Add Boruvka's algorithm to find Minimum Spanning Tree (#4964)

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

@@ -0,0 +1,217 @@
+package com.thealgorithms.datastructures.graphs;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Boruvka's algorithm to find Minimum Spanning Tree
+ * (https://en.wikipedia.org/wiki/Bor%C5%AFvka%27s_algorithm)
+ *
+ * @author itakurah (https://github.com/itakurah)
+ */
+
+final class BoruvkaAlgorithm {
+    private BoruvkaAlgorithm() {
+    }
+
+    /**
+     * Represents an edge in the graph
+     */
+    static class Edge {
+        final int src;
+        final int dest;
+        final int weight;
+
+        Edge(final int src, final int dest, final int weight) {
+            this.src = src;
+            this.dest = dest;
+            this.weight = weight;
+        }
+    }
+
+    /**
+     * Represents the graph
+     */
+    static class Graph {
+        final int vertex;
+        final List<Edge> edges;
+
+        /**
+         * Constructor for the graph
+         *
+         * @param vertex number of vertices
+         * @param edges  list of edges
+         */
+        Graph(final int vertex, final List<Edge> edges) {
+            if (vertex < 0) {
+                throw new IllegalArgumentException("Number of vertices must be positive");
+            }
+            if (edges == null || edges.isEmpty()) {
+                throw new IllegalArgumentException("Edges list must not be null or empty");
+            }
+            for (final var edge : edges) {
+                checkEdgeVertices(edge.src, vertex);
+                checkEdgeVertices(edge.dest, vertex);
+            }
+
+            this.vertex = vertex;
+            this.edges = edges;
+        }
+    }
+
+    /**
+     * Represents a subset for Union-Find operations
+     */
+    private static class Component {
+        int parent;
+        int rank;
+
+        Component(final int parent, final int rank) {
+            this.parent = parent;
+            this.rank = rank;
+        }
+    }
+
+    /**
+     * Represents the state of Union-Find components and the result list
+     */
+    private static class BoruvkaState {
+        List<Edge> result;
+        Component[] components;
+        final Graph graph;
+
+        BoruvkaState(final Graph graph) {
+            this.result = new ArrayList<>();
+            this.components = initializeComponents(graph);
+            this.graph = graph;
+        }
+
+        /**
+         * Adds the cheapest edges to the result list and performs Union operation on the subsets.
+         *
+         * @param cheapest Array containing the cheapest edge for each subset.
+         */
+        void merge(final Edge[] cheapest) {
+            for (int i = 0; i < graph.vertex; ++i) {
+                if (cheapest[i] != null) {
+                    final var component1 = find(components, cheapest[i].src);
+                    final var component2 = find(components, cheapest[i].dest);
+
+                    if (component1 != component2) {
+                        result.add(cheapest[i]);
+                        union(components, component1, component2);
+                    }
+                }
+            }
+        }
+
+        /**
+         * Checks if there are more edges to add to the result list
+         *
+         * @return true if there are more edges to add, false otherwise
+         */
+        boolean hasMoreEdgesToAdd() {
+            return result.size() < graph.vertex - 1;
+        }
+
+        /**
+         * Computes the cheapest edges for each subset in the Union-Find structure.
+         *
+         * @return an array containing the cheapest edge for each subset.
+         */
+        private Edge[] computeCheapestEdges() {
+            Edge[] cheapest = new Edge[graph.vertex];
+            for (final var edge : graph.edges) {
+                final var set1 = find(components, edge.src);
+                final var set2 = find(components, edge.dest);
+
+                if (set1 != set2) {
+                    if (cheapest[set1] == null || edge.weight < cheapest[set1].weight) {
+                        cheapest[set1] = edge;
+                    }
+                    if (cheapest[set2] == null || edge.weight < cheapest[set2].weight) {
+                        cheapest[set2] = edge;
+                    }
+                }
+            }
+            return cheapest;
+        }
+
+        /**
+         * Initializes subsets for Union-Find
+         *
+         * @param graph the graph
+         * @return the initialized subsets
+         */
+        private static Component[] initializeComponents(final Graph graph) {
+            Component[] components = new Component[graph.vertex];
+            for (int v = 0; v < graph.vertex; ++v) {
+                components[v] = new Component(v, 0);
+            }
+            return components;
+        }
+    }
+
+    /**
+     * Finds the parent of the subset using path compression
+     *
+     * @param components array of subsets
+     * @param i          index of the subset
+     * @return the parent of the subset
+     */
+    static int find(final Component[] components, final int i) {
+        if (components[i].parent != i) {
+            components[i].parent = find(components, components[i].parent);
+        }
+        return components[i].parent;
+    }
+
+    /**
+     * Performs the Union operation for Union-Find
+     *
+     * @param components array of subsets
+     * @param x          index of the first subset
+     * @param y          index of the second subset
+     */
+    static void union(Component[] components, final int x, final int y) {
+        final int xroot = find(components, x);
+        final int yroot = find(components, y);
+
+        if (components[xroot].rank < components[yroot].rank) {
+            components[xroot].parent = yroot;
+        } else if (components[xroot].rank > components[yroot].rank) {
+            components[yroot].parent = xroot;
+        } else {
+            components[yroot].parent = xroot;
+            components[xroot].rank++;
+        }
+    }
+
+    /**
+     * Boruvka's algorithm to find the Minimum Spanning Tree
+     *
+     * @param graph the graph
+     * @return list of edges in the Minimum Spanning Tree
+     */
+    static List<Edge> boruvkaMST(final Graph graph) {
+        var boruvkaState = new BoruvkaState(graph);
+
+        while (boruvkaState.hasMoreEdgesToAdd()) {
+            final var cheapest = boruvkaState.computeCheapestEdges();
+            boruvkaState.merge(cheapest);
+        }
+        return boruvkaState.result;
+    }
+
+    /**
+     * Checks if the edge vertices are in a valid range
+     *
+     * @param vertex     the vertex to check
+     * @param upperBound the upper bound for the vertex range
+     */
+    private static void checkEdgeVertices(final int vertex, final int upperBound) {
+        if (vertex < 0 || vertex >= upperBound) {
+            throw new IllegalArgumentException("Edge vertex out of range");
+        }
+    }
+}