题解:
最小费用流;
拆点法;
#include<iostream> #include<cstdio> #include<cstring> #include<vector> #include<queue> using namespace std; const int maxn=1000; const int inf=100000000; int n,m; int totn,s,t; struct Edge{ int from,to,cap,flow,cost; }; vector<int>G[maxn]; vector<Edge>edges; int 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.to=x;e.from=y;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); } queue<int>q; int inq[maxn]; int d[maxn]; int p[maxn]; int spfa(int &nowflow,int &nowcost){ for(int i=1;i<=totn;++i){ d[i]=inf;inq[i]=0; } d[s]=0;q.push(s);inq[s]=1;p[s]=0; 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; p[e.to]=G[x][i]; if(!inq[e.to]){ q.push(e.to); inq[e.to]=1; } } } } if(d[t]==inf)return 0; int f=inf,x=t; while(x!=s){ Edge e=edges[p[x]]; f=min(f,e.cap-e.flow); x=e.from; } nowflow+=f;nowcost+=f*d[t]; x=t; while(x!=s){ edges[p[x]].flow+=f; edges[p[x]^1].flow-=f; x=edges[p[x]].from; } return 1; } int Mcmf(){ int flow=0,cost=0; while(spfa(flow,cost)); printf("%d %d\n",flow,cost); } int minit(){ for(int i=1;i<=n+n;++i)G[i].clear(); edges.clear(); while(!q.empty())q.pop(); } int main(){ scanf("%d%d",&n,&m); minit(); while(m--){ int x,y,z; scanf("%d%d%d",&x,&y,&z); addedge(x+n,y,1,z); } addedge(1,1+n,inf,0); addedge(n,n+n,inf,0); for(int i=2;i<=n-1;++i)addedge(i,i+n,1,0); totn=n+n;s=1;t=n+n; Mcmf(); return 0; }