如何找到图形缩合/成分图？

问题描述

有向图作为输入给出，在输出中，我需要指出输入图及其缩合图的所有SCC。我编写了Graph类和Kosarayu算法，以在有向图中找到强连接的组件。问题是-我如何找到和指出有向图的图凝聚？我想到的一种解决方案没有考虑边缘的方向（可能不会在线性时间内进行）。

graph.h

#include <list> 
#include <stack>

class Graph
{
public:
  Graph(std::size_t vertex);
  ~Graph();
  void addEdge(std::size_t from,std::size_t to);

  Graph getTranspose();
  void kosarajuSSC();
private:
  std::size_t vertex_;
  std::list<int>* adjList_;

  void fillPostVisitOrder(std::size_t vertex,bool visited[],std::stack<int>& stack);
  void auxiliaryDFS(std::size_t vertex,bool visited[]);
};

graph.cpp

#include "graph.h"
#include <iostream> 

Graph::Graph(std::size_t vertex)
{
  vertex_ = vertex;
  adjList_ = new std::list<int>[vertex];
}

Graph::~Graph()
{}

void Graph::addEdge(std::size_t from,std::size_t to)
{
  adjList_[from].push_back(to);
}

Graph Graph::getTranspose()
{
  Graph graph(vertex_);
  for (std::size_t i = 0; i < vertex_; ++i)
  {
    std::list<int>::iterator j;
    for (j = adjList_[i].begin(); j != adjList_[i].end(); ++j)
    {
      graph.adjList_[*j].push_back(i);
    }
  }
  return graph;
}

void Graph::kosarajuSSC()
{
  std::stack<int> vertexStack;

  bool* visited = new bool[vertex_];
  for (std::size_t i = 0; i < vertex_; ++i)
  {
    visited[i] = false;
  }

  for (std::size_t i = 0; i < vertex_; ++i)
  {
    if (!visited[i])
    {
      fillPostVisitOrder(i,visited,vertexStack);
    }
  }

  Graph transposeGraph = getTranspose();

  for (std::size_t i = 0; i < vertex_; ++i)
  {
    visited[i] = false;
  }

  std::size_t counterSCC = 0;
  while (!vertexStack.empty())
  {
    std::size_t currVertex = vertexStack.top();
    vertexStack.pop();

    if (!visited[currVertex])
    {
      std::cout << "SCC " << counterSCC++ << ": ";
      transposeGraph.auxiliaryDFS(currVertex,visited);
      std::cout << '\n';
    }
  }
}

void Graph::fillPostVisitOrder(std::size_t vertex,std::stack<int>& stack)
{
  visited[vertex] = true;

  for (std::list<int>::iterator i = adjList_[vertex].begin(); i != adjList_[vertex].end(); ++i)
  {
    if (!visited[*i])
    {
      fillPostVisitOrder(*i,stack);
    }
  }
  stack.push(vertex);
}

void Graph::auxiliaryDFS(std::size_t vertex,bool visited[])
{
  visited[vertex] = true;
  std::cout << vertex << " ";

  for (std::list<int>::iterator i = adjList_[vertex].begin(); i != adjList_[vertex].end(); ++i)
  {
    if (!visited[*i])
    {
      auxiliaryDFS(*i,visited);
    }
  }
}

main.cpp

#include <iostream>
#include "graph.h"

int main()
{
  Graph g(9);
  g.addEdge(0,1);
  g.addEdge(1,2);
  g.addEdge(2,3);
  g.addEdge(2,4);
  g.addEdge(3,0);
  g.addEdge(4,5);
  g.addEdge(5,6);
  g.addEdge(6,4);
  g.addEdge(7,6);
  g.addEdge(7,8);

  std::cout << "\nFollowing are strongly connected components in "
    "given graph \n";
  g.kosarajuSSC();

  return 0;
}

解决方法

暂无找到可以解决该程序问题的有效方法，小编努力寻找整理中！

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