Feature/kruskal algorithm

src/main/java/com/thealgorithms/greedyalgorithms/KruskalAlgorithm.java

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+package com.thealgorithms.greedyalgorithms;
+
+/**
+ * An encapsulated, self-contained implementation of Kruskal's algorithm
+ * for computing the Minimum Spanning Tree (MST) of a weighted, undirected graph.
+ * You can find more about this algorithm in the following link:
+ * <a href="https://www.geeksforgeeks.org/dsa/kruskals-minimum-spanning-tree-algorithm-greedy-algo-2/">Kruskal algorithm - Geeks for Geeks</a>
+ * <p>
+ * To avoid namespace conflicts and maintain isolation within larger projects,
+ * all collaborators (Edge, Graph, DisjointSet) are implemented as private
+ * static nested classes. This ensures no type leakage outside this file while
+ * preserving clean internal architecture.
+ * </p>
+ *
+ * <h2>Usage</h2>
+ * <pre>
+ *     KruskalAlgorithm algo = new KruskalAlgorithm();
+ *     KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(4);
+ *     graph.addEdge(0,1,10);
+ *     graph.addEdge(1,2,5);
+ *     List&lt;KruskalAlgorithm.Edge&gt; mst = algo.computeMST(graph);
+ * </pre>
+ *
+ * <h2>Design Notes</h2>
+ * <ul>
+ *     <li>Implements a fully isolated module without risk of polluting global scope.</li>
+ *     <li>Inner classes preserve encapsulation but keep responsibilities separate.</li>
+ *     <li>Algorithm complexity: O(e log e), dominated by edge sorting.</li>
+ * </ul>
+ */
+public class KruskalAlgorithm {
+
+    /**
+     * Computes the Minimum Spanning Tree (or Minimum Spanning Forest if the graph
+     * is disconnected) using Kruskal’s greedy strategy.
+     *
+     * @param graph the graph instance to process
+     * @return a list of edges forming the MST
+     */
+    public java.util.List<Edge> computeMST(Graph graph) {
+        java.util.List<Edge> mst = new java.util.ArrayList<>();
+        java.util.List<Edge> edges = new java.util.ArrayList<>(graph.edges);
+
+        // Sort edges by ascending weight
+        java.util.Collections.sort(edges);
+
+        DisjointSet ds = new DisjointSet(graph.numberOfVertices);
+
+        for (Edge e : edges) {
+            int rootA = ds.find(e.source);
+            int rootB = ds.find(e.target);
+
+            if (rootA != rootB) {
+                mst.add(e);
+                ds.union(rootA, rootB);
+
+                if (mst.size() == graph.numberOfVertices - 1) {
+                    break;
+                }
+            }
+        }
+
+        return mst;
+    }
+
+    /**
+     * Represents an immutable weighted edge between two vertices.
+     */
+    public static final class Edge implements Comparable<Edge> {
+        private final int source;
+        private final int target;
+        private final int weight;
+
+        public Edge(int source, int target, int weight) {
+            if (weight < 0) {
+                throw new IllegalArgumentException("Weight cannot be negative.");
+            }
+            this.source = source;
+            this.target = target;
+            this.weight = weight;
+        }
+
+        public int getSource() {
+            return source;
+        }
+
+        public int getTarget() {
+            return target;
+        }
+
+        public int getWeight() {
+            return weight;
+        }
+
+        @Override
+        public int compareTo(Edge o) {
+            return Integer.compare(this.weight, o.weight);
+        }
+    }
+
+    /**
+     * Lightweight graph representation consisting solely of vertices and edges.
+     * All algorithmic behavior is delegated to higher-level components.
+     */
+    public static final class Graph {
+        private final int numberOfVertices;
+        private final java.util.List<Edge> edges = new java.util.ArrayList<>();
+
+        public Graph(int numberOfVertices) {
+            if (numberOfVertices <= 0) {
+                throw new IllegalArgumentException("Graph must have at least one vertex.");
+            }
+            this.numberOfVertices = numberOfVertices;
+        }
+
+        /**
+         * Adds an undirected edge to the graph.
