POJ 3281 Dining

Description

Cows are such finicky eaters. Each cow has a preference for certain foods and drinks, and she will consume no others.

Farmer John has cooked fabulous meals for his cows, but he forgot to check his menu against their preferences. Although he might not be able to stuff everybody, he wants to give a complete meal of both food and drink to as many cows as possible.

Farmer John has cooked F (1 ≤ F ≤ 100) types of foods and preparedD (1 ≤ D ≤ 100) types of drinks. Each of his N (1 ≤ N ≤ 100) cows has decided whether she is willing to eat a particular food or drink a particular drink. Farmer John must assign a food type and a drink type to each cow to maximize the number of cows who get both.

Each dish or drink can only be consumed by one cow (i.e., once food type 2 is assigned to a cow, no other cow can be assigned food type 2).

Input

Line 1: Three space-separated integers: N, F, and D
Lines 2.. N+1: Each line i starts with a two integers F_i and D_i, the number of dishes that cow i likes and the number of drinks that cow i likes. The next F_i integers denote the dishes that cow i will eat, and the D_i integers following that denote the drinks that cow i will drink.

Output

Line 1: A single integer that is the maximum number of cows that can be fed both food and drink that conform to their wishes

Sample Input

4 3 3
2 2 1 2 3 1
2 2 2 3 1 2
2 2 1 3 1 2
2 1 1 3 3

Sample Output

3

Hint

One way to satisfy three cows is:
Cow 1: no meal
Cow 2: Food #2, Drink #2
Cow 3: Food #1, Drink #1
Cow 4: Food #3, Drink #3
The pigeon-hole principle tells us we can do no better since there are only three kinds of food or drink. Other test data sets are more challenging, of course.

Source

USACO 2007 Open Gold

解析
这道题转换为最大流模型，但是为了保证一头牛只吃一道菜喝一种饮料就要将牛拆点。如图

//dinic
#include<cstdio>
#include<queue>
#include<cstring>
#include<algorithm>

using namespace std;

#define INF ~0u>>2

int N,F,D,Map[410][410],SuperS,SuperT,dis[410];

void readdata()
{
	memset(Map,0,sizeof(Map));
	memset(dis,0,sizeof(dis));

	SuperS=0; SuperT=2*N+F+D+1;
	for(int i=1;i<=F;i++) Map[SuperS][i]=1;
	for(int i=1;i<=D;i++) Map[F+2*N+i][SuperT]=1;

	for(int i=1;i<=N;i++)
	{
		Map[F+i][F+N+i]=1;
		int fi,di; scanf("%d%d",&fi,&di);
		for(int j=1;j<=fi;j++)
		{
			int a; scanf("%d",&a);
			Map[a][F+i]=1;
		}
		for(int j=1;j<=di;j++)
		{
			int a; scanf("%d",&a);
			Map[F+N+i][F+2*N+a]=1;
		}
	}
}

bool bfs()
{
	memset(dis,0,sizeof(dis));
	queue<int> q;
	dis[SuperS]=1;q.push(SuperS);
	while(!q.empty())
	{
		int v=q.front();q.pop();
		for(int u=SuperS;u<=SuperT;u++)
			if(!dis[u] && Map[v][u]>0)
			{
				dis[u]=dis[v]+1;
				q.push(u);
				if(u==SuperT) return 1;
			}
	}
	return 0;
}

int dfs(int v,int flow)
{
	if(v==SuperT || flow==0) return flow;

	int ans=0;
	for(int u=SuperS;u<=SuperT;u++)
		if(dis[v]+1==dis[u] && Map[v][u]>0)
		{
			int tmp=dfs(u,min(flow-ans,Map[v][u]));
			ans+=tmp;
			Map[v][u]-=tmp; Map[u][v]+=tmp;
		}

	return ans;
}

void dinic()
{
	int ans=0;
	while(bfs()) 
		ans+=dfs(SuperS,INF);
	printf("%d",ans);
}

int main()
{
	freopen("poj3281.in","r",stdin);

	while(scanf("%d%d%d",&N,&F,&D)==3)
	{
		readdata();
		dinic();
		printf("\n");
	}

	while(1);
	return 0;
}

//sap
#include<cstdio>
#include<queue>
#include<cstring>
#include<algorithm>

using namespace std;

#define INF ~0u>>2

int N,F,D,SuperS,SuperT,Map[410][410],dis[410],vd[410];

void readdata()
{
	memset(dis,0,sizeof(dis));
	memset(Map,0,sizeof(Map));
	memset(vd,0,sizeof(vd));
	SuperS=0; SuperT=F+2*N+D+1;

	for(int i=1;i<=F;i++) Map[SuperS][i]=1;
	for(int i=1;i<=D;i++) Map[F+2*N+i][SuperT]=1;

	for(int i=1;i<=N;i++)
	{
		Map[F+i][F+N+i]=1;
		int fi,di;scanf("%d%d",&fi,&di);
		for(int j=1;j<=fi;j++)
		{
			int a;scanf("%d",&a);
			Map[a][F+i]=1;
		}

		for(int j=1;j<=di;j++)
		{
			int a;scanf("%d",&a);
			Map[F+N+i][F+N*2+a]=1;
		}
	}
}

int dfs(int v,int flow)
{
	if(v==SuperT) return flow;

	int ans=0;
	for(int u=SuperS;u<=SuperT;u++)
		if(dis[v]==dis[u]+1 && Map[v][u]>0)
		{
			int tmp=dfs(u,min(flow-ans,Map[v][u]));
			ans+=tmp;
			Map[v][u]-=tmp;Map[u][v]+=tmp;
			if(flow==ans) return ans;
		}
	if(dis[SuperS]>=F+D+2*N+2) return ans;
	if(--vd[dis[v]]<=0) dis[SuperS]=F+D+2*N+2;
	dis[v]++;vd[dis[v]]++;
	return ans;
}

void sap()
{
	vd[SuperS]=F+D+2*N+2;
	int ans=0;
	while(dis[SuperS]<F+D+2*N+2) 
		ans+=dfs(SuperS,INF);

	printf("%d",ans);
}

int main()
{
	freopen("poj3281.in","r",stdin);

	while(scanf("%d%d%d",&N,&F,&D)==3)
	{
		readdata();
		sap();
		printf("\n");
	}

	while(1);
	return 0;
}