diff --git a/src/main/java/com/thealgorithms/datastructures/graphs/WelshPowell.java b/src/main/java/com/thealgorithms/datastructures/graphs/WelshPowell.java new file mode 100644 index 000000000000..3b823f02388d --- /dev/null +++ b/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[] 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 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(); + } +} diff --git a/src/test/java/com/thealgorithms/datastructures/graphs/WelshPowellTest.java b/src/test/java/com/thealgorithms/datastructures/graphs/WelshPowellTest.java new file mode 100644 index 000000000000..b37657db5c05 --- /dev/null +++ b/src/test/java/com/thealgorithms/datastructures/graphs/WelshPowellTest.java @@ -0,0 +1,124 @@ +package com.thealgorithms.datastructures.graphs; + +import static org.junit.jupiter.api.Assertions.assertEquals; +import static org.junit.jupiter.api.Assertions.assertThrows; +import static org.junit.jupiter.api.Assertions.assertTrue; + +import com.thealgorithms.datastructures.graphs.WelshPowell.Graph; +import java.util.Arrays; +import org.junit.jupiter.api.Test; + +class WelshPowellTest { + + @Test + void testSimpleGraph() { + final var graph = WelshPowell.makeGraph(4, new int[][] {{0, 1}, {1, 2}, {2, 3}}); + int[] colors = WelshPowell.findColoring(graph); + assertTrue(isColoringValid(graph, colors)); + assertEquals(2, countDistinctColors(colors)); + } + + @Test + void testDisconnectedGraph() { + final var graph = WelshPowell.makeGraph(3, new int[][] {}); // No edges + int[] colors = WelshPowell.findColoring(graph); + assertTrue(isColoringValid(graph, colors)); + assertEquals(1, countDistinctColors(colors)); + } + + @Test + void testCompleteGraph() { + final var graph = WelshPowell.makeGraph(3, new int[][] {{0, 1}, {1, 2}, {2, 0}}); + int[] colors = WelshPowell.findColoring(graph); + assertTrue(isColoringValid(graph, colors)); + 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 + }; + + final var graph = WelshPowell.makeGraph(11, edges); // 11 vertices from A (0) to K (10) + int[] colors = WelshPowell.findColoring(graph); + + assertTrue(isColoringValid(graph, colors), "The coloring should be valid with no adjacent vertices sharing the same color."); + assertEquals(3, countDistinctColors(colors), "The chromatic number of the graph should be 3."); + } + + @Test + void testNegativeVertices() { + assertThrows(IllegalArgumentException.class, () -> { WelshPowell.makeGraph(-1, new int[][] {}); }, "Number of vertices cannot be negative"); + } + + @Test + void testSelfLoop() { + assertThrows(IllegalArgumentException.class, () -> { WelshPowell.makeGraph(3, new int[][] {{0, 0}}); }, "Self-loops are not allowed"); + } + + @Test + void testInvalidVertex() { + assertThrows(IllegalArgumentException.class, () -> { WelshPowell.makeGraph(3, new int[][] {{0, 3}}); }, "Vertex out of bounds"); + assertThrows(IllegalArgumentException.class, () -> { WelshPowell.makeGraph(3, new int[][] {{0, -1}}); }, "Vertex out of bounds"); + } + + @Test + void testInvalidEdgeArray() { + assertThrows(IllegalArgumentException.class, () -> { WelshPowell.makeGraph(3, new int[][] {{0}}); }, "Edge array must have exactly two elements"); + } + + @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); + } + } + + private boolean isColoringValid(Graph graph, int[] colors) { + if (Arrays.stream(colors).anyMatch(n -> n < 0)) { + return false; + } + for (int i = 0; i < graph.getNumVertices(); i++) { + for (int neighbor : graph.getAdjacencyList(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 + } + + private int countDistinctColors(int[] colors) { + return (int) Arrays.stream(colors).distinct().count(); + } +}