POJ3281 Dining

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 prepared D (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 32 2 1 2 3 12 2 2 3 1 22 2 1 3 1 22 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.

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题目的意思是给牛喂食物和饮料，每头牛有各自的喜爱的食物和饮料，只有当它同时拿到喜爱的食物和饮料他会满足，问最多多少头牛满足。

思路：网络最大流。 我们可以把食物和牛连边流量为1，饮料和牛连边流量为1，为了防止每头牛得到多个食物和饮料，我们可以把一头牛拆成2个点，再加上一个源点和一个汇点，源点和所有食物连边流量为1，汇点和所有饮料连边流量为1，这样计算源点到汇点的最大流就可以了。

#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <cmath>#include <string>#include <queue>#include <vector>#include <stack>#include <set>#include <map>using namespace std;const int MAXN =100010;//点maxconst int MAXM=400010;//边maxconst int INF=0x3f3f3f3f;struct Edge{    int to,next,cap,flow;} edge[MAXM];int tol;int head[MAXN];int gap[MAXN],dep[MAXN],cur[MAXN];void init(){    tol=0;    memset(head,-1,sizeof(head));}void addedge(int u,int v,int w,int rw=0){    edge[tol].to=v;    edge[tol].cap=w;    edge[tol].flow=0;    edge[tol].next=head[u];    head[u]=tol++;    edge[tol].to=u;    edge[tol].cap=rw;    edge[tol].flow=0;    edge[tol].next=head[v];    head[v]=tol++;}int Q[MAXN];void BFS(int start,int end){    memset(dep,-1,sizeof(dep));    memset(gap,0,sizeof(gap));    gap[0]=1;    int front=0,rear=0;    dep[end]=0;    Q[rear++]=end;    while(front!=rear)    {        int u=Q[front++];        for(int i=head[u]; i!=-1; i=edge[i].next)        {            int v=edge[i].to;            if(dep[v]!=-1)                continue;            Q[rear++]=v;            dep[v]=dep[u]+1;            gap[dep[v]]++;        }    }}int S[MAXN];int sap(int start,int end,int N){    BFS(start,end);    memcpy(cur,head,sizeof(head));    int top=0;    int u =start;    int ans=0;    while(dep[start]<N)    {        if(u==end)        {            int Min=INF;            int inser;            for(int i=0; i<top; i++)            {                if(Min>edge[S[i]].cap-edge[S[i]].flow)                {                    Min=edge[S[i]].cap-edge[S[i]].flow;                    inser=i;                }            }            for(int i=0; i<top; i++)            {                edge[S[i]].flow+=Min;                edge[S[i]^1].flow-=Min;            }            ans+=Min;            top=inser;            u=edge[S[top]^1].to;            continue;        }        bool flag=false;        int v;        for(int i=cur[u]; i!=-1; i=edge[i].next)        {            v=edge[i].to;            if(edge[i].cap-edge[i].flow&&dep[v]+1==dep[u])            {                flag=true;                cur[u]=i;                break;            }        }        if(flag)        {            S[top++]=cur[u];            u=v;            continue;        }        int Min=N;        for(int i=head[u]; i!=-1; i=edge[i].next)        {            if(edge[i].cap-edge[i].flow&&dep[edge[i].to]<Min)            {                Min=dep[edge[i].to];                cur[u]=i;            }        }        gap[dep[u]]--;        if(!gap[dep[u]])return ans;        dep[u]=Min+1;        gap[dep[u]]++;        if(u!=start)            u=edge[S[--top]^1].to;    }    return ans;}int main(){    int n,f,d,a,b,x;//f:1~f,牛:f+1~f+n&&f+n+1~f+2*n,d:f+2*n+1~f+2*n+d    while(~scanf("%d%d%d",&n,&f,&d))    {        init();        for(int i=0;i<n;i++)        {            scanf("%d%d",&a,&b);            for(int j=0;j<a;j++)            {                scanf("%d",&x);                addedge(x,f+1+i,1,0);            }            for(int j=0;j<b;j++)            {                scanf("%d",&x);                addedge(f+n+1+i,f+2*n+x,1,0);            }        }            for(int i=0;i<f;i++)            {                addedge(0,i+1,1,0);            }            for(int i=0;i<d;i++)            {                addedge(f+2*n+i+1,f+d+2*n+1,1,0);            }            for(int i=0;i<n;i++)            {                addedge(f+i+1,f+i+1+n,1,0);            }            printf("%d\n",sap(0,f+d+2*n+1,2+f+d+2*n));    }    return 0;}