Kruskal algorithm in c++

Sore Sardine answered on May 26, 2022 Popularity 10/10 Helpfulness 2/10

answer Kruskal algorithm in c++

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Kruskal algorithm in c++

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Kruskal MST

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Contributed on May 26 2022

Sore Sardine

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kruskal algorithm

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Take all weighted edges and sort them from smallest to highest
Pick the smallest edge and check if it forms a cycle with the existing tree. If so discard. If not add to tree.
Keep picking until you have v-1 edges. 
All answers should have v-1 edges

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Contributed on Jul 26 2022

Javasper

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kruskal's algorithm

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// Java program for Kruskal's algorithm to
// find Minimum Spanning Tree of a given
// connected, undirected and  weighted graph
 
import java.util.ArrayList;
import java.util.Comparator;
import java.util.List;
 
public class KruskalsMST {
 
      // defines edge structure
    static class Edge {
        int src, dest, weight;
 
        public Edge(int src, int dest, int weight) {
            this.src = src;
            this.dest = dest;
            this.weight = weight;
        }
    }
     
  // defines subset element structure
    static class Subset {
        int parent, rank;
 
        public Subset(int parent, int rank) {
            this.parent = parent;
            this.rank = rank;
        }
    }
 
    // Starting point of program execution
    public static void main(String[] args) {
        /*****************************************
         * Let us create following weighted graph
                10
           0--------1
           | -      |
          6|   5-   |15
           |      - |
           2--------3
               4      
         *****************************************/
        int V = 4;
        List<Edge> graphEdges = new ArrayList<Edge>(List.of(
                new Edge(0, 1, 10),               
                new Edge(0, 2, 6),   
                new Edge(0, 3, 5),
                new Edge(1, 3, 15),
                new Edge(2, 3, 4)
        ));
       
          // Step 1: sort the edges in non-decreasing order
        // (increasing with repetition allowed)
        graphEdges.sort(new Comparator<Edge>() {
            @Override
            public int compare(Edge o1, Edge o2) {
                return o1.weight - o2.weight;
            }
        });
 
        kruskals(V, graphEdges);
    }
 
 
    private static void kruskals(int V, List<Edge> edges) {
        int j = 0;
        int noOfEdges = 0;
        // Allocate memory for creating V subsets
        Subset subsets[] = new Subset[V];
       
          // Allocate memory for results
        Edge results[] = new Edge[V];
 
        // Create V subsets with single elements
        for (int i = 0; i < V; i++) {
            subsets[i] = new Subset(i, 0);
        }
 
        // Number of edges to be taken is equal to V-1
        while (noOfEdges < V - 1) {
            // Step 2: Pick the smallest edge. And increment
            // the index for next iteration
            Edge nextEdge = edges.get(j);
            int x = findRoot(subsets, nextEdge.src);
            int y = findRoot(subsets, nextEdge.dest);
 
            // If including this edge doesn't cause cycle,
            // include it in result and increment the index
            // of result for next edge
            if (x != y) {
                results[noOfEdges] = nextEdge;
                union(subsets, x, y);
                noOfEdges++;
            }
 
            j++;
        }
 
        // print the contents of result[] to display the built MST
        System.out.println("Following are the edges of the constructed MST:");
        System.out.println("-----------------------------------------------");
        int minCost = 0;
        for (int i = 0; i < noOfEdges; i++) {
            System.out.println(results[i].src + " - " + results[i].dest + ": " + results[i].weight);
            minCost += results[i].weight;
        }
        System.out.println("-----------------------------------------------");
        System.out.println("Total cost of MST: "+minCost);
 
    }
 
    private static void union(Subset[] subsets, int x, int y) {
        int rootX = findRoot(subsets, x);
        int rootY = findRoot(subsets, y);
 
        if (subsets[rootY].rank < subsets[rootX].rank) {
            subsets[rootY].parent = rootX;
        } else if (subsets[rootX].rank < subsets[rootY].rank) {
            subsets[rootX].parent = rootY;
        } else {
            subsets[rootY].parent = rootX;
            subsets[rootX].rank++;
        }
    }
 
    private static int findRoot(Subset[] subsets, int i) {
        if (subsets[i].parent == i)
            return subsets[i].parent;
 
        subsets[i].parent = findRoot(subsets, subsets[i].parent);
        return subsets[i].parent;
    }
}
// This code is contributed by Salvino D'sa

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Contributed on Feb 11 2023

vinay giri goswami

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kruskal algorithm

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// C++ program for the above approach
 
#include <bits/stdc++.h>
using namespace std;
 
// DSU data structure
// path compression + rank by union
 
class DSU {
    int* parent;
    int* rank;
 
public:
    DSU(int n)
    {
        parent = new int[n];
        rank = new int[n];
 
        for (int i = 0; i < n; i++) {
            parent[i] = -1;
            rank[i] = 1;
        }
    }
 
    // Find function
    int find(int i)
    {
        if (parent[i] == -1)
            return i;
 
        return parent[i] = find(parent[i]);
    }
 
    // Union function
    void unite(int x, int y)
    {
        int s1 = find(x);
        int s2 = find(y);
 
        if (s1 != s2) {
            if (rank[s1] < rank[s2]) {
                parent[s1] = s2;
                rank[s2] += rank[s1];
            }
            else {
                parent[s2] = s1;
                rank[s1] += rank[s2];
            }
        }
    }
};
 
class Graph {
    vector<vector<int> > edgelist;
    int V;
 
public:
    Graph(int V) { this->V = V; }
 
    void addEdge(int x, int y, int w)
    {
        edgelist.push_back({ w, x, y });
    }
 
    void kruskals_mst()
    {
        // 1. Sort all edges
        sort(edgelist.begin(), edgelist.end());
 
        // Initialize the DSU
        DSU s(V);
        int ans = 0;
        cout << "Following are the edges in the "
                "constructed MST"
             << endl;
        for (auto edge : edgelist) {
            int w = edge[0];
            int x = edge[1];
            int y = edge[2];
 
            // Take this edge in MST if it does
            // not forms a cycle
            if (s.find(x) != s.find(y)) {
                s.unite(x, y);
                ans += w;
                cout << x << " -- " << y << " == " << w
                     << endl;
            }
        }
 
        cout << "Minimum Cost Spanning Tree: " << ans;
    }
};
 
// Driver's code
int main()
{
    /* Let us create following weighted graph
                   10
              0--------1
              |  \     |
             6|   5\   |15
              |      \ |
              2--------3
                  4       */
    Graph g(4);
    g.addEdge(0, 1, 10);
    g.addEdge(1, 3, 15);
    g.addEdge(2, 3, 4);
    g.addEdge(2, 0, 6);
    g.addEdge(0, 3, 5);
 
    // Function call
    g.kruskals_mst();
    return 0;
}

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Source: www.geeksforgeeks.org

Tags: algorithm algo

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Contributed on Nov 11 2022

Fantastic Flatworm

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Kruskal algorithm in c++

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