BAEL-3883: Boruvka's Algorithm for Minimum-Spanning Trees (#8816)

* BAEL-3883: Boruvka's Algorithm for Minimum-Spanning Trees

* BAEL-3883: checking in pom.xml

algorithms-miscellaneous-5/pom.xml

@@ -39,6 +39,16 @@
             <artifactId>guava</artifactId>
             <version>${guava.version}</version>
         </dependency>
+        <dependency>
+            <groupId>com.fasterxml.jackson.core</groupId>
+            <artifactId>jackson-databind</artifactId>
+            <version>${jackson.version}</version>
+        </dependency>
+        <dependency>
+            <groupId>org.junit.platform</groupId>
+            <artifactId>junit-platform-commons</artifactId>
+            <version>${junit.platform.version}</version>
+        </dependency>
 
         <dependency>
             <groupId>org.assertj</groupId>
@@ -66,6 +76,8 @@
         <commons-codec.version>1.11</commons-codec.version>
         <commons-math3.version>3.6.1</commons-math3.version>
         <guava.version>28.1-jre</guava.version>
+        <jackson.version>2.10.2</jackson.version>
+        <junit.platform.version>1.6.0</junit.platform.version>
     </properties>
 
 </project>

algorithms-miscellaneous-5/src/main/java/com/baeldung/algorithms/boruvka/BoruvkaMST.java

@@ -0,0 +1,61 @@
+package com.baeldung.algorithms.boruvka;
+
+public class BoruvkaMST {
+
+    private static Tree mst = new Tree();
+    private static int totalWeight;
+
+    public BoruvkaMST(Graph graph) {
+        DisjointSet dSet = new DisjointSet(graph.getNodes());
+
+        // repeat at most log N times or until we have N-1 edges
+        for (int t = 1; t < graph.getNodes() && mst.getEdgeCount() < graph.getNodes() - 1; t = t + t) {
+
+            // foreach tree in forest, find closest edge
+            Edge[] closestEdgeArray = new Edge[graph.getNodes()];
+            for (Edge edge : graph.getAllEdges()) {
+                int first = edge.getFirst();
+                int second = edge.getSecond();
+                int firstParent = dSet.getParent(first);
+                int secondParent = dSet.getParent(second);
+                if (firstParent == secondParent) {
+                    continue; // same tree
+                }
+                if (closestEdgeArray[firstParent] == null || edge.getWeight() < closestEdgeArray[firstParent].getWeight()) {
+                    closestEdgeArray[firstParent] = edge;
+                }
+                if (closestEdgeArray[secondParent] == null || edge.getWeight() < closestEdgeArray[secondParent].getWeight()) {
+                    closestEdgeArray[secondParent] = edge;
+                }
+            }
+
+            // add newly discovered edges to MST
+            for (int i = 0; i < graph.getNodes(); i++) {
+                Edge edge = closestEdgeArray[i];
+                if (edge != null) {
+                    int first = edge.getFirst();
+                    int second = edge.getSecond();
+                    // don't add the same edge twice
+                    if (dSet.getParent(first) != dSet.getParent(second)) {
+                        mst.addEdge(edge);
+                        totalWeight += edge.getWeight();
+                        dSet.union(first, second);
+                    }
+                }
+            }
+        }
+    }
+
+    public Iterable<Edge> getMST() {
+        return mst;
+    }
+
+    public int getTotalWeight() {
+        return totalWeight;
+    }
+
+    public String toString() {
+        return "MST: " + mst.toString() + " | Total Weight: " + totalWeight;
+    }
+
+}

algorithms-miscellaneous-5/src/main/java/com/baeldung/algorithms/boruvka/DisjointSet.java

@@ -0,0 +1,49 @@
+package com.baeldung.algorithms.boruvka;
+
+import java.util.Arrays;
+
+public class DisjointSet {
+
+    private int[] nodeParents;
+    private int[] nodeRanks;
+
+    public DisjointSet(int n) {
+        nodeParents = new int[n];
+        nodeRanks = new int[n];
+        for (int i = 0; i < n; i++) {
+            nodeParents[i] = i;
+            nodeRanks[i] = 0;
+        }
+    }
+
+    public int getParent(int node) {
+        while (node != nodeParents[node]) {
+            node = nodeParents[node];
+        }
+        return node;
+    }
+
+    public void union(int node1, int node2) {
+        int node1Parent = getParent(node1);
+        int node2Parent = getParent(node2);
+        if (node1Parent == node2Parent) {
+            return;
+        }
+
+        if (nodeRanks[node1Parent] < nodeRanks[node2Parent]) {
+            nodeParents[node1Parent] = node2Parent;
+        }
+        else if (nodeRanks[node1Parent] > nodeRanks[node2Parent]) {
+            nodeParents[node2Parent] = node1Parent;
+        }
+        else {
+            nodeParents[node2Parent] = node1Parent;
+            nodeRanks[node1Parent]++;
+        }
+    }
+
+    public String toString() {
+        return "Parent: " + Arrays.toString(nodeParents) + "Rank: " + Arrays.toString(nodeRanks);
+    }
+
+}

