HDU 1083

HDU 1083 http://acm.hdu.edu.cn/showproblem.php?pid=1083

PKU 1469 http://poj.org/problem?id=1469

【二分匹配】

网络流版本:

//只要求出course的最大匹配数,再跟P比较即可.网络流实现
  2  #include <iostream>
  3 #include <cstdio>
  4 #include <string>
  5 #include <cstring>
  6 #include <algorithm>
  7 #include <vector>
  8 #include <map>
  9 #include <queue>
 10 
 11  using namespace std;
 12 
 13 const int MAXN=100+300+10;
 14 int Flow[MAXN][MAXN];
 15 int Vis[MAXN];
 16 int Path[MAXN];
 17 void creat_net(vector<int> box[], int studentNum, int courseNum)
 18 {
 19     for( int i=1; i<=studentNum; ++i )
 20     {
 21         box[0].push_back(i);
 22     }
 23     for( int i=1; i<=courseNum; ++i )
 24     {
 25         box[i+studentNum].push_back(studentNum+courseNum+1);
 26     }
 27 }
 28 int bfs_net(vector<int> box[], int s, int t)
 29 {
 30     memset(Flow, 0, sizeof(Flow));
 31     bool isFind;
 32     int ans=0;
 33     Path[0]=-1;
 34     while( 1 )
 35     {
 36         queue<int> que;
 37         memset(Vis, 0, sizeof(Vis));
 38         que.push(s);
 39         Vis[s]=1;
 40         isFind=false;
 41         while( !que.empty() )
 42         {
 43             int from=que.front();
 44             vector<int>::iterator ix=box[from].begin();
 45             while( ix!=box[from].end() )
 46             {
 47                 if( !Vis[*ix] && ((from<*ix && 1>Flow[from][*ix] )||(from>*ix && 0>Flow[from][*ix])) )
 48                 {
 49                     que.push(*ix);
 50                     Path[*ix]=from;
 51                     Vis[*ix]=1;
 52                     if( *ix==t )
 53                     {
 54                         isFind=true;
 55                         break;
 56                     }
 57                 }
 58                 ++ix;
 59             }
 60             if( isFind )
 61             {
 62                 break;
 63             }
 64             que.pop();
 65         }
 66         if( isFind==false )
 67         {
 68             return ans;
 69         }
 70         int from=Path[t];
 71         int to=t;
 72         for( ; ; )
 73         {
 74             if( from==-1 )
 75             {
 76                 break;
 77             }
 78             Flow[from][to]++;
 79             Flow[to][from]--;
 80             to=from;
 81             from=Path[to];
 82         }
 83         ans++;
 84     }
 85 }
 86 int main()
 87 {
 88     freopen("in.txt","r",stdin);
 89     int Case, P, N, preNum, temp;
 90     scanf("%d", &Case);
 91     while( Case-- )
 92     {
 93         scanf("%d%d", &P, &N);
 94         vector<int> box[P+N+2];
 95         for( int i=1; i<=P; ++i )
 96         {
 97             scanf("%d", &preNum);
 98             for( int j=1; j<=preNum; ++j )
 99             {
100                 scanf("%d", &temp);
101                 box[i+N].push_back(temp);
102                 box[temp].push_back(i+N);
103             }
104         }
105         creat_net(box, N, P);
106         printf(bfs_net(box,0,P+N+1)==P?"YES\n":"NO\n");
107     }
108     return 0;
109 }
110 
111

匈牙利算法:

//匈牙利算法模版.
 2  #include <iostream>
 3 #include <algorithm>
 4 #include <cstdio>
 5 #include <cstring>
 6 
 7 using namespace std;
 8 
 9 const int MAXN=301;
10 const int INF=0x7f7f7f7f;
11 int P, N;
12 int Cap[MAXN][MAXN];
13 int Vis[MAXN];
14 int Match[MAXN];
15 
16 bool dfs( int from )
17 {
18     for( int i=1; i<=P; ++i )
19     {
20         if( Cap[from][i] && !Vis[i] )
21         {
22             Vis[i]=1;
23             int temp=Match[i];
24             Match[i]=from;
25             if( temp==INF || dfs(temp) )
26             {
27                 return true;
28             }
29             Match[i]=temp;
30         }
31     }
32     return false;
33 }
34 int main()
35 {
36     freopen("in","r",stdin);
37     freopen("out","w",stdout);
38 
39     int t, num, temp;
40     scanf("%d", &t);
41     while( t-- )
42     {
43         memset(Cap, 0, sizeof(Cap));
44         scanf("%d%d", &P, &N);
45         for( int i=1; i<=P; ++i )
46         {
47             scanf("%d", &num);
48             while( num-- )
49             {
50                 scanf("%d", &temp);
51                 Cap[temp][i]=1;
52             }
53         }
54         int ans=0;
55         memset(Match, 0x7f, sizeof(Match));
56         for( int i=1; i<=N; ++i )
57         {
58             memset(Vis, 0, sizeof(Vis));
59             if( dfs(i) )
60             {
61                 ans++;
62             }
63         }
64         printf(ans==P?"YES\n":"NO\n");
65     }
66     return 0;
67 }
68