Check if a given graph is Bipartite using DFS
Given a connected graph, check if the graph is bipartite or not. A bipartite graph is possible if the graph coloring is possible using two colors such that vertices in a set are colored with the same color. Note that it is possible to color a cycle graph with even cycle using two colors. For example, see the following graph.
It is not possible to color a cycle graph with an odd cycle using two colors.
In the previous post, an approach using BFS has been discussed. In this post, an approach using DFS has been implemented.
Given below is the algorithm to check for bipartiteness of a graph.
- Use a color[] array which stores 0 or 1 for every node which denotes opposite colors.
- Call the function DFS from any node.
- If the node u has not been visited previously, then assign !color[v] to color[u] and call DFS again to visit nodes connected to u.
- If at any point, color[u] is equal to color[v], then the node is bipartite.
- Modify the DFS function such that it returns a boolean value at the end.
Below is the implementation of the above approach:
C++
// C++ program to check if a connected// graph is bipartite or not suing DFS#include <bits/stdc++.h>using namespace std;// function to store the connected nodesvoid addEdge(vector<int> adj[], int u, int v){ adj[u].push_back(v); adj[v].push_back(u);}// function to check whether a graph is bipartite or notbool isBipartite(vector<int> adj[], int v, vector<bool>& visited, vector<int>& color){ for (int u : adj[v]) { // if vertex u is not explored before if (visited[u] == false) { // mark present vertic as visited visited[u] = true; // mark its color opposite to its parent color[u] = !color[v]; // if the subtree rooted at vertex v is not bipartite if (!isBipartite(adj, u, visited, color)) return false; } // if two adjacent are colored with same color then // the graph is not bipartite else if (color[u] == color[v]) return false; } return true;}// Driver Codeint main(){ // no of nodes int N = 6; // to maintain the adjacency list of graph vector<int> adj[N + 1]; // to keep a check on whether // a node is discovered or not vector<bool> visited(N + 1); // to color the vertices // of graph with 2 color vector<int> color(N + 1); // adding edges to the graph addEdge(adj, 1, 2); addEdge(adj, 2, 3); addEdge(adj, 3, 4); addEdge(adj, 4, 5); addEdge(adj, 5, 6); addEdge(adj, 6, 1); // marking the source node as visited visited[1] = true; // marking the source node with a color color[1] = 0; // Function to check if the graph // is Bipartite or not if (isBipartite(adj, 1, visited, color)) { cout << "Graph is Bipartite"; } else { cout << "Graph is not Bipartite"; } return 0;} |
Java
// Java program to check if a connected// graph is bipartite or not suing DFSimport java.util.*;class GFG{// Function to store the connected nodesstatic void addEdge(ArrayList<ArrayList<Integer>> adj, int u, int v){ adj.get(u).add(v); adj.get(v).add(u);}// Function to check whether a// graph is bipartite or notstatic boolean isBipartite(ArrayList<ArrayList<Integer>> adj, int v, boolean visited[], int color[]){ for(int u : adj.get(v)) { // If vertex u is not explored before if (visited[u] == false) { // Mark present vertic as visited visited[u] = true; // Mark its color opposite to its parent color[u] = 1 - color[v]; // If the subtree rooted at vertex // v is not bipartite if (!isBipartite(adj, u, visited, color)) return false; } // If two adjacent are colored with // same color then the graph is // not bipartite else if (color[u] == color[v]) return false; } return true;}// Driver Codepublic static void main(String args[]){ // No of nodes int N = 6; // To maintain the adjacency list of graph ArrayList< ArrayList<Integer>> adj = new ArrayList< ArrayList<Integer>>(N + 1); // Initialize all the vertex for(int i = 0; i <= N; i++) { adj.add(new ArrayList<Integer>()); } // To keep a check on whether // a node is discovered or not boolean visited[] = new boolean[N + 1]; // To color the vertices // of graph with 2 color int color[] = new int[N + 1]; // The value '-1' of colorArr[i] is // used to indicate that no color is // assigned to vertex 'i'. The value // 1 is used to indicate first color // is assigned and value 0 indicates // second color is assigned. Arrays.fill(color, -1); // Adding edges to the graph addEdge(adj, 1, 2); addEdge(adj, 2, 3); addEdge(adj, 3, 4); addEdge(adj, 4, 5); addEdge(adj, 5, 6); addEdge(adj, 6, 1); // Marking the source node as visited visited[1] = true; // Marking the source node with a color color[1] = 0; // Function to check if the graph // is Bipartite or not if (isBipartite(adj, 1, visited, color)) { System.out.println("Graph is Bipartite"); } else { System.out.println("Graph is not Bipartite"); }}}// This code is contributed by adityapande88 |
