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.


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 C++ representation :





// 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)
    // 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
    cout << compute(graph, N);




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