algorithms-miscellaneous-5/src/main/java/com/baeldung/algorithms/boruvka/Edge.java

@@ -0,0 +1,40 @@
+package com.baeldung.algorithms.boruvka;
+
+public class Edge {
+
+    private final int first;
+    private final int second;
+    private final int weight;
+
+    public Edge(int first, int second, int weight) {
+        this.first = first;
+        this.second = second;
+        this.weight = weight;
+    }
+
+    public double getWeight() {
+        return weight;
+    }
+
+    public int getFirst() {
+        return first;
+    }
+    
+    public int getSecond() {
+        return second;
+    }
+
+    public int getOtherNode(int firstNode) {
+        int secondNode = 0;
+        if (firstNode == first)
+            secondNode = second;
+        else if (firstNode == second)
+            secondNode = first;
+        return secondNode;
+    }
+
+    public String toString() {
+        return String.format("%d-%d %d", first, second, weight);
+    }
+
+}

algorithms-miscellaneous-5/src/main/java/com/baeldung/algorithms/boruvka/Graph.java

@@ -0,0 +1,64 @@
+package com.baeldung.algorithms.boruvka;
+
+import java.io.IOException;
+
+import com.fasterxml.jackson.core.JsonParseException;
+import com.fasterxml.jackson.databind.JsonMappingException;
+
+public class Graph {
+
+    private int nodes;
+    private int edges;
+    private Tree[] trees;
+
+    public Graph(Input jsonGraph) throws JsonParseException, JsonMappingException, IOException {
+        nodes = jsonGraph.getNodes();
+        trees = (Tree[]) new Tree[nodes];
+        for (int i = 0; i < nodes; i++) {
+            trees[i] = new Tree();
+        }
+
+        int edgesFromInput = jsonGraph.getEdges();
+        for (int i = 0; i < edgesFromInput; i++) {
+            int first = jsonGraph.getEdgeList()
+                .get(i)
+                .getFirst();
+            int second = jsonGraph.getEdgeList()
+                .get(i)
+                .getSecond();
+            int weight = jsonGraph.getEdgeList()
+                .get(i)
+                .getWeight();
+            Edge edge = new Edge(first, second, weight);
+            
+            trees[first].addEdge(edge);
+            trees[second].addEdge(edge);
+            edges++;
+        }
+
+    }
+
+    public int getNodes() {
+        return nodes;
+    }
+
+    public int getEdges() {
+        return edges;
+    }
+
+    public Iterable<Edge> iterableTree(int i) {
+        return trees[i];
+    }
+
+    public Iterable<Edge> getAllEdges() {
+        Iterable<Edge> list = new Tree();
+        for (int i = 0; i < nodes; i++) {
+            for (Edge edge : iterableTree(i)) {
+                if (edge.getOtherNode(i) > i) {
+                    ((Tree) list).addEdge(edge);
+                }
+            }
+        }
+        return list;
+    }
+}

algorithms-miscellaneous-5/src/main/java/com/baeldung/algorithms/boruvka/Input.java

@@ -0,0 +1,65 @@
+package com.baeldung.algorithms.boruvka;
+
+import java.util.List;
+
+public class Input {
+    private int nodes;
+    private int edges;
+    private List<E> edgeList;
+
+    public int getNodes() {
+        return nodes;
+    }
+
+    public void setNodes(int nodes) {
+        this.nodes = nodes;
+    }
+
+    public int getEdges() {
+        return edges;
+    }
+
+    public void setEdges(int edges) {
+        this.edges = edges;
+    }
+
+    public List<E> getEdgeList() {
+        return edgeList;
+    }
+
+    public void setEdgeList(List<E> edgeList) {
+        this.edgeList = edgeList;
+    }
+
+    static class E {
+        private int first;
+        private int second;
+        private int weight;
+
+        public int getFirst() {
+            return first;
+        }
+
+        public void setFirst(int first) {
+            this.first = first;
+        }
+
+        public int getSecond() {
+            return second;
+        }
+
+        public void setSecond(int second) {
+            this.second = second;
+        }
+
+        public int getWeight() {
+            return weight;
+        }
+
+        public void setWeight(int weight) {
+            this.weight = weight;
+        }
+
+    }
+
+}

algorithms-miscellaneous-5/src/main/java/com/baeldung/algorithms/boruvka/Tree.java

