judge loop in undirected graph

一 深度优先遍历，参考前面DFS(white and gray and black)

二 根据定点以及边数目进行判断

如果m(edge)大于n(vertex),那么肯定存在环

算法如下：

1 删除所有入度小于等于1的顶点， 并且将和这些顶点相关的顶点入度减1

2 将入度变为1的顶点全部删除，重复上述动作，如果最后还有顶点那么图中存在环

具体代码如下：

#include <iostream>
using namespace std;

#define MAX_VERTEX_NUM 128
enum color{WHITE, GRAY = 1, BLACK};
bool M[MAX_VERTEX_NUM][MAX_VERTEX_NUM];
int colour[MAX_VERTEX_NUM];
int dfsNum[MAX_VERTEX_NUM], num;
int indegree[MAX_VERTEX_NUM];
int vexnum, edgenum;

void init_graph(){
    cout<<"enter vertex number:"<<endl;
    cin>>vexnum;
    cout<<"enter edge number:"<<endl;
    cin>>edgenum;

    int i, j;
    while(edgenum){
        cout<<"add new edge:"<<endl;
        cin>>i>>j;
        M[i - 1][j - 1] = true;
        //initialize in vertex degree
        indegree[i - 1]++;
        indegree[j - 1]++;
        edgenum--;
    }
}
/*
void dfs(int u, int p){
    colour[u] = GRAY;
    dfsNum[u] = num++;
    for( int v = 0; v < vexnum; v++){
        if(M[u][v] && v != p){
            if(colour[v] == WHITE) dfs(v, u);
            else if(colour[v] == GRAY)
                cout<<"back edge between"<<u + 1<<" and"<<v + 1<<endl;
            else if(colour[v] == BLACK)
                cout<<"cross edge between"<<u + 1<<" and"<<v + 1<<endl;;
        }
    }
    colour[u] = BLACK;
}
void print_dfs_num(){
    for(int v = 0; v < vexnum; v++)
        cout<<dfsNum[v]<<" ";
}
*/

void LoopJudge(){
    bool loop = false;

    int twice = 2;
    int k, i, j;
    cout<<"line: "<<__LINE__<<endl;
    for( k = twice; k > 0; k--){
        cout<<"line: "<<__LINE__<<"k: "<<k<<endl;
        for( i = 0; i < vexnum; i++){
            cout<<"line: "<<__LINE__<<"i: "<<i<<endl;
            if(indegree[i] <= 1){
                indegree[i] = 0;   //delete vertex in degree equal one
                for( j = 0; j < vexnum; j++){
                     cout<<"line: "<<__LINE__<<"j: "<<j<<endl;
                    if(M[i][j]){
                        M[i][j] = false;
                        M[j][i] = false;
                        indegree[j]--;
                        }//if(M[i][j])
                }//for(int j = 0; j < vexnum; j++)
            }//if(indegree[i] <= 1)
        }//for(int i = 0; i < vexnum; i++)
    }

      for( k = 0; k < vexnum; k++){
            if(indegree[k] != 0){
                loop = true;
            }
      }

      if(loop)
        cout<<"There is loop in undirected graph!"<<endl;
      else
        cout<<"There is no loop in undirected graph!"<<endl;
}

int main()
{
    init_graph();
    //dfs(0, -1);
    //print_dfs_num();
    LoopJudge();

    int ch;
    cin>>ch;
    return 0;
}

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