DFS: How to indicate the nodes of the connected components in C++

Question

I am making a problem of ACM competitions to determine the number of connected components that have an undirected graph G and vertices belonging to each component. 've Already done with a DFS algorithm, counting the number of connected components of undirected graph (the hard part of problem), but I can not think of anything to indicate the nodes belonging to each component or have a record of the nodes.

Input: The first line of input will an integer C, which indicates the number of test cases. The first line of each test case contains two integers N and E, where N represents the number of nodes in the graph and E the number of edges in it. Then follow E lines, each with 2 integers I and J, where I and J represent the existence of an edge between node I and node J (0 ≤ I, J

Output: In the first line of each test case must display the following string "Case G: P component (s) connected (s)", where G represents the number of test case (starting at 1) and P the number of components connected in the graph. Then X lines, each containing the nodes belonging to a connected component (in order from smallest to largest) separated by spaces. After each test case should print a blank line. The output should be written in the "output.out."

Example:

Input:

2
6 9
0 1
0 2
1 2
5 4
3 1
2 4
2 5
3 4
3 5
8 7
0 1
2 1
2 0
3 4
4 5
5 3
7 6

Output:

Case 1: 1 component (s) connected (s)
0 1 2 3 4 5

Case 2: 3 component (s) connected (s)
0 1 2
3 4 5
6 7

Here's my code:

#include <stdio.h>
#include <vector>
#include <stdlib.h>
#include <string.h>
using namespace std;
vector<int> adjacency[10000];
bool visited[10000];

/// @param Standard algorithm DFS
void dfs(int u){
    visited[ u ] = true;
    for( int v = 0 ; v < adjacency[u].size(); ++v ){
        if( !visited[ adjacency[u][v] ] ){
            dfs( adjacency[u][v] );
        }
    }
}

    int main(int argc, char *argv []){
    #ifndef ONLINE_JUDGE
    #pragma warning(disable: 4996)
        freopen("input.in", "r", stdin);
            freopen("output.out", "w", stdout);
    #endif

         ///enumerate vertices from 1 to vertex
        int vertex, edges , originNode ,destinationNode, i, j,cont =1;
        ///number of test cases
        int testCases;
        int totalComponents;
        scanf ("%d", &testCases);

        for (i=0; i<testCases; i++){

        memset( visited , 0 , sizeof( visited ) );
        scanf("%d %d" , &vertex , &edges );
        for (j=0; j<edges; j++){
            scanf("%d %d" , &originNode ,&destinationNode );
            adjacency[ originNode ].push_back( destinationNode );
            adjacency[ destinationNode ].push_back( originNode );
        }
            totalComponents =0;
            for( int i = 0 ; i < vertex ; ++i ){    // Loop through all possible vertex
                if( !visited[ i ] ){          //if we have not visited any one component from that node
                    dfs( i );                  //we travel from node i the entire graph is formed
                    totalComponents++;                   //increased amount of components
                }
            }
            printf("Case %d: %d component (s) connected (s)\n" ,cont++, totalComponents);

            for (j=0;j<total;j++){
        /*here should indicate the vertices of each connected component*/
    }
        memset( adjacency , 0 , sizeof( adjacency ) );
        }
    return 0;
    }

I have doubts about how to carry memory of the nodes belonging to each connected component or structure should be used to store, how I should modify my code to do this?, I would like to hear suggestions, ideas or any implementation in pseudocode. Thanks to all

Answer 1

General algorithm to test if 2 nodes are connected:

1. Split your entire graph into edges. Add each edge to a set.
2. On next iteration, draw edges between the 2 outer nodes of the edge you made in step 2. This means adding new nodes (with their corresponding sets) to the set the original edge was from. (basically set merging)
3. Repeat 2 until the 2 nodes you're looking for are in the same set. You will also need to do a check after step 1 (just in case the 2 nodes are adjacent).

At first your nodes will be each in its set,

o   o1   o   o   o   o   o   o2
 \ /     \ /     \ /     \ /
 o o     o o     o o     o o
   \     /         \     /
   o o o o         o o o o 
      \               /
       o o1 o o o o o o2

As the algorithm progresses and merges the sets, it relatively halves the input.

In the example above I was looking to see if there was a path between o1 and o2. I found this path only at the end after merging all edges. Some graphs may have separate components (disconnected) which entails that you will not be able to have one set at the end. In such a case you can use this algorithm to test for connectedness and even count the number of components in a graph. The number of components is the number of sets you are able to get when the algorithm finishes.

A possible graph (for the tree above):

o-o1-o-o-o2
  |    |
  o    o
       |
       o

Answer 2

the solution is much easier, you must declare two arrays of size the number of vertices

int vertexNodes  [vertex] / / / array to store the nodes
int vertexComponents [vertex] / / / array to store the number of components

Then, when you call to DFS each vertex is stored in the array of vertices, and stored at that component belongs

for( int i = 0 ; i < vertex ; ++i ) //iterate on all vertices
        {
                vertexNodes [i]=i;  //fill the array with the vertices of the graph
            if( !visited[ i ] )
            { ///If any node is visited DFS call
                    dfs(i);
                totalComponents++; ///increment number of components
            }
            vertexComponents [i]=totalComponents; ///is stored at each node component belongs to
        }

Finally, it prints the total components and created a flag with the value of the first component which is compared with the component of each vertex

printf("Case %d: %d component (s) connected (s)\n" ,cont++, totalComponents);
int flag = vertexComponents[0]; ///Create a flag with the value of the first component
            for (k=0; k <totalComponents; ++k) ///do a cycle length of the number of components
            {
                if (flag == vertexComponents [k] ) ///check if the vertex belongs to the first component
                {
                    printf ("%d ", vertexComponents[k]); ///print on the same line as belonging to the same component
                }else {
                    printf ("\n"); ///else  we make newline and update the flag to the next component
                    flag = vertexComponents[k];
                    printf ("%d ", vertexComponents[k]);///and print the vertices of the new connected component
                }
            }

Answer 3

The algorithm is roughly:

• Get a graph node.
• Find all nodes directly or indirectly connected to it (in both directions).
• Mark all of them as "traversed" and put them into a new component.
• Find the next node that is not traversed and repeat the process.

