HDU1179-二分图最大匹配

朱雀 2022-07-12 05:03 173阅读 0赞

# Ollivanders: Makers of Fine Wands since 382 BC. #

**Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 131072/65536 K (Java/Others)  
Total Submission(s): 1740    Accepted Submission(s): 983**

Problem Description

In Diagon Alley ,there is only one Wand-seller,peeling gold letters over the door read Ollivanders: Makers of Fine Wands since 382 BC.A single wand lay on a faded purple cushion in the dusty window.   
A tinkling bell rang somewhere in the depths of the shop as they stepped inside.It was a tiny place,empty execpt for a single spindly chair which Hagrid sat on to wait.Harry felt strangely as though he had entered a very strict library;he swallowd a log of new questions which had just occurred to him and looked instead at the thousands of narrow boxes piled neatly right up to the ceiling.For some reason,the back of his neck prickled.The very dust and silence in here seemed to tingle with some secret magic.   
'Good afternoon,'said a soft voice.Harry jumped.Hagrid must have jumped,too,because there was a loud crunching noise and he got quickly off the spindly chair.   
An old man was standing before them, his wide pale eyes shining like moons through the gloom of the shop.   
'Hello,' said Harry awkwardly.   
'Ah yes,' said the man. 'Yes,yes. I thought I'd be seeing you soon,Harry Potter.'It wasn't a question.You have your mother's eyes. It seems only yesterday she was in here herself,buying her first wand. Ten and a quarter inches long, swishy, made of willow. Nice wand for charm work.'   
Mor Ollivander moved closer to Harry.Harry wished he would blink.Those sivery eyes were a bit creepy.   
'Your father, on the other hand, favoured a mahogany wand.Eleven inches.Pliable.A little more power and excellent for transfiguration.Well ,I say your father favoured it - it's really the wand that choosed the wizard, of cource.'   
  
Yes, some wands fit some wizards ,as we all know.But what Harry doesn't know is Ollivander have met a big trouble.That's more than twenty years ago,When Harry's father James Potter was still a student in Hogwarts.He went Diagon Alley to buy new books,passing by Ollivander's shop.Ollivander was crazy for a problem:He was too busy to choose most suitable wand for every wizard.Even more,there are too many customer that day.Though Ollivader knew every wand's favourite,he could not choose as many wizards as possible to get the wands. So James Potter,a very clever man ,gave him a magic disk with your program ,to help him sell wands as many as possible.   
  
Please notice: one wand can only be sold to one wizard, and one wizard can only buy one wand,too.

Input

There are several cases. For each case, there is two integers N and M in the first line,which mean there is N wizards and M wands(0 < N <= M <= 100).  
Then M lines contain the choices of each wand.The first integer in i+1th line is Ki,and after these there are Ki integers Bi,j which are the wizards who fit that wand. (0<=Ki<=N,1<=Bi,j<=N)

Output

Only one integer,shows how many wands Ollivander can sell.

Sample Input

3 4
    3 1 2 3
    1 1
    1 1
    0

题目大意：

题目读起来有点费劲，所以我也只好选择翻译~~哈哈~~，大概意思就是有n种魔杖和m个客人，每个客人有自己喜欢的魔杖，但每种魔杖只有一个，每个客人只买一个自己喜欢的，问最多能满足多少个客人

题目思路：

最大二分匹配的裸题，所以直接上最大匹配代码，对于二分匹配可以见博客：[最大二分匹配][Link 1]

ac代码

#include<cstring>
    #include<cstdio>
    
    const int maxn = 2e2+10;
    
    bool vis[maxn],mp[maxn][maxn];
    int link[maxn];
    
    int n,m,k;
    
    bool dfs(int u){
        for(int i=n+1;i<=n+m;i++){
            if(!vis[i]&&mp[u][i]){
                vis[i]=true;
                if(link[i]==-1||dfs(link[i])){
                    link[i]=u;
                    return true;
                }
            }
        }
        return false;
    }
    
    int main()
    {
        while(~scanf("%d%d",&n,&m)){
            memset(link,-1,sizeof(link));
            memset(mp,false,sizeof(mp));
            for(int i=1;i<=m;i++){
                int a,b;
                scanf("%d",&a);
                while(a--){
                    scanf("%d",&b);
                    mp[i][m+b]=true;
                }
            }
            int ans = 0;
            for(int i=1;i<=m;i++){
                memset(vis,false,sizeof(vis));
                if(dfs(i))ans++;
            }
            printf("%d\n",ans);
        }
        return 0;
    }

[Link 1]: http://blog.csdn.net/qq_34731703/article/details/54985554