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:

C++

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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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Java

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// Java implementation of the approach
import java.util.*;
  
class GFG 
{
    static int N = 100000;
  
    // To keep correct and reverse direction
    @SuppressWarnings("unchecked")
    static Vector<Integer>[] gr1 = new Vector[N];
    @SuppressWarnings("unchecked")
    static Vector<Integer>[] gr2 = new Vector[N];
  
    static boolean[] vis1 = new boolean[N];
    static boolean[] vis2 = new boolean[N];
  
    static {
        for (int i = 0; i < N; i++)
        {
            gr1[i] = new Vector<>();
            gr2[i] = new Vector<>();
        }
    }
  
    // Function to add edges
    static void Add_edge(int u, int v)
    {
        gr1[u].add(v);
        gr2[v].add(u);
    }
  
    // DFS function
    static void dfs1(int x)
    {
        vis1[x] = true;
        for (int i : gr1[x])
            if (!vis1[i])
                dfs1(i);
    }
  
    // DFS function
    static void dfs2(int x) 
    {
        vis2[x] = true;
        for (int i : gr2[x])
            if (!vis2[i])
                dfs2(i);
    }
  
    static boolean Is_connected(int n)
    {
  
        // Call for correct direction
        Arrays.fill(vis1, false);
        dfs1(1);
  
        // Call for reverse direction
        Arrays.fill(vis2, false);
        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] && !vis2[i])
                return false;
        }
  
        // If graph is connected
        return true;
    }
  
    // Driver Code
    public static void main(String[] args)
    {
        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))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
  
// This code is contributed by
// sanjeev2552

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Python3

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# Python3 implementation of the approach 
N = 100000
  
# To keep correct and reverse direction 
gr1 = {}; gr2 = {}; 
  
vis1 = [0] * N; vis2 = [0] * N; 
  
# Function to add edges 
def Add_edge(u, v) : 
  
    if u not in gr1 :
        gr1[u] = [];
          
    if v not in gr2 :
        gr2[v] = [];
          
    gr1[u].append(v);
    gr2[v].append(u); 
  
# DFS function 
def dfs1(x) : 
    vis1[x] = True;
    if x not in gr1 :
        gr1[x] = {};
          
    for i in gr1[x] :
        if (not vis1[i]) :
            dfs1(i) 
  
# DFS function 
def dfs2(x) : 
  
    vis2[x] = True
  
    if x not in gr2 :
        gr2[x] = {};
          
    for i in gr2[x] : 
        if (not vis2[i]) :
            dfs2(i); 
  
def Is_Connected(n) : 
  
    global vis1;
    global vis2;
      
    # Call for correct direction
    vis1 = [False] * len(vis1);
    dfs1(1);
      
    # Call for reverse direction
    vis2 = [False] * len(vis2);
    dfs2(1);
      
    for i in range(1, n + 1) :
          
        # If any vertex it not visited in any direction
        # Then graph is not connected
        if (not vis1[i] and not vis2[i]) :
            return False;
              
    # If graph is connected
    return True
  
# Driver code 
if __name__ == "__main__"
  
    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)) :
        print("Yes"); 
    else :
        print("No"); 
  
# This code is contributed by AnkitRai01

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C#

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// C# implementation of the approach
using System;
using System.Collections.Generic;
  
class GFG 
{
    static int N = 100000;
  
    // To keep correct and reverse direction
    static List<int>[] gr1 = new List<int>[N];
  
    static List<int>[] gr2 = new List<int>[N];
  
    static bool[] vis1 = new bool[N];
    static bool[] vis2 = new bool[N];
  
    // Function to add edges
    static void Add_edge(int u, int v)
    {
        gr1[u].Add(v);
        gr2[v].Add(u);
    }
  
    // DFS function
    static void dfs1(int x)
    {
        vis1[x] = true;
        foreach (int i in gr1[x])
            if (!vis1[i])
                dfs1(i);
    }
  
    // DFS function
    static void dfs2(int x) 
    {
        vis2[x] = true;
        foreach (int i in gr2[x])
            if (!vis2[i])
                dfs2(i);
    }
  
    static bool Is_connected(int n)
    {
  
        // Call for correct direction
        for (int i = 0; i < n; i++)
            vis1[i] = false;
        dfs1(1);
  
        // Call for reverse direction
        for (int i = 0; i < n; i++)
            vis2[i] = false;
        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] && !vis2[i])
                return false;
        }
  
        // If graph is connected
        return true;
    }
  
    // Driver Code
    public static void Main(String[] args)
    {
        int n = 4;
        for (int i = 0; i < N; i++)
        {
            gr1[i] = new List<int>();
            gr2[i] = new List<int>();
        }
          
        // Add edges
        Add_edge(1, 2);
        Add_edge(1, 3);
        Add_edge(2, 3);
        Add_edge(3, 4);
  
        // Function call
        if (Is_connected(n))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}
  
// This code is contributed by PrinciRaj1992

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Output:

Yes

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