     private static int firstUnusedColor(boolean[] usedColors) {
         return IntStream.range(0, usedColors.length).filter(color -> !usedColors[color]).findFirst().getAsInt();
     }

src/test/java/com/thealgorithms/datastructures/graphs/WelshPowellTest.java

@@ -34,26 +34,25 @@ void testCompleteGraph() {
         assertEquals(3, countDistinctColors(colors));
     }
 
-    // The following test originates from the following website : https://www.geeksforgeeks.org/welsh-powell-graph-colouring-algorithm/
     @Test
     void testComplexGraph() {
         int[][] edges = {
-            {0, 7}, // A-H
-            {0, 1}, // A-B
-            {1, 3}, // B-D
-            {2, 3}, // C-D
-            {3, 8}, // D-I
-            {3, 10}, // D-K
-            {4, 10}, // E-K
-            {4, 5}, // E-F
-            {5, 6}, // F-G
-            {6, 10}, // G-K
-            {6, 7}, // G-H
-            {7, 8}, // H-I
-            {7, 9}, // H-J
-            {7, 10}, // H-K
-            {8, 9}, // I-J
-            {9, 10}, // J-K
+            {0, 7},
+            {0, 1},
+            {1, 3},
+            {2, 3},
+            {3, 8},
+            {3, 10},
+            {4, 10},
+            {4, 5},
+            {5, 6},
+            {6, 10},
+            {6, 7},
+            {7, 8},
+            {7, 9},
+            {7, 10},
+            {8, 9},
+            {9, 10},
         };
 
         final var graph = WelshPowell.makeGraph(11, edges); // 11 vertices from A (0) to K (10)
@@ -86,24 +85,35 @@ void testInvalidEdgeArray() {
 
     @Test
     void testWithPreColoredVertex() {
-        // Create a linear graph with 4 vertices and edges connecting them in sequence
         final var graph = WelshPowell.makeGraph(4, new int[][] {{0, 1}, {1, 2}, {2, 3}});
-
-        // Apply the Welsh-Powell coloring algorithm to the graph
         int[] colors = WelshPowell.findColoring(graph);
-
-        // Validate that the coloring is correct (no two adjacent vertices have the same color)
         assertTrue(isColoringValid(graph, colors));
-
-        // Check if the algorithm has used at least 2 colors (expected for a linear graph)
         assertTrue(countDistinctColors(colors) >= 2);
-
-        // Verify that all vertices have been assigned a color
         for (int color : colors) {
             assertTrue(color >= 0);
         }
     }
 
+    @Test
+    void testLargeGraph() {
+        int[][] edges = {{0, 1}, {1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 0}, {6, 7}, {7, 8}, {8, 6}, {9, 10}, {10, 11}, {11, 9}, {12, 13}, {13, 14}, {14, 15}};
+
+        final var graph = WelshPowell.makeGraph(16, edges); // 16 vertices
+        int[] colors = WelshPowell.findColoring(graph);
+        assertTrue(isColoringValid(graph, colors));
+        assertEquals(3, countDistinctColors(colors)); // Expecting a maximum of 3 colors
+    }
+
+    @Test
+    void testStarGraph() {
+        int[][] edges = {{0, 1}, {0, 2}, {0, 3}, {0, 4}};
+
+        final var graph = WelshPowell.makeGraph(5, edges); // 5 vertices in a star formation
+        int[] colors = WelshPowell.findColoring(graph);
+        assertTrue(isColoringValid(graph, colors));
+        assertEquals(2, countDistinctColors(colors)); // Star graph can be colored with 2 colors
+    }
+
     private boolean isColoringValid(Graph graph, int[] colors) {
         if (Arrays.stream(colors).anyMatch(n -> n < 0)) {
             return false;