Thursday 9 July 2015

Java Implementation of Kruskal's algorithm for calculating the Minimum Spanning Tree (MST).

Hi Friends,

Lets see the Java Implementation of Kruskal's algorithm for calculating the Minimum Spanning Tree (MST).

I have used the concept of disjoint sets and path compression for the implementation.  The solution is based upon the discussion on geeksforgeeks :
http://www.geeksforgeeks.org/greedy-algorithms-set-2-kruskals-minimum-spanning-tree-mst/






 For the above graph we have MST as below :






Below is the Code for the implementation of the  algorithm.

public class KrushkalAlgorithm {
    
    public static void main(String[] args) {
        /* Let us create following weighted graph
        10
   1--------2
   |  \     |
  6|   5\   |15
   |      \ |
   3--------4
       4       */
        
        Graph graph = new Graph(4);
        graph.addVertex(1);
        graph.addVertex(2);
        graph.addVertex(3);
        graph.addVertex(4);
        graph.addEdge(1, 2, 10);
        graph.addEdge(1, 3, 6);
        graph.addEdge(1, 4, 5);
        graph.addEdge(3, 4, 4);
        graph.addEdge(2, 4, 15);
        graph.applyKrushkalAlgo();
    }
    public static class Graph {
        Vertex[] vertices;
        Edge edgeList;
        int maxSize;
        int size;
        int edgeNum;

        public Graph(int maxSize) {
            this.maxSize = maxSize;
            vertices = new Vertex[maxSize];
        }

        public class Vertex {
            int rank;
            Vertex representative;
            int name;
            Neighbour adj;

            Vertex(int name) {
                this.name = name;
                representative = this; // makeset
            }
        }

        public class Neighbour {
            int index;
            Neighbour next;
            int weight;

            Neighbour(int index, int weight, Neighbour next) {
                this.index = index;
                this.weight = weight;
                this.next = next;
            }
        }

        public class Edge {
            Vertex src;
            Vertex desti;
            Edge next;
            int weight;

            Edge(Vertex src, Vertex desti, int weight, Edge next) {
                this.src = src;
                this.desti = desti;
                this.weight = weight;
                this.next = next;
            }
        }

        public void addVertex(int name) {
            vertices[size++] = new Vertex(name);
        }

        public void addEdge(int src, int dest, int weight) {
            vertices[src - 1].adj = new Neighbour(dest - 1, weight, vertices[src - 1].adj);
            edgeList = new Edge(vertices[src - 1], vertices[dest - 1], weight, edgeList);
            edgeNum++;
        }

        public void applyKrushkalAlgo() {
            Edge[] edges = new Edge[edgeNum];
            int i = 0;
            while (edgeList != null) {
                edges[i] = edgeList;
                i++;
                edgeList = edgeList.next;
            }
            quicksort(edges, 0, edgeNum - 1);
            for (i = 0; i < edgeNum; i++) {
                Vertex u = findSet(edges[i].src);
                Vertex v = findSet(edges[i].desti);
                if (u != v) {
                    System.out.println(edges[i].src.name + " - " + edges[i].desti.name+" weight "+edges[i].weight);
                    union(u, v);
                }
            }
        }

        public Vertex findSet(Vertex u) {
            if (u.representative != u) {
                u.representative = findSet(u.representative); // path compression
            }
            return u.representative;
        }

        public void union(Vertex u, Vertex v) {
            if(u.rank == v.rank){
                v.representative = u;
                u.rank++;
            }else if(u.rank < v.rank){
                v.representative = u;
            }else{
                u.representative = v;
            }
        }

        public void quicksort(Edge[] edges, int start, int end) {
            if (start < end) {
                swap(edges, end, start + (end - start) / 2);
                int pIndex = pivot(edges, start, end);
                quicksort(edges, start, pIndex - 1);
                quicksort(edges, pIndex + 1, end);
            }
        }

        public int pivot(Edge[] edges, int start, int end) {
            int pIndex = start;
            Edge pivot = edges[end];
            for (int i = start; i < end; i++) {
                if (edges[i].weight < pivot.weight) {
                    swap(edges, i, pIndex);
                    pIndex++;
                }
            }
            swap(edges, end, pIndex);
            return pIndex;
        }

        public void swap(Edge[] edges, int index1, int index2) {
            Edge temp = edges[index1];
            edges[index1] = edges[index2];
            edges[index2] = temp;
        }
    }
}



Output :
3 - 4 weight 4
1 - 4 weight 5
1 - 2 weight 10

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