Description
Open-pit mining is a surface mining technique of extracting rock or minerals from the earth by their removal from an open pit or borrow. Open-pit mines are used when deposits of commercially useful minerals or rocks are found near the surface. Automatic Computer Mining (ACM) is a company that would like to maximize its profits by open-pit mining. ACM has hired you to write a program that will determine the maximum profit it can achieve given the description of a piece of land.
Each piece of land is modelled as a set of blocks of material. Block i has an associated value (vi), as well as a cost (ci), to dig that block from the land. Some blocks obstruct or bury other blocks. So for example if block i is obstructed by blocks j and k, then one must first dig up blocks j and k before block i can be dug up. A block can be dug up when it has no other blocks obstructing it.
Input
The first line of input is an integer N(1≤N≤200)N(1≤N≤200) which is the number of blocks. These blocks are numbered 1 through N. Then follow N lines describing these blocks. The ith such line describes block i and starts with two integers vi, ci denoting the value and cost of the ith block (0≤vi,ci≤200)(0≤vi,ci≤200) . Then a third integer 0≤mi≤N−10≤mi≤N−1 on this line describes the number of blocks that block i obstructs. Following that are mi distinct space separated integers between 1 and N (but excluding i) denoting the label(s) of the blocks that block i obstructs. You may assume that it is possible to dig up every block for some digging order. The sum of values mi over all blocks i will be at most 500.
Output
Output a single integer giving the maximum profit that ACM can achieve from the given piece of land.
Sample Input
5 0 3 2 2 3 1 3 2 4 5 4 8 1 4 5 3 0 9 2 0
Sample Output
2
Hint
数论：网络流：最大权闭合子图，模板题
#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#include<cmath>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1e6+5;
const int INF=0x3f3f3f3f;
struct node{
ll t,cap,flow,next;
}e[N];
int head[N],cur[N],cnt;
void init(){
memset(head,-1,sizeof(head));
cnt=0;
}
void add(int u,int v,ll cap)
{
e[cnt]=node{v,cap,0,head[u]};
head[u]=cnt++;
e[cnt]=node{u,0,0,head[v]};
head[v]=cnt++;
}
int d[N];
bool bfs(int s,int t) //O(n+m)
{
memset(d,0,sizeof(d));
queue<int>q;
q.push(s);
d[s]=1;
while(!q.empty())
{
int u=q.front();q.pop();
for(int i=head[u];~i;i=e[i].next)
{
int v=e[i].t;
if(d[v]==0&&e[i].cap-e[i].flow>0)
{
d[v]=d[u]+1;
q.push(v);
}
}
}
return d[t]>0;
}
ll dfs(int s,int t,ll minedge)
{
if(s==t)return minedge;
ll flow=0;
for(int &i=cur[s];~i;i=e[i].next)
{
int v=e[i].t;
if(d[v]==d[s]+1&&e[i].cap-e[i].flow>0)
{
ll temp=dfs(v,t,min(minedge-flow,e[i].cap-e[i].flow));
e[i].flow+=temp;
e[i^1].flow-=temp;
flow+=temp;
if(flow==minedge)return flow;
}
}
if(flow==0)d[s]=0;
return flow;
}
ll dinic(int s,int t)
{
ll maxflow=0;
while(bfs(s,t))
{
memcpy(cur,head,sizeof(head));
maxflow+=dfs(s,t,INF);
}
return maxflow;
}
int pro[220];
int main()
{
int n,u,v,x,k;
init();
scanf("%d",&n);
for(int i=1;i<=n;i++)
{
scanf("%d%d%d",&u,&v,&k);
pro[i]=u-v;
while(k--){
scanf("%d",&x);
add(x,i,INF);
}
}
ll sum=0;
for(int i=1;i<=n;i++)
{
if(pro[i]>0){
add(0,i,pro[i]);
sum+=pro[i];
}
else if(pro[i]<0)add(i,n+1,-pro[i]);
}
int ans=dinic(0,n+1);
cout<<sum-ans<<endl;
return 0;
}