The result is a set of "component" data structures (std::vectors in my implementation), each containing a set of exclusively inter-connected nodes.

Considerations:

• We need to store the graph in a structure that can be efficiently traversed both "down" (from parents to children) and "up" (from children to parents) and recursively find all the connected nodes (in both directions), marking the nodes as "traversed" as we go. Since nodes are identified by a continuous range of integers, we can build this structure efficiently just by using random-access properties std::vector.
• The concept of edges and nodes are separated, so a single "traversed" flag can exist at the level of a node, no matter how many other nodes are connected to it (i.e. no matter how many parent and child edges there are). This enables us to cut the recursion efficiently for already-reached nodes.

Here is the working code. Note that some C++11 features were used, but they should be easy to replace if older compiler is used. The error handling is left as exercise for the reader.

#include <iostream>
#include <vector>
#include <algorithm>

// A set of inter-connected nodes.
typedef std::vector<unsigned> Component;

// Graph node.
struct Node {
    Node() : Traversed(false) {
    }
    std::vector<unsigned> Children;
    std::vector<unsigned> Parents;
    bool Traversed;
};

// Recursive portion of the FindGraphComponents implementation.
//   graph: The graph constructed in FindGraphComponents().
//   node_id: The index of the current element of graph.
//   component: Will receive nodes that comprise the current component.
static void FindConnectedNodes(std::vector<Node>& graph, unsigned node_id, Component& component) {

    Node& node = graph[node_id];
    if (!node.Traversed) {

        node.Traversed = true;
        component.push_back(node_id);

        for (auto i = node.Children.begin(); i != node.Children.end(); ++i)
            FindConnectedNodes(graph, *i, component);

        for (auto i = node.Parents.begin(); i != node.Parents.end(); ++i)
            FindConnectedNodes(graph, *i, component);

    }

}

// Finds self-connected sub-graphs (i.e. "components") on already-prepared graph.
std::vector<Component> FindGraphComponents(std::vector<Node>& graph) {

    std::vector<Component> components;
    for (unsigned node_id = 0; node_id < graph.size(); ++node_id) {
        if (!graph[node_id].Traversed) {
            components.push_back(Component());
            FindConnectedNodes(graph, node_id, components.back());
        }
    }

    return components;

}

// Finds self-connected sub-graphs (i.e. "components") on graph that should be read from the input stream.
//   in: The input test case.
std::vector<Component> FindGraphComponents(std::istream& in) {

    unsigned node_count, edge_count;
    std::cin >> node_count >> edge_count;

    // First build the structure that can be traversed recursively in an efficient way.
    std::vector<Node> graph(node_count); // Index in this vector corresponds to node ID.
    for (unsigned i = 0; i < edge_count; ++i) {
        unsigned from, to;
        in >> from >> to;
        graph[from].Children.push_back(to);
        graph[to].Parents.push_back(from);
    }

    return FindGraphComponents(graph);

}

void main() {

    size_t test_case_count;
    std::cin >> test_case_count;

    for (size_t test_case_i = 1; test_case_i <= test_case_count; ++test_case_i) {

        auto components = FindGraphComponents(std::cin);

        // Sort components by descending size and print them.
        std::sort(
            components.begin(),
            components.end(),
            [] (const Component& a, const Component& b) { return a.size() > b.size(); }
        );

        std::cout << "Case " << test_case_i <<  ": " << components.size() << " component (s) connected (s)" << std::endl;
        for (auto components_i = components.begin(); components_i != components.end(); ++components_i) {
            for (auto edge_i = components_i->begin(); edge_i != components_i->end(); ++edge_i)
                std::cout << *edge_i << ' ';
            std::cout << std::endl;
        }
        std::cout << std::endl;

    }

}

Call this program as...

GraphComponents.exe < input.in > output.out

...where input.in contains data in format described in your question and it will produce the desired result in output.out.

Answer 4

You could store the components like this:

typedef vector<int> Component;
vector<Component> components;

and modify the code:

void dfs(int u){
    components.back().push_back(u);
    visited[ u ] = true;
    for( int v = 0 ; v < adjacency[u].size(); ++v ){
        if( !visited[ adjacency[u][v] ] ){
            dfs( adjacency[u][v] );
        }
    }
}

for( int i = 0 ; i < vertex ; ++i ){    // Loop through all possible vertex
    if( !visited[ i ] ){          //if we have not visited any one component from that node
        components.push_back(Component());
        dfs( i );                  //we travel from node i the entire graph is formed
    }
}

now totalComponents is components.size() :

printf("Case %d: %d component (s) connected (s)\n" ,cont++, components.size());

        for (j=0;j<components.size();j++){
           Component& component = components[j];
           std::sort(component.begin(), component.end());
           for(int k=0; k<component.size(); k++) {
             printf("%d ", component[k]);
           }
           printf("\n");
        }
        components.clear();

Note that the code is not tested. Include <algorithm> to get the sort function.