如何根据 C++ 中的边缘度对图进行排序

Question

I'm new with C++ and sort algorithms. I would like to have the ordered list of vertexes based on their degrees.

I'm constructing my graph as below:

void addEdge(vector<int> adj[], int u, int v)
{
    adj[u].push_back(v);
    adj[v].push_back(u);
} 
        
int main(){

int V = 4;
vector<int> adj[V];
addEdge(adj, 0, 2);
addEdge(adj, 0, 1);
addEdge(adj, 0, 3);
addEdge(adj, 2, 1);
printGraph(adj, V);
return 0;

}

Output desirable:

• Vertex 0, degree 3
• Vertex 1, degree 2
• Vertex 2, degree 2
• Vertex 3, degree 1

Someone can help me indicating how can I solve this? I appreciate it!

Answer 1

Create an vector of vertex indices and sort them in descending order of vector sizes in adj . You can use std::sort (or std::stable_sort in case elements with the same degree should be ordered in ascending order of vertex indices) passing a comparison object to sort the indices:

void printGraph(std::vector<int> const* adj, size_t count)
{
    std::vector<size_t> indices;
    for (size_t i = 0; i != count; ++i)
    {
        indices.push_back(i);
    }

    std::stable_sort(indices.begin(), indices.end(), [=](size_t index1, size_t index2)
        {
            return adj[index1].size() > adj[index2].size();
        });

    for (auto index : indices)
    {
        std::cout << "Vertex " << index << ", degree " << adj[index].size() << '\n';
    }
}

Answer 2

If you only want to sort it, there are sorting functions in the standard libraries, but if you want to implement it yourself, a good approach for a beginner is the insertion sort . It is not the most efficient method, but it is easy to understand and clean to implement.

Here's a possible implementation for your case:

vector<int> sortedVertices(vector<int> adj[], int size){
  vector<int> result;
  vector<int> degrees;

  for(int vertex=0; vertex < size; vertex++){
    
    // calculate the degree of the vertex and store it
    int degree = adj[vertex].size();
    degrees.push_back(degree);
    
    // look for the first position in the result where the degree is 
    // lesser than the current vertex degree and insert it there (or in 
    // the end of the list, if it is the smallest)
    int pos = 0;
    while(pos < result.size() && degree < degrees[result[pos]]){
      pos++;
    }
    result.insert(result.begin()+pos, vertex);
    
  }

  // Now you can print it if you want
  for(int i=0; i < result.size(); i++){
    cout << "Vertex " << result[i] << ", degree" << degrees[result[i]] << endl;
  }

  return result;
}

So you can use it in your case like this:

int V = 4;
vector<int> adj[V];
addEdge(adj, 0, 2);
addEdge(adj, 0, 1);
addEdge(adj, 0, 3);
addEdge(adj, 2, 1);
printGraph(adj, V);
sortedVertices(adj, V);
return 0;