HDU——1068 Girls and Boys

最新推荐文章于 2024-07-22 15:30:00 发布

转载最新推荐文章于 2024-07-22 15:30:00 发布 · 104 阅读

0 ·

CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/z360/p/7424451.html

文章标签：

#java

本文介绍了一道经典的二分图最大匹配问题，通过使用深度优先搜索（DFS）的方法来解决大学学生之间的浪漫关系研究问题，旨在找出最大的不相交匹配集合。

　　　　　　　　　　Girls and Boys

　　　　　　　　　　Time Limit: 20000/10000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
　　　　　　　　　　　　　　Total Submission(s): 12246 Accepted Submission(s): 5768

Problem Description

the second year of the university somebody started a study on the romantic relations between the students. The relation “romantically involved” is defined between one girl and one boy. For the study reasons it is necessary to find out the maximum set satisfying the condition: there are no two students in the set who have been “romantically involved”. The result of the program is the number of students in such a set.

The input contains several data sets in text format. Each data set represents one set of subjects of the study, with the following description:

the number of students
the description of each student, in the following format
student_identifier:(number_of_romantic_relations) student_identifier1 student_identifier2 student_identifier3 ...
or
student_identifier:(0)

The student_identifier is an integer number between 0 and n-1, for n subjects.
For each given data set, the program should write to standard output a line containing the result.

Sample Input

7 0: (3) 4 5 6 1: (2) 4 6 2: (0) 3: (0) 4: (2) 0 1 5: (1) 0 6: (2) 0 1 3 0: (2) 1 2 1: (1) 0 2: (1) 0

Sample Output

5 2

Source

Southeastern Europe 2000

二分图的最大匹配数（裸题）

#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<iostream>
#include<algorithm>
#define N 1010
using namespace std;
bool vis[N];
int t,n,m,x,y,ans,girl[N],map[N][N];
int read()
{
    int x=0,f=1; char ch=getchar();
    while(ch<'0'||ch>'9') {if(ch=='-') f=-1; ch=getchar();}
    while(ch<='9'&&ch>='0'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int find(int x)
{
    for(int i=1;i<=n;i++)
    {
        if(!vis[i]&&map[x][i])
        {
            vis[i]=true;
            if(girl[i]==-1||find(girl[i])) {girl[i]=x;return 1;}
        }
    }
    return 0;
}
int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        ans=0;
        memset(map,0,sizeof(map));
        memset(girl,-1,sizeof(girl));
        for(int i=1;i<=n;i++)
        {
            x=read();m=read();
            while(m--)
              y=read(),map[x+1][y+1]=1; 
        }
        for(int i=1;i<=n;i++)
        {
            memset(vis,0,sizeof(vis));
            ans+=find(i);
        }
        printf("%d\n",(2*n-ans)/2);
    }
    return 0;
}