Divide Groups 二分图的判定

最新推荐文章于 2019-08-18 16:13:33 发布

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原文链接：http://www.cnblogs.com/zsyacm666666/p/5299477.html

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#java

本文介绍了一个特定场景下的图论问题解决方法，即如何将参与者合理地分为两组以确保每组内部成员相互认识，以此来优化活动效果。通过深度优先搜索（DFS）实现对图的遍历，并判断是否能成功进行分组。

Divide Groups

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1835 Accepted Submission(s): 657

Problem Description

  This year is the 60th anniversary of NJUST, and to make the celebration more colorful, Tom200 is going to invite distinguished alumnus back to visit and take photos.
  After carefully planning, Tom200 announced his activity plan, one that contains two characters:
  1. Whether the effect of the event are good or bad has nothing to do with the number of people join in.
  2. The more people joining in one activity know each other, the more interesting the activity will be. Therefore, the best state is that, everyone knows each other.
  The event appeals to a great number of alumnus, and Tom200 finds that they may not know each other or may just unilaterally recognize others. To improve the activities effects, Tom200 has to divide all those who signed up into groups to take part in the activity at different time. As we know, one's energy is limited, and Tom200 can hold activity twice. Tom200 already knows the relationship of each two person, but he cannot divide them because the number is too large.
  Now Tom200 turns to you for help. Given the information, can you tell if it is possible to complete the dividing mission to make the two activity in best state.

Input

  The input contains several test cases, terminated by EOF.
  Each case starts with a positive integer n (2<=n<=100), which means the number of people joining in the event.
  N lines follow. The i-th line contains some integers which are the id
of students that the i-th student knows, terminated by 0. And the id starts from 1.

Output

If divided successfully, please output "YES" in a line, else output "NO".

Sample Input

3 3 0 1 0 1 2 0

Sample Output

YES

#include <cstdio>
#include <cmath>
#include <vector>
#include <cstring>
#include <iostream>
using namespace std;
const int Max=111;
int G[Max][Max];
int path[Max][Max],book[Max],color[Max],book1[Max];
int n;
bool dfs(int u,int co)
{
//  cout<<u<<" "<<color[u]<<" "<<co<<endl;
  if(color[u]!=-1&&color[u]!=co) return true;
  if(color[u]==co) return false;
  color[u]=!co;
  for(int i=1;i<=n;i++)
  {
      if(u==i) continue;
      if(path[u][i]||path[i][u])
      if(book[i]) if(!dfs(i,!co)) return false;
  }
  return true;
}
int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        memset(book,0,sizeof(book));
        memset(book1,-1,sizeof(book1));
        memset(G,0,sizeof(G));
        memset(path,0,sizeof(path));
        memset(color,-1,sizeof(color));
        int tmp;
        for(int i=1;i<=n;i++)
        {
            while(scanf("%d",&tmp))
            {
                if(tmp==0) break;
                G[i][tmp]=1;
            }
        }
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=n;j++)
            {
                 if(G[i][j]!=1||G[j][i]!=1)
                 {
                     if(i==j) continue;
                     book[i]=book[j]=1;
                     path[i][j]=1;
                 }
            }
        }
        int flag=0;
        for(int i=1;i<=n;i++)
        {
          if(book[i])
           if(!dfs(i,1)) {flag=1;break;}
          memset(color,-1,sizeof(color));
        }
        if(flag) printf("NO\n");
        else     printf("YES\n");
    }
    return 0;
}