Count the number of non-reachable nodes

Given an undirected graph and a set of vertices, we have to count the number of non reachable nodes from the given head node using depth first search.

Consider below undirected graph with two disconnected components:


In this graph if we consider 0 as head node, then the node 0, 1 and 2 are reachable. We mark all the reachable nodes as visited. All those nodes which are not mark as visited i.e, node 3 and 4 are non reachable nodes. Hence their count is 2.


Input :   5
          0 1
          0 2
          1 2
          3 4
Output : 2

We can either use BFS or DFS for this purpose. In below implementation DFS is used. We do DFS from given source. Since the given graph is undirected, all the vertices that belong to the disconnected component are non-reachable nodes. We use the visit array for this purpose, the array which is used to keep track of non-visited vertices in DFS. In DFS, if we start from head node it will mark all the nodes connected to the head node as visited. Then after traversing the graph we count the number of nodes that are not mark as visited from the head node.

// C++ program to count non-reachable nodes
// from a given source using DFS.
#include <iostream>
#include <list>
using namespace std;

// Graph class represents a directed graph
// using adjacency list representation
class Graph {
    int V; // No. of vertices

    // Pointer to an array containing
    // adjacency lists
    list<int>* adj;

    // A recursive function used by DFS
    void DFSUtil(int v, bool visited[]);

    Graph(int V); // Constructor

    // function to add an edge to graph
    void addEdge(int v, int w);

    // DFS traversal of the vertices
    // reachable from v
    int countNotReach(int v);

Graph::Graph(int V)
    this->V = V;
    adj = new list<int>[V];

void Graph::addEdge(int v, int w)
    adj[v].push_back(w); // Add w to v’s list.
    adj[w].push_back(v); // Add v to w's list.

void Graph::DFSUtil(int v, bool visited[])
    // Mark the current node as visited and
    // print it
    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);

// Returns count of not reachable nodes from
// vertex v.
// It uses recursive DFSUtil()
int Graph::countNotReach(int v)
    // Mark all the vertices as not visited
    bool* visited = new bool[V];
    for (int i = 0; i < V; i++)
        visited[i] = false;

    // Call the recursive helper function
    // to print DFS traversal
    DFSUtil(v, visited);

    // Return count of not visited nodes
    int count = 0;
    for (int i = 0; i < V; i++) {
        if (visited[i] == false)
    return count;

int main()
    // Create a graph given in the above diagram
    Graph g(8);
    g.addEdge(0, 1);
    g.addEdge(0, 2);
    g.addEdge(1, 2);
    g.addEdge(3, 4);
    g.addEdge(4, 5);
    g.addEdge(6, 7);

    cout << g.countNotReach(2);

    return 0;



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