判断有向图是否有环&拓扑排序

//有向图判断是否有环

#include <iostream>
#include <list>
#include <vector>
#include <algorithm>

using namespace std;

#define TRUE  1
#define FALSE 0

typedef struct{
  int vexs[10];
  int edges[10][10];
  int n;
  int e;
}MGraph;

void CreateGraphM(MGraph *G){

  int N1,N2;
  int i,j,k;

  cout<<"Enter the number of vertexs and edges: "<<endl;
  cin>>(G->n)>>(G->e);
  k=G->n;

  for(i=0;i<k;i++)
    cin>>(G->vexs[i]);

  for(i=0;i<G->n;i++)
    for(j=0;j<G->n;j++)
      G->edges[i][j]=0;
  

  cout<<"EDGES: "<<endl;

  for(k=0;k<G->e;k++){
    cin>>N1>>N2;
    G->edges[N1-1][N2-1]=1;
  }

  return;
}


typedef struct{

  int visited[10];
  int finishing_time[10];
  int discovery_time[10];
  int times;

}DFS_DATA;


void DFSM(MGraph *G,int index,DFS_DATA *DATA){

  DATA->times++;

  DATA->discovery_time[index]=DATA->times;

  DATA->visited[index]=1;

  for(int i=0;i<G->n;i++)
    if(G->edges[index][i]==1 && DATA->visited[i]==0){
      DFSM(G,i,DATA);
    }

  DATA->finishing_time[index]=DATA->times;
  DATA->times++;
}

void DFS(MGraph *G,DFS_DATA *DATA){

  for(int i=0;i<G->n;i++){
    DATA->visited[i]=0;
  }

  for(int i=0;i<G->n;i++){
    DATA->finishing_time[i]=0;
    DATA->discovery_time[i]=0;
  }

  DATA->times=0;

  for(int i=0;i<G->n;i++){
    if(DATA->visited[i]==0)
      DFSM(G,i,DATA);
  }
}

vector<int> Topological_Sort(MGraph *G){

  DFS_DATA *DATA = new DFS_DATA;

  vector<int> RESULT;
  vector<int> tmp;

  DFS(G,DATA);

  for(int i=0;i<G->n;i++)
    tmp.push_back(DATA->finishing_time[i]);

  sort(tmp.begin(),tmp.end());

  for(int i=G->n-1;i>=0;i--)
    for(int j=0;j<G->n;j++)
      if(DATA->finishing_time[j]==tmp[i]){
        RESULT.push_back(j);
      }

  delete DATA;
  
  return RESULT;
}

int Acyclic(MGraph *G){

  vector<int> CHECK;

  CHECK = Topological_Sort(G);

  for(int i=1;i<G->n;i++)
    for(int j=0;j<i;j++){
      
      if(G->edges[CHECK[i]][CHECK[j]]==1)
        return 1;
    }

  return 0;
}

int main()
{
  MGraph *G = new MGraph;

  CreateGraphM(G);

  if(Acyclic(G)==1)
    cout<<"There is Acyclic"<<endl;
  else
    cout<<"There is NO Acyclic"<<endl;

  return 0;
}

先用DFS对图G拓扑排序 然后看 拓扑排序的结果有没冲突  就是 后面的顶点 要是有对前面顶点的边  有冲突 就表示有环