BZOJ 3876 [Ahoi2014&Jsoi2014]支线剧情

题解：

带下界的费用流

对于x->y边权为z Addedge(x,t,1,0) Addedge(s,y,1,z) Addedge(x,y,inf,0)

然后对每个点Addedge(i,1,inf,0)

然后跑最小费用最大流即可

因为这是DAG，所以每一个循环流都是从1到某个点再到1的路径

也就是说用几个费用最小的循环流来满足下界

#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
#include<queue>
using namespace std;
const int maxn=3000;
const int oo=1000000000;

int n;
struct Edge{
	int from,to,cap,flow,cost;
};
vector<int>G[maxn];
vector<Edge>edges;
void Addedge(int x,int y,int z,int w){
	Edge e;
	e.from=x;e.to=y;e.cap=z;e.flow=0;e.cost=w;
	edges.push_back(e);
	e.from=y;e.to=x;e.cap=0;e.flow=0;e.cost=-w;
	edges.push_back(e);
	int c=edges.size();
	G[x].push_back(c-2);
	G[y].push_back(c-1);
}

int s,t,totn;
int inq[maxn];
int d[maxn];
int pre[maxn];
queue<int>q;
int Spfa(int &nowflow,int &nowcost){
	for(int i=1;i<=totn;++i){
		inq[i]=0;d[i]=oo;
	}
	d[s]=0;inq[s]=1;q.push(s);
	while(!q.empty()){
		int x=q.front();q.pop();inq[x]=0;
		for(int i=0;i<G[x].size();++i){
			Edge e=edges[G[x][i]];
			if((e.cap>e.flow)&&(d[x]+e.cost<d[e.to])){
				d[e.to]=d[x]+e.cost;
				pre[e.to]=G[x][i];
				if(!inq[e.to]){
					inq[e.to]=1;
					q.push(e.to);
				}
			}
		}
	}
	if(d[t]==oo)return 0;

	int x=t,f=oo;
	while(x!=s){
		Edge e=edges[pre[x]];
		f=min(f,e.cap-e.flow);
		x=e.from;
	}
	nowflow+=f;nowcost+=f*d[t];
	x=t;
	while(x!=s){
		edges[pre[x]].flow+=f;
		edges[pre[x]^1].flow-=f;
		x=edges[pre[x]].from;
	}
	return 1;
}

int Mincost(){
	int flow=0,cost=0;
	while(Spfa(flow,cost)){
	}
	return cost;
}

int main(){
	scanf("%d",&n);
	s=n+1;t=n+2;totn=t;
	for(int i=1;i<=n;++i){
		int m;scanf("%d",&m);
		Addedge(i,t,m,0);
		while(m--){
			int y,z;
			scanf("%d%d",&y,&z);
//			Addedge(i,y,oo,z);
			Addedge(s,y,1,z);
		}
	}
	for(int i=2;i<=n;++i)Addedge(i,1,oo,0);

	printf("%d\n",Mincost());
	return 0;
}