使用DFS来拆分强连通分量的算法实现

主要方法：

参考：https://www.cnblogs.com/LLGemini/p/4725952.html

一些数据类型的定义：

 

 Seperate strongly connected components in a directed graph with DFS:

int MaxIndex(int* v, int size) {
    int max = v[0];
    int i = 0;
    for (auto it = 1; it < size; it++) {
        if (v[it] > max) {
            max = v[it];
            i = it;
        }

    }
    return i;
}
void Graph::StronglyConnectedComp(int nbNodes,int startFrom) {
    cout << "Detecting strongly connected components: " << endl;
    /*choose a vertex randomly or designate with parameter*/
    srand((unsigned int)time(NULL));
    Vertex* tempV;
    if (startFrom == -1) {
        int sze = listVertex.size();
        int rdm = rand() % sze;//[0,sze)
        tempV = listVertex[rdm];
    }
    else
        tempV = listVertex[startFrom - 1];
    int count = 0;// to check if all vertices have been visited
    int* mark = new int[nbNodes];// to store the numbers marked on vertex
    stack<Vertex* > myStack;// to assist dfs algo
    myStack.push(tempV);//initialization
    /*DFS algo to mark the vertices from leaves*/
    while (!myStack.empty()) {
        cout << "colored:" << myStack.top()->id << endl;
        myStack.top()->color = 1;// visit the vertex on top
        int visited = 0;// to check if all adjacent vertices have been visited
        
        for (auto it = myStack.top()->nextEdgeNode.begin(); it != myStack.top()->nextEdgeNode.end(); it++) {
            if (listVertex[it->first - 1]->color == 0)//O black(unvisited) & 1 white(visited))
            {
                myStack.push(listVertex[it->first - 1]);
                break;
            }
            else
                visited++;
        }
        /*if the vertex and all its adjacent vertices have been visited, 
        which means the end of DFS, then mark it and pop it out*/
        if (visited == myStack.top()->nextEdgeNode.size() && myStack.top()->color == 1) {
            cout << "mark:" << myStack.top()->id<<endl;
            count++;
            mark[myStack.top()->id] = count;// mark the vertex
            myStack.pop();
        }
        /*check if all vertices in graph have been visited*/
        if (myStack.empty() && count < nbNodes) {
            for (auto it = listVertex.begin(); it != listVertex.end(); it++) {
                if ((*it)->color == 0) {//O black(unvisited) & 1 white(visited)
                    myStack.push(*it);
                    break;
                }    
            }
        }
    }
    /*end of DFS and the marking procedure*/
    /*restore the visit flag*/
    for (auto it = listVertex.begin(); it != listVertex.end(); it++) {
        (*it)->color = 0;//O black(unvisited) & 1 white(visited)
    }

    for (auto it = 0; it < nbNodes; it++)
        cout << "it:" << it << "number:" << mark[it] << endl;
    /*begin to reverse the edges with no change of original data*/
    vector<int>* tempAdjList = new vector<int>[nbNodes];//temporary assisting structure
    int max = MaxIndex(mark,nbNodes);
    cout << "maxindex:" << max << endl;
    for (auto it = listEdges.begin(); it != listEdges.end(); it++) {
        Vertex* temp;
        temp = (*it)->destination;
        (*it)->destination = (*it)->source;
        (*it)->source = temp;
        //store the just reversed data
        tempAdjList[(*it)->source->id].push_back((*it)->destination->id);
    }
    myStack.push(listVertex[max]);//initialization
    mark[max] = 0;
    int component = 0;
    int pushchecker = 1;
    while (!myStack.empty()) {
        if (myStack.top()->color == 0) {
            cout << "This is strongly connected component " << component+1 << "." << endl;
            myStack.top()->color = 1;//O black(unvisited) & 1 white(visited)
            mark[myStack.top()->id] = 0;//exclude visited vertex
            cout << "Vertex: " << myStack.top()->id + 1 << endl;
        }
        int popchecker = 0;
        for (auto it = tempAdjList[myStack.top()->id].begin(); it != tempAdjList[myStack.top()->id].end(); it++) {
            if (listVertex[*it]->color == 0) {//O black(unvisited) & 1 white(visited)
                myStack.push(listVertex[*it]);
                pushchecker++;
                break;
            }
            else
                popchecker++;
        }
        if (popchecker == tempAdjList[myStack.top()->id].size() && myStack.top()->color == 1)//O black(unvisited) & 1 white(visited)
        {// end of the road, pop 
            myStack.pop();
        }
        /*if the current component is all visited and not all vertices in graph are visited,
        then add the vertex with the biggest number marked into stack*/
        if (myStack.empty() && pushchecker < nbNodes) {
            myStack.push(listVertex[MaxIndex(mark,nbNodes)]);
            pushchecker++;
            component++;
        }
    }

    delete[] mark;
}

测试数据1：

 

 结果：

 成功

测试数据2：

 

 结果：

 成功