+         */
+        public void addEdge(int source, int target, int weight) {
+            if (source < 0 || source >= numberOfVertices || target < 0 || target >= numberOfVertices) {
+                throw new IndexOutOfBoundsException("Vertex index out of range.");
+            }
+
+            edges.add(new Edge(source, target, weight));
+        }
+    }
+
+    /**
+     * Disjoint Set Union data structure supporting path compression
+     * and union-by-rank — essential for cycle detection in Kruskal's algorithm.
+     */
+    private static final class DisjointSet {
+        private final int[] parent;
+        private final int[] rank;
+
+        DisjointSet(int size) {
+            parent = new int[size];
+            rank = new int[size];
+            for (int i = 0; i < size; i++) {
+                parent[i] = i;
+            }
+        }
+
+        public int find(int x) {
+            if (parent[x] != x) {
+                parent[x] = find(parent[x]); // Path compression
+            }
+            return parent[x];
+        }
+
+        public void union(int a, int b) {
+            int ra = find(a);
+            int rb = find(b);
+            if (ra == rb) {
+                return;
+            }
+            if (rank[ra] < rank[rb]) {
+                parent[ra] = rb;
+            } else if (rank[ra] > rank[rb]) {
+                parent[rb] = ra;
+            } else {
+                parent[rb] = ra;
+                rank[ra]++;
+            }
+        }
+    }
+}

src/test/java/com/thealgorithms/greedyalgorithms/KruskalAlgorithmTest.java

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+package com.thealgorithms.greedyalgorithms;
+
+import static org.junit.jupiter.api.Assertions.assertDoesNotThrow;
+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 java.util.List;
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Comprehensive test suite for the KruskalAlgorithm implementation.
+ * Ensures correctness, stability, and coverage of all internal logic.
+ */
+public class KruskalAlgorithmTest {
+
+    // -------------------------------------------------------------
+    // BASIC ALGORITHM CORRECTNESS
+    // -------------------------------------------------------------
+
+    @Test
+    @DisplayName("MST for a normal connected graph is computed correctly")
+    void testBasicMST() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(4);
+
+        graph.addEdge(0, 1, 10);
+        graph.addEdge(0, 2, 6);
+        graph.addEdge(0, 3, 5);
+        graph.addEdge(2, 3, 4);
+
+        KruskalAlgorithm algo = new KruskalAlgorithm();
+        List<KruskalAlgorithm.Edge> mst = algo.computeMST(graph);
+
+        assertEquals(3, mst.size());
+
+        int weight = mst.stream().mapToInt(KruskalAlgorithm.Edge::getWeight).sum();
+        assertEquals(19, weight);
+    }
+
+    @Test
+    @DisplayName("Single-vertex graph must return empty MST")
+    void testSingleVertexGraph() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(1);
+
+        KruskalAlgorithm algo = new KruskalAlgorithm();
+        assertTrue(algo.computeMST(graph).isEmpty());
+    }
+
+    @Test
+    @DisplayName("Graph with no edges returns empty MST")
+    void testGraphWithNoEdges() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(5);
+        KruskalAlgorithm algo = new KruskalAlgorithm();
+
+        assertTrue(algo.computeMST(graph).isEmpty());
+    }
+
+    @Test
+    @DisplayName("Disconnected graph produces a forest")
+    void testDisconnectedGraph() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(4);
+
+        graph.addEdge(0, 1, 3);
+        graph.addEdge(2, 3, 1);
+
+        KruskalAlgorithm algo = new KruskalAlgorithm();
+        List<KruskalAlgorithm.Edge> mst = algo.computeMST(graph);
+
+        assertEquals(2, mst.size());
+    }
+
+    // -------------------------------------------------------------
+    // GRAPH CONSTRUCTOR & EDGE VALIDATION
+    // -------------------------------------------------------------
+
+    @Test
+    @DisplayName("Graph constructor rejects invalid vertex counts")
+    void testInvalidGraphSize() {
+        assertThrows(IllegalArgumentException.class, () -> new KruskalAlgorithm.Graph(0));
+        assertThrows(IllegalArgumentException.class, () -> new KruskalAlgorithm.Graph(-3));
+    }
+
+    @Test
