#include "graph_tree/min_cost_flow.hpp"
#pragma once #include<vector> #include<queue> #include<cmath> #include"push_relabel.hpp" /** * @brief 最小費用流(CostScaling) */ //Resは答えがlong longの最大値を超える時用 template<typename T,typename Res=T> struct min_cost_flow{ int v; Res ans=0; struct edge{ int to; T cap,cost,st; int rev; bool is_rev,edge_rev; int id; }; push_relabel<T> mf; std::vector<T>p; std::vector<vector<edge*>>e;//辺のキャパシティ std::vector<T>d;//頂点のキャパシティ std::queue<int>active; std::vector<tuple<int,int,T,T,T>>edges; T eps=1; int idx=0; std::vector<T>res; min_cost_flow(int v):v(v),mf(v+2),p(v,0),e(v),d(v,0){} void add_edge(int from,int to,T mn,T mx,T cost){ edges.emplace_back(from,to,mn,mx,cost); res.push_back(0); if(from==to){ if(cost<0)res[idx++]=mx,ans+=mx*cost; else res[idx++]=mn,ans+=mn*cost; return; } if(cost>=0){ e[from].push_back(new edge{to,mx-mn,cost*v,mn,(int)e[to].size(),0,0,idx}); e[to].push_back(new edge{from,0,-cost*v,mn,(int)e[from].size()-1,1,0,idx++}); ans+=mn*cost; d[from]-=mn;d[to]+=mn; eps=max(eps,cost*v*v); mf.add_edge(from,to,mx-mn); } else{ e[to].push_back(new edge{from,mx-mn,-cost*v,mx,(int)e[from].size(),0,1,idx}); e[from].push_back(new edge{to,0,cost*v,mx,(int)e[to].size()-1,1,1,idx++}); ans+=mx*cost; d[from]-=mx;d[to]+=mx; eps=max(eps,-cost*v*v); mf.add_edge(to,from,mx-mn); } } void add_edge(int from,int to,T cap,T cost){ add_edge(from,to,T(),cap,cost); } Res flow(){ for(;eps;eps>>=1){ for(int i=0;i<v;i++){ for(auto ed:e[i]){ if(ed->is_rev)continue; if(ed->cost-p[i]+p[ed->to]<0){ T f=ed->cap; ed->cap-=f; d[i]-=f; d[ed->to]+=f; e[ed->to][ed->rev]->cap+=f; } if(ed->cost-p[i]+p[ed->to]>0){ T f=-e[ed->to][ed->rev]->cap; ed->cap-=f; d[i]-=f; d[ed->to]+=f; e[ed->to][ed->rev]->cap+=f; } } } for(int i=0;i<v;i++)if(d[i]>0){active.emplace(i);} while(!active.empty()){ int node=active.front(); active.pop(); if(d[node]<=0)continue; bool b=0; for(auto ed:e[node]){ if(!d[node])break; if(-eps<=ed->cost-p[node]+p[ed->to]&&ed->cost-p[node]+p[ed->to]<0){ auto f=std::min(d[node],ed->cap); if(!f)continue; ed->cap-=f; d[node]-=f; d[ed->to]+=f; e[ed->to][ed->rev]->cap+=f; if(d[ed->to]>0)active.emplace(ed->to); b=1; } } if(d[node]>0)active.emplace(node); if(!b)p[node]+=eps; } } for(int i=0;i<v;i++)for(auto ed:e[i]){ if(ed->is_rev)continue; ans+=e[ed->to][ed->rev]->cap*(ed->cost/v); } return ans; } bool ok(std::vector<T>b){ T tmp=0,tmp2=0; for(int i=0;i<v;++i){ if(d[i]+b[i]>=0){ mf.add_edge(v,i,d[i]+b[i]); tmp2+=d[i]+b[i]; } else{ mf.add_edge(i,v+1,-(d[i]+b[i])); tmp+=-(d[i]+b[i]); } } return tmp==tmp2&&mf.run(v,v+1)==tmp; } Res run(int s,int t,T f){ d[s]+=f; d[t]-=f; return flow(); } Res run(std::vector<T>b){ for(int i=0;i<v;++i)d[i]+=b[i]; return flow(); } std::vector<T> flow_result(){ for(int i=0;i<v;i++)for(auto ed:e[i]){ if(ed->is_rev)continue; res[ed->id]=ed->st+e[ed->to][ed->rev]->cap*(ed->edge_rev?-1:1); } return res; } //flow_resultを渡す std::vector<T>potential(const std::vector<T>& f){ std::vector<T>p(v,0); std::vector<tuple<int,int,T>>g; int idx=0; for(auto [from,to,mn,mx,cost]:edges){ if(mn<f[idx])g.emplace_back(to,from,-cost); if(f[idx]<mx)g.emplace_back(from,to,cost); idx++; } for(int i=0;i<v;++i)for(auto [s,t,c]:g){ p[t]=std::min(p[t],p[s]+c); } return p; } };
