Finding connected components in graph (adjA) using DFS

Question

I've been searching around the internet today trying to figure out how to run DFS on an adjacency list vector<list<edge>> adjA, but I just cannot figure out how to do this correctly. The best example I could find online was: Find connected components in a graph but using his first method does not seem to work and I am not confident enough with unions / sets to try his other method. This is what I have so far: (disregard test_vector and cc, I'm focusing on getting the cc_count to work)

edge is a struct that contains:

struct edge{
    int to; //copy of to_original (dont worry about this it's for a different functionality)
    int w; //weight of edge
    int from_original; //from vertex
    int to_original;  //to vertex
}

somewhere in int main:

cout << "conn: " << connected(adjA, test_vector) << endl;

---

int connected(vector<list<edge>> &adjA, vector<short int> &cc){
        int v_size = adjA.size();
        vector<bool> discovered(false,v_size);
        int cc_count = 0;
        for(unsigned int u = 0; u < adjA.size(); u++){
            if(!discovered[u]){
                cout << u << endl;
                discovered[u] = true;
                cc_count+=1;
                dfs(adjA,discovered,cc,cc_count,u);
            }
        }
        return cc_count;
    }

---

    void dfs(vector<list<edge>>&adjA, vector<bool> &discovered, vector<short int> &cc, int &cc_count,int u){
    for(unsigned int v = 0; v < adjA[u].size();v++){
        if(!discovered[v]){
            cout << v << endl;
            discovered[v] = true;
            dfs(adjA, discovered,cc,cc_count,v);
        }
    }

    }

from the line cout << v << endl; and cout << u << endl it will print showing that it was able to visit every node once. However, I am incrementing the cc_count incorrectly I think. In this adjacency list:

0->[1]->[3]->[5]
1->[0]->[2]->[3]->[4]
2->[1]->[4]
3->[0]->[1]->[4]->[5]
4->[1]->[2]->[3]->[5]->[6]
5->[0]->[3]->[4]->[6]
6->[4]->[5]

the program will output:

0
1
2
3
4
5
6
conn: 7

when conn should be 1, since the whole graph is a single component. I feel like I might be going about this the wrong way. Is there a change I should do? Is there a better way to do this using DFS or BFS?

I apologize for the poor formatting, I spent almost an hour just trying to get the stack overflow errors to go away.

graph represented by adjacency list

Answer 1

Your dfs method is not looking at the edges at all. I don't know from the question what an edge is, but lets just assume it is pair-like (both endpoints).

Then

for(unsigned int v = 0; v < adjA[u].size();v++) {
    // do something with v
}

should actually be

for (auto const & e: adjA[u]) {
    // do something with the endpoint of e other than u
}