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hdu2768-Cat vs. Dog：图论：二分匹配

2024-07-26 06:00:36   217人阅读

Cat vs. Dog

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1602    Accepted Submission(s): 606


Problem Description
The latest reality show has hit the TV: ``Cat vs. Dog‘‘. In this show, a bunch of cats and dogs compete for the very prestigious Best Pet Ever title. In each episode, the cats and dogs get to show themselves off, after which the viewers vote on which pets should stay and which should be forced to leave the show.

Each viewer gets to cast a vote on two things: one pet which should be kept on the show, and one pet which should be thrown out. Also, based on the universal fact that everyone is either a cat lover (i.e. a dog hater) or a dog lover (i.e. a cat hater), it has been decided that each vote must name exactly one cat and exactly one dog.

Ingenious as they are, the producers have decided to use an advancement procedure which guarantees that as many viewers as possible will continue watching the show: the pets that get to stay will be chosen so as to maximize the number of viewers who get both their opinions satisfied. Write a program to calculate this maximum number of viewers.
 

 

Input
On the first line one positive number: the number of testcases, at most 100. After that per testcase:

* One line with three integers c, d, v (1 ≤ c, d ≤ 100 and 0 ≤ v ≤ 500): the number of cats, dogs, and voters.
* v lines with two pet identifiers each. The first is the pet that this voter wants to keep, the second is the pet that this voter wants to throw out. A pet identifier starts with one of the characters `C‘ or `D‘, indicating whether the pet is a cat or dog, respectively. The remaining part of the identifier is an integer giving the number of the pet (between 1 and c for cats, and between 1 and d for dogs). So for instance, ``D42‘‘ indicates dog number 42.
 

 

Output
Per testcase:

* One line with the maximum possible number of satisfied voters for the show.
 

 

Sample Input
21 1 2C1 D1D1 C11 2 4C1 D1C1 D1C1 D2D2 C1
 

 

Sample Output
13
 

 

Source
NWERC 2008
算法：将喜欢猫和喜欢狗的人分开，就形成了一个二分图，这样喜欢猫（狗）的人一定不会冲突的，然后扫描一次，将互相矛盾的人连一条边。
二分图的最大独立集就是答案。由已知定理有：二分图最大独立集=顶点数-二分图最大匹配。求二分图最大匹配即可。
 
 
 1 const int MAXN = 510; 2 int uN,vN;//u,v的数目，使用前面必须赋值 3 int g[MAXN][MAXN];//邻接矩阵 4 int linker[MAXN]; 5 bool used[MAXN]; 6 #include <memory.h> 7 bool dfs(int u) 8 { 9     for(int v = 0; v < vN; v++)10         if(g[u][v] && !used[v])11         {12             used[v] = true;13             if(linker[v] == -1 || dfs(linker[v]))14             {15                 linker[v] = u;16                 return true;17             }18         }19     return false;20 }21 int hungary()22 {23     int res = 0;24     memset(linker,-1,sizeof(linker));25     for(int u = 0; u < uN; u++)26     {27         memset(used,false,sizeof(used));28         if(dfs(u))res++;29     }30     return res;31 }32 33 #include <iostream>34 #include <stdio.h>35 #include <string.h>36 using namespace std;37 38 39 int getint(char s[])40 {41     int ans=0;42     for(int i=0; i<strlen(s); i++)43     {44         ans=ans*10+s[i]-‘0‘;45     }46     return ans;47 }48 49 typedef pair<int,int> CPair;50 51 CPair upair[510],vpair[510];52 int main()53 {54     #ifndef ONLINE_JUDGE55     freopen("in.txt","r",stdin);56     #endif // ONLINE_JUDGE57     int T;58     cin>>T;59     while(T--)60     {61         memset(g,0,sizeof g);62         int nc,nd,n;63         uN=vN=0;64         scanf("%d%d%d",&nc,&nd,&n);65         for(int i=0; i<n; i++) // 人的数量66         {67             char s1[20],s2[20];68             scanf("%s%s",s1,s2); // C1 D169             int ci=getint(s1+1),di=getint(s2+1);70             if(s1[0]==‘C‘)71             {72                 // 放到第一个集合73                 upair[uN++]=CPair(ci,di);74             }75             else76             {77                 vpair[vN++]=CPair(ci,di);78             }79         }80         // 构图81         for(int i=0;i<uN;i++)82             for(int j=0;j<vN;j++)83             {84                 // 矛盾的话就连一条边85                 if(upair[i].first==vpair[j].second || upair[i].second==vpair[j].first)86                     g[i][j]=1;87             }88 89         int ans=uN+vN-hungary();90         printf("%d\n",ans);91     }92     return 0;93 }

 

 
 

hdu2768-Cat vs. Dog：图论：二分匹配


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