Add WelshPowell (Graph Colouring) (#5034)

* Welsh Powell Algorithm + Test


---------

Co-authored-by: Piotr Idzik <65706193+vil02@users.noreply.github.com>

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

@@ -0,0 +1,113 @@
+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 final class WelshPowell {
+    private static final int BLANK_COLOR = -1; // Representing uncolored state
+
+    private WelshPowell() {
+    }
+
+    static class Graph {
+        private HashSet<Integer>[] adjacencyLists;
+
+        private Graph(int vertices) {
+            if (vertices < 0) {
+                throw new IllegalArgumentException("Number of vertices cannot be negative");
+            }
+
+            adjacencyLists = new HashSet[vertices];
+            Arrays.setAll(adjacencyLists, i -> new HashSet<>());
+        }
+
+        private void addEdge(int nodeA, int nodeB) {
+            validateVertex(nodeA);
+            validateVertex(nodeB);
+            if (nodeA == nodeB) {
+                throw new IllegalArgumentException("Self-loops are not allowed");
+            }
+            adjacencyLists[nodeA].add(nodeB);
+            adjacencyLists[nodeB].add(nodeA);
+        }
+
+        private void validateVertex(int vertex) {
+            if (vertex < 0 || vertex >= getNumVertices()) {
+                throw new IllegalArgumentException("Vertex " + vertex + " is out of bounds");
+            }
+        }
+
+        HashSet<Integer> getAdjacencyList(int vertex) {
+            return adjacencyLists[vertex];
+        }
+
+        int getNumVertices() {
+            return adjacencyLists.length;
+        }
+    }
+
+    public static Graph makeGraph(int numberOfVertices, int[][] listOfEdges) {
+        Graph graph = new Graph(numberOfVertices);
+        for (int[] edge : listOfEdges) {
+            if (edge.length != 2) {
+                throw new IllegalArgumentException("Edge array must have exactly two elements");
+            }
+            graph.addEdge(edge[0], edge[1]);
+        }
+        return graph;
+    }
+
+    public static int[] findColoring(Graph graph) {
+        int[] colors = initializeColors(graph.getNumVertices());
+        Integer[] sortedVertices = getSortedNodes(graph);
+        for (int vertex : sortedVertices) {
+            if (isBlank(colors[vertex])) {
+                boolean[] usedColors = computeUsedColors(graph, vertex, colors);
+                final var newColor = firstUnusedColor(usedColors);
+                colors[vertex] = newColor;
+                Arrays.stream(sortedVertices).forEach(otherVertex -> {
+                    if (isBlank(colors[otherVertex]) && !isAdjacentToColored(graph, otherVertex, colors)) {
+                        colors[otherVertex] = newColor;
+                    }
+                });
+            }
+        }
+        return colors;
+    }
+
+    private static boolean isBlank(int color) {
+        return color == BLANK_COLOR;
+    }
+
+    private static boolean isAdjacentToColored(Graph graph, int vertex, int[] colors) {
+        return graph.getAdjacencyList(vertex).stream().anyMatch(otherVertex -> !isBlank(colors[otherVertex]));
+    }
+
+    private static int[] initializeColors(int numberOfVertices) {
+        int[] colors = new int[numberOfVertices];
+        Arrays.fill(colors, BLANK_COLOR);
+        return colors;
+    }
+
+    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);
+    }
+
+    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;
+    }
+
+    private static int firstUnusedColor(boolean[] usedColors) {
+        return IntStream.range(0, usedColors.length).filter(color -> !usedColors[color]).findFirst().getAsInt();
+    }
+}