Count single node isolated sub-graphs in a disconnected graph

A disconnected Graph with N vertices and K edges is given. The task is to find the count of singleton sub-graphs. A singleton graph is one with only single vertex.

Examples:

Input : 
Vertices : 6
Edges :    1 2
           1 3
           5 6
Output : 1
Explanation :  The Graph has 3 components : {1-2-3}, {5-6}, {4}
Out of these, the only component forming singleton graph is {4}.

The idea is simple for graph given as adjacency list representation. We traverse the list and find the indices(representing a node) with no elements in list, i.e. no connected components.

Below is the representation :

C++

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// CPP code to count the singleton sub-graphs
// in a disconnected graph
#include <bits/stdc++.h>
using namespace std;
  
// Function to compute the count
int compute(vector<int> graph[], int N)
{
    // Storing intermediate result
    int count = 0;
  
    // Traversing the Nodes
    for (int i = 1; i <= N; i++)
  
        // Singleton component
        if (graph[i].size() == 0)
            count++;    
  
    // Returning the result
    return count;
}
  
// Driver
int main()
{
    // Number of nodes
    int N = 6;
  
    // Adjacency list for edges 1..6
    vector<int> graph[7];
  
    // Representing edges
    graph[1].push_back(2);
    graph[2].push_back(1);
  
    graph[2].push_back(3);
    graph[3].push_back(2);
  
    graph[5].push_back(6);
    graph[6].push_back(5);
  
    cout << compute(graph, N);
}

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Java

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// Java code to count the singleton sub-graphs 
// in a disconnected graph 
import java.util.*;
  
class GFG
{
  
// Function to compute the count 
static int compute(int []graph, int N) 
    // Storing intermediate result 
    int count = 0
      
    // Traversing the Nodes 
    for (int i = 1; i < 7; i++) 
    {
        // Singleton component 
        if (graph[i] == 0
            count++;     
    }
          
    // Returning the result 
    return count; 
  
// Driver Code
public static void main(String[] args)
{
    // Number of nodes 
    int N = 6
  
    // Adjacency list for edges 1..6 
    int []graph = new int[7];
    // Representing edges 
    graph[1] = 2;
    graph[2] = 1;
    graph[2] = 3;
    graph[3] = 2;
    graph[5] = 6;
    graph[6] = 5;
  
    System.out.println(compute(graph, N)); 
}
}
  
// This code is contributed by PrinciRaj1992 

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Python3

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# Python code to count the singleton sub-graphs 
# in a disconnected graph 
   
# Function to compute the count 
def compute(graph, N):
    # Storing intermediate result 
    count = 0 
    
    # Traversing the Nodes
    for i in range(1, N+1):
    
        # Singleton component 
        if (len(graph[i]) == 0):
            count += 1    
    
    # Returning the result 
    return count
    
# Driver 
if __name__ == '__main__':
  
    # Number of nodes 
    N = 6 
    
    # Adjacency list for edges 1..6 
    graph = [[] for i in range(7)] 
    
    # Representing edges 
    graph[1].append(2
    graph[2].append(1
    
    graph[2].append(3
    graph[3].append(2
    
    graph[5].append(6
    graph[6].append(5
    
    print(compute(graph, N))

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C#

// C# code to count the singleton sub-graphs
// in a disconnected graph
using System;

class GFG
{

// Function to compute the count
static int compute(int []graph, int N)
{
// Storing intermediate result
int count = 0;

// Traversing the Nodes
for (int i = 1; i < 7; i++) { // Singleton component if (graph[i] == 0) count++; } // Returning the result return count; } // Driver Code public static void Main(String[] args) { // Number of nodes int N = 6; // Adjacency list for edges 1..6 int []graph = new int[7]; // Representing edges graph[1] = 2; graph[2] = 1; graph[2] = 3; graph[3] = 2; graph[5] = 6; graph[6] = 5; Console.WriteLine(compute(graph, N)); } } // This code is contributed by 29AjayKumar [tabbyending] Output:

1

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