Check if a directed graph is connected or not

Given a directed graph. The task is to check if the given graph is connected or not.



Output: Yes


Output: No


  1. Take two bool arrays vis1 and vis2 of size N (number of nodes of a graph) and keep false in all indexes.
  2. Start at a random vertex v of the graph G, and run a DFS(G, v).
  3. Make all visited vertices v as vis1[v] = true.
  4. Now reverse the direction of all the edges.
  5. Start DFS at the vertex which was chosen at step 2.
  6. Make all visited vertices v as vis2[v] = true.
  7. If any vertex v has vis1[v] = false and vis2[v] = false then the graph is not connected.

Below is the implementation of the above approach:





// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define N 100000
// To keep correct and reverse direction
vector<int> gr1[N], gr2[N];
bool vis1[N], vis2[N];
// Function to add edges
void Add_edge(int u, int v)
// DFS function
void dfs1(int x)
    vis1[x] = true;
    for (auto i : gr1[x])
        if (!vis1[i])
// DFS function
void dfs2(int x)
    vis2[x] = true;
    for (auto i : gr2[x])
        if (!vis2[i])
bool Is_Connected(int n)
    // Call for correct direction
    memset(vis1, false, sizeof vis1);
    // Call for reverse direction
    memset(vis2, false, sizeof vis2);
    for (int i = 1; i <= n; i++) {
        // If any vertex it not visited in any direction
        // Then graph is not connected
        if (!vis1[i] and !vis2[i])
            return false;
    // If graph is connected
    return true;
// Driver code
int main()
    int n = 4;
    // Add edges
    Add_edge(1, 2);
    Add_edge(1, 3);
    Add_edge(2, 3);
    Add_edge(3, 4);
    // Function call
    if (Is_Connected(n))
        cout << "Yes";
        cout << "No";
    return 0;




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