Add WelshPowell (Graph Colouring)

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

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+package com.thealgorithms.datastructures.graphs;
+
+import java.util.LinkedList;
+import java.util.Scanner;
+
+/*
+ *  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
+ */
+public class Welsh_Powell {
+
+    public static void main(String[] args) {
+        Scanner scanner = new Scanner(System.in);
+
+        // Input for the number of vertices in the graph
+        System.out.print("Enter the number of vertices: ");
+        int numVertices = scanner.nextInt();
+        scanner.nextLine();
+        // Initialize the graph with the given number of vertices
+        WPGraph graph = new WPGraph(numVertices);
+
+        // Input for the number of edges
+        System.out.print("Enter the number of edges: ");
+        int numEdges = scanner.nextInt();
+        scanner.nextLine();
+        // Adding edges to the graph based on user input
+        for (int i = 0; i < numEdges; i++) {
+            System.out.print("Enter both vertices for edge " + (i + 1) + " (format: 'src dest'): ");
+            String[] vertices = scanner.nextLine().split(" ");
+            int src = Integer.parseInt(vertices[0]);
+            int dest = Integer.parseInt(vertices[1]);
+
+            graph.addEdge(src, dest);
+        }
+
+        // Apply Welsh Powell coloring algorithm
+        int colors[] = graph.welshPowellColoring();
+
+        // Output the color of each vertex
+        for (int i = 0; i < numVertices; i++) {
+            System.out.println("Vertex " + (i + 1) + " is colored with color " + colors[i]);
+        }
+
+        scanner.close();
+    }
+
+    public static class WPGraph {
+
+        private int numVer; // Number of vertices in the graph
+        public LinkedList<Integer>[] adjLists; // Adjacency lists for the graph
+
+        // Constructor to initialize the graph with a certain number of vertices
+        public WPGraph(int vertices) {
+            numVer = vertices;
+            adjLists = new LinkedList[vertices];
+
+            for (int i = 0; i < vertices; i++) {
+                adjLists[i] = new LinkedList<>();
+            }
+        }
+
+        // Method to add an edge to the graph (undirected)
+        public void addEdge(int src, int dest) {
+            // Check to prevent duplicate edges
+            if (!adjLists[src].contains(dest)) {
+                adjLists[src].add(dest);
+                adjLists[dest].add(src); // For undirected graphs, add the reverse edge as well
+            }
+        }
+
+        // Method implementing Welsh Powell coloring algorithm
+        public int[] welshPowellColoring() {
+            int[] colors = new int[numVer]; // Array to store color of each vertex
+            for (int i = 0; i < numVer; i++) {
+                colors[i] = -1; // Initialize all vertices as uncolored
+            }
+
+            // Creating a list of vertices sorted by descending degree
+            LinkedList<Integer> sortedVertices = new LinkedList<>();
+            for (int i = 0; i < numVer; i++) {
+                sortedVertices.add(i);
+            }
+            sortedVertices.sort((v1, v2) -> adjLists[v2].size() - adjLists[v1].size());
+
+            // Coloring vertices
+            for (int vertex : sortedVertices) {
+                if (colors[vertex] == -1) {
+                    boolean[] usedColors = new boolean[numVer]; // Track used colors
+                    for (int neighbor : adjLists[vertex]) {
+                        if (colors[neighbor] != -1) {
+                            usedColors[colors[neighbor]] = true; // Mark neighbor's color as used
+                        }
+                    }
+
+                    // Assign the first unused color
+                    for (int color = 0; color < numVer; color++) {
+                        if (!usedColors[color]) {
+                            colors[vertex] = color;
+                            break;
+                        }
+                    }
+                }
+            }
+
+            return colors; // Return the array of colors for each vertex
+        }
+    }
+}

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

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+package com.thealgorithms.datastructures.graphs;
+
+import com.thealgorithms.datastructures.graphs.Welsh_Powell.WPGraph;
+public class WelshPowellAlgorithmTest {
+
+        public static void main(String[] args) {
+            // Creating the graph for the test case
+            int numVertices = 6; // Number of vertices
+            WPGraph graph = new WPGraph(numVertices);
+
+            // Adding the edges
+            graph.addEdge(0, 1);
+            graph.addEdge(0, 2);
+            graph.addEdge(1, 3);
+            graph.addEdge(2, 3);
+            graph.addEdge(2, 4);
+            graph.addEdge(3, 4);
+            graph.addEdge(3, 5);
+            graph.addEdge(4, 5);
+
+            // Executing the method
+            int[] colors = graph.welshPowellColoring();
+
+            // Checking the results
+            boolean testPassed = true;
+            for (int i = 0; i < numVertices; i++) {
+                for (int neighbor : graph.adjLists[i]) {
+                    if (colors[i] == colors[neighbor]) {
+                        testPassed = false;
+                        break;
+                    }
+                }
+                if (!testPassed) {
+                    break;
+                }
+            }
+
+            if (testPassed) {
+                System.out.println("Test Passed.");
+            } else {
+                System.out.println("Test Failed.");
+            }
+        }
+}