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.

Examples:

Input:

Output: Yes

Input:

Output: No

Approach:

  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:

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// 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)
{
    gr1[u].push_back(v);
    gr2[v].push_back(u);
}
  
// DFS function
void dfs1(int x)
{
    vis1[x] = true;
  
    for (auto i : gr1[x])
        if (!vis1[i])
            dfs1(i);
}
  
// DFS function
void dfs2(int x)
{
    vis2[x] = true;
  
    for (auto i : gr2[x])
        if (!vis2[i])
            dfs2(i);
}
  
bool Is_Connected(int n)
{
    // Call for correct direction
    memset(vis1, false, sizeof vis1);
    dfs1(1);
  
    // Call for reverse direction
    memset(vis2, false, sizeof vis2);
    dfs2(1);
  
    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";
    else
        cout << "No";
  
    return 0;
}

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Output:

Yes


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