poj 3281 Dining【拆点网络流】
| Time Limit: 2000MS | Memory Limit: 65536K | |
| Total Submissions: 11828 | Accepted: 5437 |
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
Lines 2..N+1: Each line i starts with a two integers Fi and Di, the number of dishes that cow i likes and the number of drinks that cow i likes. The next Fi integers denote the dishes that cow i will eat, and the Di integers following that denote the drinks that cow i will drink.
Output
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
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.
如图，例如当1到4这条路走过后 4连上5，当2经过4后4又可以连上6，这就造成了一头牛吃了多种食物和饮料
2、食物->左牛->右牛->饮料
这种情况当左牛选中一个食物之后经过右牛，左右牛之间的路径已经满流不能继续走，就避免了一头牛吃多种食物和饮料的情况
AC代码：
#include<stdio.h>
#include<string.h>
#include<queue>
#include<stack>
#include<algorithm>
#define MAX 1000
#define MAXM 200100
#define INF 0x7fffff
using namespace std;
int n,f,d;
int ans,head[MAX];
int cur[MAX];
int dis[MAX];
int vis[MAX];
int sect;
struct node
{
int from,to,cap,flow,next;
}edge[MAXM];
void init()
{
ans=0;
memset(head,-1,sizeof(head));
}
void add(int u,int v,int w)
{
edge[ans]={u,v,w,0,head[u]};
head[u]=ans++;
edge[ans]={v,u,0,0,head[v]};
head[v]=ans++;
}
void getmap()
{
int i,j,a,b,fi,di;
for(i=1;i<=n;i++)
{
scanf("%d%d",&fi,&di);
while(fi--)
{
scanf("%d",&a);
///xxx//add(0,a,1);//源点连食物
add(a,f+i,1);//食物连左牛
}
add(f+i,n+i+f,1);//左牛连右牛
while(di--)
{
scanf("%d",&b);
add(n+i+f,2*n+f+b,1);//右牛连饮料
}
}
int db=2*n+f+1,de=2*n+f+d;
for(i=1;i<=f;i++)
add(0,i,1);//源点连食物
for(i=db;i<=de;i++)
add(i,de+1,1);//饮料连超级汇点
sect=2*n+f+d+1;
}
int bfs(int beg,int end)
{
int i;
memset(vis,0,sizeof(vis));
memset(dis,-1,sizeof(dis));
queue<int>q;
while(!q.empty())
q.pop();
vis[beg]=1;
dis[beg]=0;
q.push(beg);
while(!q.empty())
{
int u=q.front();
q.pop();
for(i=head[u];i!=-1;i=edge[i].next)//遍历所有的与u相连的边
{
node E=edge[i];
if(!vis[E.to]&&E.cap>E.flow)//如果边未被访问且流量未满继续操作
{
dis[E.to]=dis[u]+1;//建立层次图
vis[E.to]=1;//将当前点标记
if(E.to==end)//如果当前点搜索到终点则停止搜索 返回1表示有从原点到达汇点的路径
return 1;
q.push(E.to);//将当前点入队
}
}
}
return 0;//返回0表示未找到从源点到汇点的路径
}
int dfs(int x,int a,int end)//把找到的这条边上的所有当前流量加上a（a是这条路径中的最小残余流量）
{
//int i;
if(x==end||a==0)//如果搜索到终点或者最小的残余流量为0
return a;
int flow=0,f;
for(int& i=cur[x];i!=-1;i=edge[i].next)//i从上次结束时的弧开始
{
node& E=edge[i];
if(dis[E.to]==dis[x]+1&&(f=dfs(E.to,min(a,E.cap-E.flow),end))>0)//如果
{//bfs中我们已经建立过层次图，现在如果 dis[E.to]==dis[x]+1表示是我们找到的路径
//如果dfs>0表明最小的残余流量还有，我们要一直找到最小残余流量为0
E.flow+=f;//正向边当前流量加上最小的残余流量
edge[i^1].flow-=f;//反向边
flow+=f;//总流量加上f
a-=f;//最小可增流量减去f
if(a==0)
break;
}
}
return flow;//所有边加上最小残余流量后的值
}
int Maxflow(int beg,int end)
{
int flow=0;
while(bfs(beg,end))//存在最短路径
{
memcpy(cur,head,sizeof(head));//复制数组
flow+=dfs(beg,INF,end);
}
return flow;//最大流量
}
int main()
{
int t;
while(scanf("%d%d%d",&n,&f,&d)!=EOF)
{
init();
getmap();
printf("%d\n",Maxflow(0,sect));
}
return 0;
}
