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Program to count Number of connected components in an undirected graph

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  • Difficulty Level : Medium
  • Last Updated : 11 Apr, 2022
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Given an undirected graph g, the task is to print the number of connected components in the graph.

Examples:  

Input: 
 

Output:
There are three connected components: 
1 – 5, 0 – 2 – 4 and 3 

Approach: 

DFS visit all the connected vertices of the given vertex.

When iterating over all vertices, whenever we see unvisited node, it is because it was not visited by DFS done on vertices so far.

That means it is not connected to any previous nodes visited so far i.e it was not part of previous components.

Hence this node belongs to new component.

This means, before visiting this node, we just finished visiting all nodes previous component and that component is now complete.

So we need to increment component counter as we completed a component.

The idea is to use a variable count to store the number of connected components and do the following steps:

Initialize all vertices as unvisited.
For all the vertices check if a vertex has not been visited, then perform DFS on that vertex and increment the variable count by 1.

Below is the implementation of the above approach: 

C++




// C++ program for above approach
#include <bits/stdc++.h>
using namespace std;
 
// Graph class represents a undirected graph
// using adjacency list representation
class Graph {
    // No. of vertices
    int V;
 
    // Pointer to an array containing adjacency lists
    list<int>* adj;
 
    // A function used by DFS
    void DFSUtil(int v, bool visited[]);
 
public:
    // Constructor
    Graph(int V);
 
    void addEdge(int v, int w);
    int NumberOfconnectedComponents();
};
 
// Function to return the number of
// connected components in an undirected graph
int Graph::NumberOfconnectedComponents()
{
 
    // Mark all the vertices as not visited
    bool* visited = new bool[V];
 
    // To store the number of connected components
    int count = 0;
    for (int v = 0; v < V; v++)
        visited[v] = false;
 
    for (int v = 0; v < V; v++) {
        if (visited[v] == false) {
            DFSUtil(v, visited);
            count += 1;
        }
    }
 
    return count;
}
 
void Graph::DFSUtil(int v, bool visited[])
{
 
    // Mark the current node as visited
    visited[v] = true;
 
    // Recur for all the vertices
    // adjacent to this vertex
    list<int>::iterator i;
 
    for (i = adj[v].begin(); i != adj[v].end(); ++i)
        if (!visited[*i])
            DFSUtil(*i, visited);
}
 
Graph::Graph(int V)
{
    this->V = V;
    adj = new list<int>[V];
}
 
// Add an undirected edge
void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w);
    adj[w].push_back(v);
}
 
// Driver code
int main()
{
    Graph g(5);
    g.addEdge(1, 0);
    g.addEdge(2, 3);
    g.addEdge(3, 4);
 
    cout << g.NumberOfconnectedComponents();
 
    return 0;
}

Java




import java.util.*;
class Graph {
    private int V; // No. of vertices in graph.
 
    private LinkedList<Integer>[] adj; // Adjacency List
                                       // representation
 
    ArrayList<ArrayList<Integer> > components
        = new ArrayList<>();
 
    @SuppressWarnings("unchecked") Graph(int v)
    {
        V = v;
        adj = new LinkedList[v];
 
        for (int i = 0; i < v; i++)
            adj[i] = new LinkedList();
    }
 
    void addEdge(int u, int w)
    {
        adj[u].add(w);
        adj[w].add(u); // Undirected Graph.
    }
 
    void DFSUtil(int v, boolean[] visited,
                 ArrayList<Integer> al)
    {
        visited[v] = true;
        al.add(v);
        System.out.print(v + " ");
        Iterator<Integer> it = adj[v].iterator();
 
        while (it.hasNext()) {
            int n = it.next();
            if (!visited[n])
                DFSUtil(n, visited, al);
        }
    }
 
    void DFS()
    {
        boolean[] visited = new boolean[V];
 
        for (int i = 0; i < V; i++) {
            ArrayList<Integer> al = new ArrayList<>();
            if (!visited[i]) {
                DFSUtil(i, visited, al);
                components.add(al);
            }
        }
    }
 
    int ConnecetedComponents() { return components.size(); }
}
public class Main {
    public static void main(String[] args)
    {
        Graph g = new Graph(6);
 
        g.addEdge(1, 5);
        g.addEdge(0, 2);
        g.addEdge(2, 4);
        System.out.println("Graph DFS:");
        g.DFS();
        System.out.println(
            "\nNumber of Conneceted Components: "
            + g.ConnecetedComponents());
    }
}
// Code contributed by Madhav Chittlangia.

Python3




# Python3 program for above approach
 
# Graph class represents a undirected graph
# using adjacency list representation
class Graph:
     
    def __init__(self, V):
 
        # No. of vertices
        self.V = V
 
        # Pointer to an array containing
        # adjacency lists
        self.adj = [[] for i in range(self.V)]
 
    # Function to return the number of
    # connected components in an undirected graph
    def NumberOfconnectedComponents(self):
         
        # Mark all the vertices as not visited
        visited = [False for i in range(self.V)]
         
        # To store the number of connected
        # components
        count = 0
         
        for v in range(self.V):
            if (visited[v] == False):
                self.DFSUtil(v, visited)
                count += 1
                 
        return count
         
    def DFSUtil(self, v, visited):
 
        # Mark the current node as visited
        visited[v] = True
 
        # Recur for all the vertices
        # adjacent to this vertex
        for i in self.adj[v]:
            if (not visited[i]):
                self.DFSUtil(i, visited)
                 
    # Add an undirected edge
    def addEdge(self, v, w):
         
        self.adj[v].append(w)
        self.adj[w].append(v)
         
# Driver code       
if __name__=='__main__':
     
    g = Graph(5)
    g.addEdge(1, 0)
    g.addEdge(2, 3)
    g.addEdge(3, 4)
     
    print(g.NumberOfconnectedComponents())
 
# This code is contributed by rutvik_56

Javascript




<script>
 
// JavaScript program for above approach
 
// Graph class represents a undirected graph
// using adjacency list representation
class Graph{
     
    constructor(V){
 
        // No. of vertices
        this.V = V
 
        // Pointer to an array containing
        // adjacency lists
        this.adj = new Array(this.V);
        for(let i=0;i<V;i++){
            this.adj[i] = new Array()
        }
    }
 
    // Function to return the number of
    // connected components in an undirected graph
    NumberOfconnectedComponents(){
         
        // Mark all the vertices as not visited
        let visited = new Array(this.V).fill(false);
         
        // To store the number of connected
        // components
        let count = 0
         
        for(let v=0;v<this.V;v++){
            if (visited[v] == false){
                this.DFSUtil(v, visited)
                count += 1
            }
        }
                 
        return count
    }
 
    DFSUtil(v, visited){
 
        // Mark the current node as visited
        visited[v] = true;
 
        // Recur for all the vertices
        // adjacent to this vertex
        for(let i of this.adj[v]){
            if (visited[i] == false){
                this.DFSUtil(i, visited)
            }
        }  
     
    }
                 
    // Add an undirected edge
    addEdge(v, w){
        this.adj[v].push(w)
        this.adj[w].push(v)
    }
     
}
         
// Driver code   
let g = new Graph(5)
g.addEdge(1, 0)
g.addEdge(2, 3)
g.addEdge(3, 4)
 
document.write(g.NumberOfconnectedComponents(),"</br>")
 
// This code is contributed by shinjanpatra
</script>

Output

2

Complexity Analysis:

Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.
Space Complexity: O(V), since an extra visited array of size V is required.


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