Python3
# Python3 program to check if a connected# graph is bipartite or not suing DFS # Function to store the connected nodesdef addEdge(adj, u, v): adj[u].append(v) adj[v].append(u)# Function to check whether a graph is# bipartite or notdef isBipartite(adj, v, visited, color): for u in adj[v]: # If vertex u is not explored before if (visited[u] == False): # Mark present vertic as visited visited[u] = True # Mark its color opposite to its parent color[u] = not color[v] # If the subtree rooted at vertex v # is not bipartite if (not isBipartite(adj, u, visited, color)): return false # If two adjacent are colored with # same color then the graph is not # bipartite elif (color[u] == color[v]): return Talse return True# Driver Codeif __name__=='__main__': # No of nodes N = 6 # To maintain the adjacency list of graph adj = [[] for i in range(N + 1)] # To keep a check on whether # a node is discovered or not visited = [0 for i in range(N + 1)] # To color the vertices # of graph with 2 color color = [0 for i in range(N + 1)] # Adding edges to the graph addEdge(adj, 1, 2) addEdge(adj, 2, 3) addEdge(adj, 3, 4) addEdge(adj, 4, 5) addEdge(adj, 5, 6) addEdge(adj, 6, 1) # Marking the source node as visited visited[1] = True # Marking the source node with a color color[1] = 0 # Function to check if the graph # is Bipartite or not if (isBipartite(adj, 1, visited, color)): print("Graph is Bipartite") else: print("Graph is not Bipartite") # This code is contributed by rutvik_56 |
C#
// C# program to check if a connected// graph is bipartite or not suing DFSusing System;using System.Collections.Generic;class GFG{// Function to store the connected nodesstatic void addEdge(List<List<int>> adj, int u, int v){ adj[u].Add(v); adj[v].Add(u);}// Function to check whether a// graph is bipartite or notstatic bool isBipartite(List<List<int>> adj, int v, bool []visited, int []color){ foreach(int u in adj[v]) { // If vertex u is not explored before if (visited[u] == false) { // Mark present vertic as visited visited[u] = true; // Mark its color opposite to its parent color[u] = 1 - color[v]; // If the subtree rooted at vertex // v is not bipartite if (!isBipartite(adj, u, visited, color)) return false; } // If two adjacent are colored with // same color then the graph is // not bipartite else if (color[u] == color[v]) return false; } return true;}// Driver Codepublic static void Main(String []args){ // No of nodes int N = 6; // To maintain the adjacency list of graph List<List<int>> adj = new List<List<int>>(N + 1); // Initialize all the vertex for(int i = 0; i <= N; i++) { adj.Add(new List<int>()); } // To keep a check on whether // a node is discovered or not bool []visited = new bool[N + 1]; // To color the vertices // of graph with 2 color int []color = new int[N + 1]; // The value '-1' of colorArr[i] is // used to indicate that no color is // assigned to vertex 'i'. The value // 1 is used to indicate first color // is assigned and value 0 indicates // second color is assigned. for(int i = 0; i <= N; i++) color[i] = -1; // Adding edges to the graph addEdge(adj, 1, 2); addEdge(adj, 2, 3); addEdge(adj, 3, 4); addEdge(adj, 4, 5); addEdge(adj, 5, 6); addEdge(adj, 6, 1); // Marking the source node as visited visited[1] = true; // Marking the source node with a color color[1] = 0; // Function to check if the graph // is Bipartite or not if (isBipartite(adj, 1, visited, color)) { Console.WriteLine("Graph is Bipartite"); } else { Console.WriteLine("Graph is not Bipartite"); }}}// This code is contributed by Princi Singh |
Output:
Graph is Bipartite
Time Complexity: O(N)
Auxiliary Space: O(N)
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