+    @DisplayName("Invalid edge indices throw exceptions")
+    void testInvalidEdgeVertices() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(3);
+
+        assertThrows(IndexOutOfBoundsException.class, () -> graph.addEdge(-1, 1, 2));
+        assertThrows(IndexOutOfBoundsException.class, () -> graph.addEdge(0, 3, 2));
+    }
+
+    @Test
+    @DisplayName("Negative weight edge must throw exception")
+    void testNegativeWeightEdge() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(3);
+        assertThrows(IllegalArgumentException.class, () -> graph.addEdge(0, 1, -5));
+    }
+
+    @Test
+    @DisplayName("Zero-weight edges are accepted")
+    void testZeroWeightEdge() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(2);
+        assertDoesNotThrow(() -> graph.addEdge(0, 1, 0));
+    }
+
+    // -------------------------------------------------------------
+    // EDGE COMPARISON & SORTING BEHAVIOR
+    // -------------------------------------------------------------
+
+    @Test
+    @DisplayName("Edges are sorted correctly when weights are equal")
+    void testEdgeSortingTies() {
+        KruskalAlgorithm.Edge e1 = new KruskalAlgorithm.Edge(0, 1, 5);
+        KruskalAlgorithm.Edge e2 = new KruskalAlgorithm.Edge(1, 2, 5);
+
+        assertEquals(0, e1.compareTo(e2));
+    }
+
+    @Test
+    @DisplayName("Algorithm chooses cheapest among parallel edges")
+    void testParallelEdges() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(3);
+
+        graph.addEdge(0, 1, 10);
+        graph.addEdge(0, 1, 3);
+        graph.addEdge(1, 2, 4);
+
+        List<KruskalAlgorithm.Edge> mst = new KruskalAlgorithm().computeMST(graph);
+
+        int weight = mst.stream().mapToInt(KruskalAlgorithm.Edge::getWeight).sum();
+        assertEquals(7, weight);
+    }
+
+    // -------------------------------------------------------------
+    // CYCLE & UNION-FIND BEHAVIOR
+    // -------------------------------------------------------------
+
+    @Test
+    @DisplayName("Graph containing cycles still produces correct MST")
+    void testCycleHeavyGraph() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(4);
+
+        graph.addEdge(0, 1, 1);
+        graph.addEdge(1, 2, 2);
+        graph.addEdge(2, 3, 3);
+
+        // Creating cycles
+        graph.addEdge(0, 2, 10);
+        graph.addEdge(1, 3, 10);
+
+        List<KruskalAlgorithm.Edge> mst = new KruskalAlgorithm().computeMST(graph);
+
+        assertEquals(3, mst.size());
+        assertEquals(6, mst.stream().mapToInt(KruskalAlgorithm.Edge::getWeight).sum());
+    }
+
+    @Test
+    @DisplayName("Union-Find path compression works (indirect test via MST)")
+    void testPathCompression() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(3);
+
+        graph.addEdge(0, 1, 1);
+        graph.addEdge(1, 2, 2);
+
+        // Forces multiple find() calls
+        new KruskalAlgorithm().computeMST(graph);
+
+        // Indirect validation:
+        // If path compression failed, algorithm would still work,
+        // but we can ensure no exception occurs (behavioral guarantee).
+        assertTrue(true);
+    }
+
+    @Test
+    @DisplayName("Union-by-rank is stable (indirect coverage)")
+    void testUnionByRank() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(4);
+
+        graph.addEdge(0, 1, 1);
+        graph.addEdge(2, 3, 1);
+        graph.addEdge(1, 2, 1);
+
+        List<KruskalAlgorithm.Edge> mst = new KruskalAlgorithm().computeMST(graph);
+
+        assertEquals(3, mst.size());
+    }
+
+    // -------------------------------------------------------------
+    // EARLY EXIT CONDITION
+    // -------------------------------------------------------------
+
+    @Test
+    @DisplayName("Algorithm stops early when MST is complete")
+    void testEarlyExit() {
+        KruskalAlgorithm.Graph graph = new KruskalAlgorithm.Graph(100);
+
+        // Only 99 edges needed, so extra edges should be ignored
+        for (int i = 0; i < 99; i++) {
+            graph.addEdge(i, i + 1, 1);
+        }
+
+        // Add a bunch of useless heavy edges
+        for (int i = 0; i < 500; i++) {
+            graph.addEdge(0, 1, 9999);
+        }
+
+        List<KruskalAlgorithm.Edge> mst = new KruskalAlgorithm().computeMST(graph);
+
+        assertEquals(99, mst.size()); // ensures early break
+    }
+}