connected components in undirected graphs in c++

Question

I wanted to count the number of groups in an undirected graphs in c++.I was trying using bfs but was unsuccessful.I have been given a range of numbers [L,R] (or think of these ranges as number of vertices) and i have to find the number of groups.How do i do this?

Like if i have (Input):

1 3
2 5
6 9

Output:

As there are 2 groups.

My code:

bool visited[MAX];
vector<int> v[MAX];
int solve(int x)
{
  queue<int> q;int ans=0;
  q.push(x);
  if(v[x].empty())
  {
      ans++;
  }
  while(!q.empty())
  {
      int curr = q.front();
      visited[curr] = true;
      q.pop();
      for(int i = 0; i < v[curr].size(); i ++)
        {
            if(!visited[v[curr][i]])
            {
                q.push(v[curr][i]);
                visited[v[curr][i]] = true;
            }
        }
        if(v[curr].empty()) ans++;
  }
  return ans;
}
int main()
{
    int t;scanf("%d",&t);

    while(t--)
    {
        int l,r,n,ans=0,min_,max_=0;
        scanf("%d",&n);
        for(int i = 0; i < n; i ++)
            visited[i] = false;
        for(int j=0;j<n;j++)
        {
            scanf("%d",&l);scanf("%d",&r);
            for(int i=l;i<r;i++)
            {
                v[i].push_back(i+1);
                 min_ = min(min_,i);
                max_ = max(max_,i+1);
            }
        }

        printf("%d\n",solve(min_));
    }
    return 0;
}

"But it was unsuccessful". What did go wrong? Did your program crash? Did it produce incorrect output? — kraskevich, Jan 06 '15 at 15:55
@user111 It seems like you have a different idea on how to define graphs. Typically they are defined by a bunch of `std::pair`s with each element of the pair representing a node. Your input is "1->3, 2->5, 6->9" and you say that will make "2" graphs? To be clear that should make **3 graphs**, you agree with that, right? — Jonathan Mee, Jan 06 '15 at 16:35
@JonathanMee It will make graphs : 1->2->3->4->5 and 6->7->8->9 . So, 2 graphs. — wen_dy, Jan 06 '15 at 17:29
@IloveCoding I got Runtime Error(SIGSEGV). I just need to know how do i count groups in an undirected graph. — wen_dy, Jan 06 '15 at 17:31
You mean like [this](http://stackoverflow.com/questions/27745166/algorithms-used-to-find-the-overlaps-sets)? And [this](http://stackoverflow.com/questions/27753830/finding-minimum-number-of-points-which-covers-entire-set-of-intervals)? And this http://www.codechef.com/JAN15/problems/ONEKING? — beaker, Jan 06 '15 at 18:16
@beaker They look different to me. This one is about finding the number of connected components, the last 2 links are about something like vertex cover. — kraskevich, Jan 06 '15 at 18:31
@beaker The first is about finding the largest set of segments. The second two are about finding the minimum number of points which connect to all segments. This question is related but is about finding the number of disconnected segment sets. (And notably not at all about graphing.) — Jonathan Mee, Jan 06 '15 at 19:18

kraskevich · Accepted Answer · 2015-01-06T18:05:23.660

0

Let's take a look at how many edges are created in the worst case. It is N * (MAX_R - MIN_L), which is 10^5 * 2000 under given constraints. You program runs out of memory and gets runtime error. A more efficient algorithm is required. Here is a simple solution that uses only O(MAX_R) memory and
O(N + MAX_R) time.

vector<int> start(MAX_R + 1);
vector<int> end(MAX_R + 1);
int n;
cin >> n;
for (int i = 0; i < n; i++) {
    int low;
    int high;
    cin >> low >> high;
    start[low]++;
    end[high]++;
}
int res = 0;
int sum = 0;
for (int pos = 0; pos <= MAX_R; pos++) {
    if (sum == 0 && start[pos] > 0)
        res++;
    sum += start[pos] - end[pos];
}
cout << res << endl;

There is no need for bfs or any other graph algorithms in this problem.

You could fix your original solution by avoiding multiple edges in the graph(there is no need to create an edge from i to i + 1 if it already exists, but I am not sure if your original solution is correct).

edited Jan 06 '15 at 18:05

answered Jan 06 '15 at 17:49

kraskevich

18,368
4
33
45

So,here MAX_R is 2000. ? @ILoveCoding – wen_dy Jan 06 '15 at 17:58
I am getting 1 as the output for the input i provided above,but it should be 2 . @ILoveCoding – wen_dy Jan 06 '15 at 18:06
@usr111 I edited my answer a couple of minutes ago. There was a bug, now it works properly. – kraskevich Jan 06 '15 at 18:08
I think it still contains some bugs ..@ILoveCoding – wen_dy Jan 06 '15 at 18:27
@user111 Why do think so? Do you have a test case which it fails? – kraskevich Jan 06 '15 at 18:27

Jonathan Mee · Answer 2 · 2015-01-06T18:32:09.320

Looks like you should start by changing to vector<pair<int,int>> v;. Then to populate v you should use:

scanf("%d", &l);scanf("%d", &r);
v.push_back(make_pair(l, r);

Then your function should become something like:

int solve(){
    vector<pair<int, int>> results;

    for(auto& vIndex : v){
        auto resultIndex = find_if(results.begin(), results.end(), [vIndex](const pair<int, int>& i){return vIndex.first >= i.first && vIndex.first <= i.second || vIndex.second >= i.first && vIndex.second <= i.second;});

        if(resultIndex == results.end()){
            results.push_back(vIndex);
        }else{
            resultIndex->first = min(vIndex.first, resultIndex->first);
            resultIndex->second = max(vIndex.second, resultIndex->second);
        }
    }
    return results.size();
}

You can see this in action here: http://ideone.com/MDQBOr Just hard code your desired inputs into v.

@user111 It's worth pointing out that what you are constructing is not a graph but an [segment tree](http://en.wikipedia.org/wiki/Segment_tree). My approach is brute force, if you needed to solve this quickly, using the tree described in the link would be a better approach. — Jonathan Mee, Jan 06 '15 at 19:05

connected components in undirected graphs in c++

2 Answers2