Add WelshPowell (Graph Colouring)

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

@@ -0,0 +1,83 @@
+package com.thealgorithms.datastructures.graphs;
+
+import java.util.Arrays;
+import java.util.Comparator;
+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
+ */
+
+public class WelshPowell {
+
+    static class WPGraph {
+        private int numVer; // Number of vertices in the graph
+        private HashSet<Integer>[] adjLists; // Adjacency lists for the graph
+
+        private WPGraph(int vertices) {
+            numVer = vertices;
+            adjLists = new HashSet[vertices];
+            Arrays.setAll(adjLists, i -> new HashSet<>());
+        }
+
+        private void addEdge(int nodeA, int nodeB) {
+            adjLists[nodeA].add(nodeB);
+            adjLists[nodeB].add(nodeA);
+        }
+
+        HashSet<Integer> getAdjList(int vertex) {
+            return adjLists[vertex];
+        }
+
+        int getNumVertices() {
+            return numVer;
+        }
+    }
+
+    public static WPGraph makeGraph(int numberOfVertices, int[][] listOfEdges) {
+        WPGraph graph = new WPGraph(numberOfVertices);
+        for (int[] edge : listOfEdges) {
+            graph.addEdge(edge[0], edge[1]);
+        }
+        return graph;
+    }
+
+    public static int[] welshPowellColoring(WPGraph graph) {
+        int[] colors = initializeColors(graph.getNumVertices());
+        Integer[] sortedVertices = getSortedNodes(graph);
+        for (int vertex : sortedVertices) {
+            if (colors[vertex] == -1) {
+                boolean[] usedColors = computeUsedColors(graph, vertex, colors);
+                colors[vertex] = firstUnusedColor(usedColors);
+            }
+        }
+        return colors;
+    }
+
+    private static int[] initializeColors(int numVer) {
+        int[] colors = new int[numVer];
+        Arrays.fill(colors, -1);
+        return colors;
+    }
+
+    private static Integer[] getSortedNodes(WPGraph graph) {
+        return IntStream.range(0, graph.getNumVertices()).boxed().sorted(Comparator.comparingInt(v -> - graph.getAdjList(v).size())).toArray(Integer[] ::new);
+    }
+
+    private static boolean[] computeUsedColors(WPGraph graph, int vertex, int[] colors) {
+        boolean[] usedColors = new boolean[graph.getNumVertices()];
+        graph.getAdjList(vertex).stream().map(neighbor -> colors[neighbor]).filter(color -> color != -1).forEach(color -> usedColors[color] = true);
+        return usedColors;
+    }
+
+    private static int firstUnusedColor(boolean[] usedColors) {
+        return IntStream.range(0, usedColors.length).filter(color -> !usedColors[color]).findFirst().getAsInt();
+    }
+
+    public static void addEdge(WPGraph graph, int nodeA, int nodeB) {
+        graph.addEdge(nodeA, nodeB);
+    }
+}

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

@@ -0,0 +1,44 @@
+package com.thealgorithms.datastructures.graphs;
+
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import com.thealgorithms.datastructures.graphs.WelshPowell.WPGraph;
+import org.junit.jupiter.api.Test;
+
+class WelshPowellAlgorithmTest {
+
+    @Test
+    void testSimpleGraph() {
+        int[][] edges = {{0, 1}, {1, 2}, {2, 3}};
+        WPGraph graph = WelshPowell.makeGraph(4, edges);
+        int[] colors = WelshPowell.welshPowellColoring(graph);
+        assertTrue(isValidColoring(graph, colors));
+    }
+
+    @Test
+    void testDisconnectedGraph() {
+        WPGraph graph = WelshPowell.makeGraph(3, new int[][] {}); // No edges
+        int[] colors = WelshPowell.welshPowellColoring(graph);
+        assertTrue(isValidColoring(graph, colors));
+    }
+
+    @Test
+    void testCompleteGraph() {
+        int[][] edges = {{0, 1}, {1, 2}, {2, 0}};
+        WPGraph graph = WelshPowell.makeGraph(3, edges);
+        int[] colors = WelshPowell.welshPowellColoring(graph);
+        assertTrue(isValidColoring(graph, colors));
+    }
+
+    private boolean isValidColoring(WPGraph graph, int[] colors) {
+        int numVertices = graph.getNumVertices();
+        for (int i = 0; i < numVertices; i++) {
+            for (int neighbor : graph.getAdjList(i)) {
+                if (i != neighbor && colors[i] == colors[neighbor]) {
+                    return false; // Adjacent vertices have the same color
+                }
+            }
+        }
+        return true; // No adjacent vertices share the same color
+    }
+}