@@ -0,0 +1,63 @@
+package com.baeldung.algorithms.boruvka;
+
+import java.util.Iterator;
+
+public class Tree implements Iterable<Edge> {
+    private Node root;
+    private int edgeCount;
+
+    private static class Node {
+        private Edge edge;
+        private Node next;
+
+        public String toString() {
+            String nextStr = next != null ? next.toString() : "";
+            return edge.toString() + " | " + nextStr;
+        }
+    }
+
+    public Tree() {
+        root = null;
+        edgeCount = 0;
+    }
+
+    public int getEdgeCount() {
+        return edgeCount;
+    }
+
+    public void addEdge(Edge edge) {
+        Node oldRoot = root;
+        root = new Node();
+        root.edge = edge;
+        root.next = oldRoot;
+        edgeCount++;
+    }
+
+    public String toString() {
+        String rootStr = root != null ? root.toString() : "";
+        return "Tree: " + rootStr + "Size: " + edgeCount;
+    }
+
+    public Iterator<Edge> iterator() {
+        return new LinkedIterator(root);
+    }
+
+    private class LinkedIterator implements Iterator<Edge> {
+        private Node current;
+
+        public LinkedIterator(Node root) {
+            current = root;
+        }
+
+        public boolean hasNext() {
+            return current != null;
+        }
+
+        public Edge next() {
+            Edge edge = current.edge;
+            current = current.next;
+            return edge;
+        }
+    }
+
+}

algorithms-miscellaneous-5/src/test/java/com/baeldung/algorithms/boruvka/BoruvkaUnitTest.java

@@ -0,0 +1,48 @@
+package com.baeldung.algorithms.boruvka;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import java.io.BufferedReader;
+import java.io.IOException;
+import java.io.InputStreamReader;
+
+import org.junit.Before;
+import org.junit.Test;
+
+import com.fasterxml.jackson.core.JsonParseException;
+import com.fasterxml.jackson.databind.JsonMappingException;
+import com.fasterxml.jackson.databind.ObjectMapper;
+
+public class BoruvkaUnitTest {
+
+    private Input input;
+    private static String INPUT_JSON = "/input.json";
+
+    @Before
+    public void convertInputJsonToObject() throws JsonParseException, JsonMappingException, IOException {
+        ObjectMapper mapper = new ObjectMapper();
+        StringBuilder jsonStr = new StringBuilder();
+        try (BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(BoruvkaMST.class.getResourceAsStream(INPUT_JSON)))) {
+            String line;
+            while ((line = bufferedReader.readLine()) != null) {
+                jsonStr.append(line)
+                    .append("\n");
+            }
+        }
+
+        input = mapper.readValue(jsonStr.toString(), Input.class);
+
+    }
+
+    @Test
+    public void givenInputGraph_whenBoruvkaPerformed_thenMinimumSpanningTree() throws JsonParseException, JsonMappingException, IOException {
+        Graph graph = new Graph(input);
+        BoruvkaMST boruvkaMST = new BoruvkaMST(graph);
+
+        Tree mst = (Tree) boruvkaMST.getMST();
+
+        assertEquals(30, boruvkaMST.getTotalWeight());
+        assertEquals(4, mst.getEdgeCount());
+    }
+
+}

algorithms-miscellaneous-5/src/test/resources/input.json

@@ -0,0 +1,41 @@
+{
+	"nodes": 5,
+	"edges": 7,
+	"edgeList": [
+		{
+			"first": 0,
+			"second": 1,
+			"weight": 8
+		},
+		{
+			"first": 0,
+			"second": 2,
+			"weight": 5
+		},
+		{
+			"first": 1,
+			"second": 2,
+			"weight": 9
+		},
+		{
+			"first": 1,
+			"second": 3,
+			"weight": 11
+		},
+		{
+			"first": 2,
+			"second": 3,
+			"weight": 15
+		},
+		{
+			"first": 2,
+			"second": 4,
+			"weight": 10
+		},
+		{
+			"first": 3,
+			"second": 4,
+			"weight": 7
+		}
+	]
+}