HDU 3081 Marriage Match II
Marriage Match II
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 3837 Accepted Submission(s): 1255
Problem Description
Presumably,
you all have known the question of stable marriage match. A girl will
choose a boy; it is similar as the game of playing house we used to play
when we are kids. What a happy time as so many friends playing
together. And it is normal that a fight or a quarrel breaks out, but we
will still play together after that, because we are kids.
Now, there are 2n kids, n boys numbered from 1 to n, and n girls numbered from 1 to n. you know, ladies first. So, every girl can choose a boy first, with whom she has not quarreled, to make up a family. Besides, the girl X can also choose boy Z to be her boyfriend when her friend, girl Y has not quarreled with him. Furthermore, the friendship is mutual, which means a and c are friends provided that a and b are friends and b and c are friend.
Once every girl finds their boyfriends they will start a new round of this game—marriage match. At the end of each round, every girl will start to find a new boyfriend, who she has not chosen before. So the game goes on and on.
Now, here is the question for you, how many rounds can these 2n kids totally play this game?
Now, there are 2n kids, n boys numbered from 1 to n, and n girls numbered from 1 to n. you know, ladies first. So, every girl can choose a boy first, with whom she has not quarreled, to make up a family. Besides, the girl X can also choose boy Z to be her boyfriend when her friend, girl Y has not quarreled with him. Furthermore, the friendship is mutual, which means a and c are friends provided that a and b are friends and b and c are friend.
Once every girl finds their boyfriends they will start a new round of this game—marriage match. At the end of each round, every girl will start to find a new boyfriend, who she has not chosen before. So the game goes on and on.
Now, here is the question for you, how many rounds can these 2n kids totally play this game?
Input
There are several test cases. First is a integer T, means the number of test cases.
Each test case starts with three integer n, m and f in a line (3<=n<=100,0<m<n*n,0<=f<n). n means there are 2*n children, n girls(number from 1 to n) and n boys(number from 1 to n).
Then m lines follow. Each line contains two numbers a and b, means girl a and boy b had never quarreled with each other.
Then f lines follow. Each line contains two numbers c and d, means girl c and girl d are good friends.
Each test case starts with three integer n, m and f in a line (3<=n<=100,0<m<n*n,0<=f<n). n means there are 2*n children, n girls(number from 1 to n) and n boys(number from 1 to n).
Then m lines follow. Each line contains two numbers a and b, means girl a and boy b had never quarreled with each other.
Then f lines follow. Each line contains two numbers c and d, means girl c and girl d are good friends.
Output
For each case, output a number in one line. The maximal number of Marriage Match the children can play.
Sample Input
1
4 5 2
1 1
2 3
3 2
4 2
4 4
1 4
2 3
Sample Output
2
二分求轮数,Dinic算法模板
1 #include <iostream> 2 #include <cstring> 3 #include <vector> 4 #include <queue> 5 #define maxn 210 6 #define INF 0X3fffffff 7 using namespace std; 8 struct Edge 9 { 10 int from,to,cap,flow; 11 Edge(){} 12 Edge(int f,int t,int c,int fl):from(f),to(t),cap(c),flow(fl){} 13 }; 14 15 struct Dinic 16 { 17 int n,m,s,t; 18 vector<Edge> edges; 19 vector<int> G[maxn]; 20 bool vis[maxn]; 21 int cur[maxn]; 22 int d[maxn]; 23 24 void init(int n,int s,int t) 25 { 26 this->n=n, this->s=s, this->t=t; 27 edges.clear(); 28 for(int i=0;i<=n;++i) G[i].clear(); 29 } 30 31 void AddEdge(int from,int to,int cap) 32 { 33 edges.push_back( Edge(from,to,cap,0) ); 34 edges.push_back( Edge(to,from,0,0) ); 35 m=edges.size(); 36 G[from].push_back(m-2); 37 G[to].push_back(m-1); 38 } 39 40 bool BFS() 41 { 42 queue<int> Q; 43 memset(vis,0,sizeof(vis)); 44 vis[s]=true; 45 d[s]=0; 46 Q.push(s); 47 while(!Q.empty()) 48 { 49 int x=Q.front(); Q.pop(); 50 for(int i=0;i<G[x].size();++i) 51 { 52 Edge& e=edges[G[x][i]]; 53 if(!vis[e.to] && e.cap>e.flow) 54 { 55 vis[e.to]=true; 56 d[e.to]=d[x]+1; 57 Q.push(e.to); 58 } 59 } 60 } 61 return vis[t]; 62 } 63 64 int DFS(int x,int a) 65 { 66 if(x==t || a==0) return a; 67 int flow=0, f; 68 for(int &i=cur[x];i<G[x].size();++i) 69 { 70 Edge &e=edges[G[x][i]]; 71 if(d[e.to]==d[x]+1 && (f=DFS(e.to,min(a,e.cap-e.flow) ) )>0) 72 { 73 e.flow +=f; 74 edges[G[x][i]^1].flow -=f; 75 flow +=f; 76 a -=f; 77 if(a==0) break; 78 } 79 } 80 return flow; 81 } 82 83 int max_flow() 84 { 85 int ans=0; 86 while(BFS()) 87 { 88 memset(cur,0,sizeof(cur)); 89 ans +=DFS(s,INF); 90 } 91 return ans; 92 } 93 }DC; 94 int parnet[maxn]; 95 bool flag[maxn][maxn]; 96 int find(int n){ 97 if(n==parnet[n]){ 98 return n; 99 } 100 else return parnet[n]=find(parnet[n]); 101 } 102 void Union(int x,int y){ 103 int xx=find(x); 104 int yy=find(y); 105 if(xx!=yy){ 106 parnet[xx]=yy; 107 } 108 } 109 bool solve(int n,int limit){ 110 int start=0,end=2*n+1; 111 DC.init(n*2+2,start,end); 112 for(int i=1;i<=n;i++){ 113 for(int j=1;j<=n;j++){ 114 if(flag[i][j]){ 115 DC.AddEdge(i,j+n,1); 116 } 117 } 118 } 119 for(int i=1;i<=n;i++){ 120 DC.AddEdge(i+n,end,limit); 121 } 122 for(int i=1;i<=n;i++){ 123 DC.AddEdge(start,i,limit); 124 } 125 return DC.max_flow()==n*limit; 126 } 127 void init(int n){ 128 for(int i=1;i<=n;i++){ 129 parnet[i]=i; 130 } 131 memset(flag,0,sizeof(flag)); 132 } 133 int main(){ 134 int n,m,f,T,a,b; 135 cin.sync_with_stdio(false); 136 cin>>T; 137 while(T--){ 138 cin>>n>>m>>f; 139 init(n); 140 while(m--){ 141 cin>>a>>b; 142 flag[a][b]=true; 143 } 144 while(f--){ 145 cin>>a>>b; 146 Union(a,b); 147 } 148 for(int i=1;i<=n;i++){ 149 for(int j=i+1;j<=n;j++){ 150 if(find(i)==find(j)){ 151 for(int k=1;k<=n;k++){ 152 flag[i][k]=flag[j][k]=(flag[i][k]||flag[j][k]); 153 } 154 } 155 } 156 } 157 int l=0,r=n; 158 while(l<r){ 159 int mid=(l+r+1)/2; 160 if(solve(n,mid)){ 161 l=mid; 162 } 163 else{ 164 r=mid-1; 165 } 166 } 167 cout<<l<<endl; 168 } 169 return 0; 170 }
2017-03-06 12:12:51