Mirko works on a pig farm that consists of M locked pig-houses and Mirko can‘t unlock any pighouse because he doesn‘t have the keys. Customers come to the farm one after another. Each of them has keys to some pig-houses and wants to buy a certain number of pigs.
All data concerning customers planning to visit the farm on that particular day are available to Mirko early in the morning so that he can make a sales-plan in order to maximize the number of pigs sold.
More precisely, the procedure is as following: the customer arrives, opens all pig-houses to which he has the key, Mirko sells a certain number of pigs from all the unlocked pig-houses to him, and, if Mirko wants, he can redistribute the remaining pigs across the unlocked pig-houses.
An unlimited number of pigs can be placed in every pig-house.
Write a program that will find the maximum number of pigs that he can sell on that day.
The first line of input contains two integers M and N, 1 <= M <= 1000, 1 <= N <= 100, number of pighouses and number of customers. Pig houses are numbered from 1 to M and customers are numbered from 1 to N.
The next line contains M integeres, for each pig-house initial number of pigs. The number of pigs in each pig-house is greater or equal to 0 and less or equal to 1000.
The next N lines contains records about the customers in the following form ( record about the i-th customer is written in the (i+2)-th line):
A K1 K2 ... KA B It means that this customer has key to the pig-houses marked with the numbers K1, K2, ..., KA (sorted nondecreasingly ) and that he wants to buy B pigs. Numbers A and B can be equal to 0.
The first and only line of the output should contain the number of sold pigs.
#include<cstdio>
#include<vector>
#include<queue>
#include<cstring>
using namespace std;
const int INF=0x3f3f3f3f,MAXN=1e3+5;
int mp[MAXN][MAXN],num[MAXN],p[MAXN],pre[MAXN],a[MAXN],m,n;
struct Edge
{
int from,to,cap,flow;
Edge(){}
Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){};
};
vector<int>G[1005];
vector<Edge>edges;
void init()
{
for(int i=0;i<n;i++)
G[i].clear();
edges.clear();
}
void addedge(int from,int to,int cap)
{
edges.push_back(Edge(from,to,cap,0));
edges.push_back(Edge(to,from,0,0));
int m=edges.size();
G[to].push_back(m-1);
G[from].push_back(m-2);
}
int maxflow(int s,int t)
{
int flow=0;
while(1)
{
memset(a,0,sizeof(a));
queue<int>q;
q.push(s);
a[s]=INF;
while(!q.empty())
{
int x=q.front();
q.pop();
for(int i=0;i<G[x].size();i++)
{
Edge& e=edges[G[x][i]];
if(!a[e.to]&&e.cap>e.flow)
{
p[e.to]=G[x][i];
a[e.to]=min(a[x],e.cap-e.flow);
q.push(e.to);
}
}
if(a[t])break;
}
if(!a[t])break;
for(int u=t;u!=s;u=edges[p[u]].from)
{
edges[p[u]].flow+=a[t];
edges[p[u]^1].flow-=a[t];
}
flow+=a[t];
}
return flow;
}
int main()
{
int m,n;
scanf("%d%d",&m,&n);
for(int i=1;i<=m;i++)scanf("%d",&num[i]);
for(int i=1;i<=n;i++)
{
int cnt;
scanf("%d",&cnt);
while(cnt--)
{
int t;
scanf("%d",&t);
if(!pre[t])
addedge(0,i,num[t]);
else
addedge(pre[t],i,INF);
pre[t]=i;
}
scanf("%d",&cnt);
addedge(i,n+1,cnt);
}
printf("%d\n",maxflow(0,n+1));
return 0;
}
