BFS to check if a graph is bipartite in c++

Question

I am implementing an algorithm to determine whether an undirected graph is bipartite or not. Based on this pseudo-code made ​​my implementation, which works for graphs connected, but when it is disconnected simply the program indicates a wrong answer. I think if its not connected, then one more loop is needed for every disjoint sub-graph. But im stuck with this. How I can solve my code for me to print a correct answer?

#include <cstdio>
#include <vector>
#include <queue>
#include <iostream>
using namespace std;

#define MAX 1000

int numberVertex, numberEdges;
int particion[MAX], visited[MAX];
vector< int > adjacencyMatrix[MAX];

bool bfs()
{
    int i, origin, destination, begin;
    queue< int > queueVertex;
    begin = 0;
    queueVertex.push(begin);
    particion[begin] = 1; // 1 left,
    visited[begin] = 1; // set adjacencyMatrixray

    while(!queueVertex.empty())
    {
        origin = queueVertex.front(); queueVertex.pop();
        for(i=0; i < adjacencyMatrix[origin].size(); i++)
        {
            destination = adjacencyMatrix[origin][i];
            if(particion[origin] == particion[destination])
            {
                return false;
            }
            if(visited[destination] == 0)
            {
                visited[destination] = 1;
                particion[destination] = 3 - particion[origin]; // alter 1 and 2 subsets
                queueVertex.push(destination);
            }
        }
    }
    return true;
}

int main()
{
 freopen("tarea2.in", "r", stdin);
    int i,j, nodeOrigin, nodeDestination;
    scanf("%d %d", &numberVertex, &numberEdges);
    for(i=0; i<numberEdges; i++)
    {
        scanf("%d %d", &nodeOrigin, &nodeDestination);
        adjacencyMatrix[nodeOrigin].push_back(nodeDestination);
        adjacencyMatrix[nodeDestination].push_back(nodeOrigin);
    }
    if(bfs()) {

        printf("Is bipartite\n");
          for (j=0; j<numberVertex; j++){
        cout<<j<<" "<<particion[j]<<endl;
        }

    }
    else {printf("Is not bipartite\n");}





    return 0;
}

For example for this input

6 4
3 0
1 0
2 5
5 4

the output should be:

Is bipartite
0 1
1 2
2 1
3 2
4 1
5 2

Instead throws me the output:

0 1
1 2
2 0
3 2
4 0
5 0

This happens because the graph is not a connected graph, ie, has two connected components.I hope you can help me because I've been stuck with this for several days.

Answer 1

You should run bfs on every connected component. Simplest way to do this is to iterate over all vertices and if they weren't visited, then just call bfs on them.

bool is_bipartite()
{
    for(int i = 0; i < numberVertex; i++)
    {
       if (visited[i] == 0 && !bfs(i)) {
           return false;
       }
    } 
    return true;
}

It is still linear because, you run bfs on every connected component once.

#include <cstdio>
#include <vector>
#include <queue>
#include <iostream>
using namespace std;

#define MAX 1000

int numberVertex, numberEdges;
int particion[MAX], visited[MAX];
vector< int > adjacencyMatrix[MAX];

bool bfs(int begin)
{
    int i, origin, destination;
    queue< int > queueVertex;
    queueVertex.push(begin);
    particion[begin] = 1; // 1 left,
    visited[begin] = 1; // set adjacencyMatrixray

    while(!queueVertex.empty())
    {
        origin = queueVertex.front(); queueVertex.pop();
        for(i=0; i < adjacencyMatrix[origin].size(); i++)
        {
            destination = adjacencyMatrix[origin][i];
            if(particion[origin] == particion[destination])
            {
                return false;
            }
            if(visited[destination] == 0)
            {
                visited[destination] = 1;
                particion[destination] = 3 - particion[origin]; // alter 1 and 2 subsets
                queueVertex.push(destination);
            }
        }
    }
    return true;
}

bool is_bipartite()
{
    for(int i=0; i< numberVertex; i++)
    {
       if (visited[i] == 0 && !bfs(i)) {
           return false;
       }
    } 
    return true;
}

int main()
{
    //freopen("tarea2.in", "r", stdin);
    int i,j, nodeOrigin, nodeDestination;
    scanf("%d %d", &numberVertex, &numberEdges);
    for(i=0; i<numberEdges; i++)
    {
        scanf("%d %d", &nodeOrigin, &nodeDestination);
        adjacencyMatrix[nodeOrigin].push_back(nodeDestination);
        adjacencyMatrix[nodeDestination].push_back(nodeOrigin);
    }
    if(is_bipartite()) {

        printf("Is bipartite\n");
          for (j=0; j<numberVertex; j++){
        cout<<j<<" "<<particion[j]<<endl;
        }

    }
    else {printf("Is not bipartite\n");}

    return 0;
}

Answer 2

The detailed implementation is as follows (C++ version). It will be able to handle several separated connected components.

Assume the graph node is defined as:

struct NODE
{
    int color;
    vector<int> neigh_list;
};

Then you can check whether the whole graph is bipartite by calling bfs().

bool checkAllNodesVisited(NODE *graph, int numNodes, int & index);

bool bfs(NODE * graph, int numNodes)
{
    int start = 0;

    do 
    {
        queue<int> Myqueue;
        Myqueue.push(start);
        graph[start].color = 0;

        while(!Myqueue.empty())
        {
            int gid = Myqueue.front();
            for(int i=0; i<graph[gid].neigh_list.size(); i++)
            {
                int neighid = graph[gid].neigh_list[i];
                if(graph[neighid].color == -1)
                {
                    graph[neighid].color = (graph[gid].color+1)%2; // assign to another group
                    Myqueue.push(neighid);
                }
                else
                {
                    if(graph[neighid].color == graph[gid].color) // touble pair in the same group
                        return false;
                }
            }
            Myqueue.pop();
        }
    } while (!checkAllNodesVisited(graph, numNodes, start)); // make sure all nodes visited 
                                            // to be able to handle several separated graphs, IMPORTANT!!!

    return true;
}

bool checkAllNodesVisited(NODE *graph, int numNodes, int & index)
{
    for (int i=0; i<numNodes; i++)
    {
        if (graph[i].color == -1)
        {
            index = i;
            return false;
        }
    }

    return true;
}

Answer 3

Bipartite graph is also known as 2-colour graph i.e we can colour all the nodes of the bipartite graph with only 2 colour such that no 2 adjacent node have same colour.

• Initially let all vertex are not having any colour.

• Start with any vertex and colour it with RED. Then Colour its all adjacent vertices with a colour other than RED let say Black.

• Keep on repeating this till all node are coloured. If at any point you found two adjacent node have same colour. Then it is not a bipartite graph.

C++ Implementation