#line 2 "graph_tree/min_cost_flow.hpp" #include<vector> #include<queue> #include<cmath> #line 5 "graph_tree/push_relabel.hpp" #include<tuple> /** * @brief 最大流(push_relabel法O(V^2√E)) */ template<typename T> class push_relabel{ int n; T f=0; using i64=long long; struct edge{ int from,to,rev; T flow,cap; }; std::vector<i64>h,d; std::vector<std::vector<edge*>>g; std::vector<size_t>seen; std::priority_queue<std::pair<i64,int>,std::vector<std::pair<i64,int>>,std::greater<std::pair<i64,int>>>que; public: push_relabel(int n):n(n){ h.resize(n,0); d.resize(n,0); g.resize(n); seen.resize(n,0); } void add_edge(int u,int v,T cap){ g[u].emplace_back(new edge{u,v,(int)g[v].size(),0,cap}); g[v].emplace_back(new edge{v,u,(int)g[u].size()-1,0,0}); } void push(edge* e){ int u=e->from,v=e->to; i64 df=std::min(d[u],e->cap-e->flow); e->flow+=df; g[v][e->rev]->flow-=df; d[u]-=df; d[v]+=df; if(d[v]>0)que.emplace(h[v],v); if(d[u]>0)que.emplace(h[u],u); } void relabel(int u){ i64 mn=n*2; for(edge* e:g[u]){ if(e->cap-e->flow>0){ mn=std::min(mn,h[e->to]); } } h[u]=1+mn; que.emplace(h[u],u); } void discharge(int u){ while(d[u]>0){ if(seen[u]<g[u].size()){ edge* e=g[u][seen[u]]; if(e->cap-e->flow>0 && h[u]==h[e->to]+1){ push(e); }else{ seen[u]+=1; } }else{ relabel(u); seen[u]=0; } } } T run(int s,int t){ h[s]=n; for(auto e:g[s]){ d[s]+=e->cap; push(e); } while(!que.empty()){ int u=que.top().second; que.pop(); if(u==s||u==t)continue; discharge(u); } for(auto e:g[s])f+=e->flow; return f; } }; #line 6 "graph_tree/min_cost_flow.hpp" /** * @brief 最小費用流(CostScaling) */ //Resは答えがlong longの最大値を超える時用 template<typename T,typename Res=T> struct min_cost_flow{ int v; Res ans=0; struct edge{ int to; T cap,cost,st; int rev; bool is_rev,edge_rev; int id; }; push_relabel<T> mf; std::vector<T>p; std::vector<vector<edge*>>e;//辺のキャパシティ std::vector<T>d;//頂点のキャパシティ std::queue<int>active; std::vector<tuple<int,int,T,T,T>>edges; T eps=1; int idx=0; std::vector<T>res; min_cost_flow(int v):v(v),mf(v+2),p(v,0),e(v),d(v,0){} void add_edge(int from,int to,T mn,T mx,T cost){ edges.emplace_back(from,to,mn,mx,cost); res.push_back(0); if(from==to){ if(cost<0)res[idx++]=mx,ans+=mx*cost; else res[idx++]=mn,ans+=mn*cost; return; } if(cost>=0){ e[from].push_back(new edge{to,mx-mn,cost*v,mn,(int)e[to].size(),0,0,idx}); e[to].push_back(new edge{from,0,-cost*v,mn,(int)e[from].size()-1,1,0,idx++}); ans+=mn*cost; d[from]-=mn;d[to]+=mn; eps=max(eps,cost*v*v); mf.add_edge(from,to,mx-mn); } else{ e[to].push_back(new edge{from,mx-mn,-cost*v,mx,(int)e[from].size(),0,1,idx}); e[from].push_back(new edge{to,0,cost*v,mx,(int)e[to].size()-1,1,1,idx++}); ans+=mx*cost; d[from]-=mx;d[to]+=mx; eps=max(eps,-cost*v*v); mf.add_edge(to,from,mx-mn); } } void add_edge(int from,int to,T cap,T cost){ add_edge(from,to,T(),cap,cost); } Res flow(){ for(;eps;eps>>=1){ for(int i=0;i<v;i++){ for(auto ed:e[i]){ if(ed->is_rev)continue; if(ed->cost-p[i]+p[ed->to]<0){ T f=ed->cap; ed->cap-=f; d[i]-=f; d[ed->to]+=f; e[ed->to][ed->rev]->cap+=f; } if(ed->cost-p[i]+p[ed->to]>0){ T f=-e[ed->to][ed->rev]->cap; ed->cap-=f; d[i]-=f; d[ed->to]+=f; e[ed->to][ed->rev]->cap+=f; } } } for(int i=0;i<v;i++)if(d[i]>0){active.emplace(i);} while(!active.empty()){ int node=active.front(); active.pop(); if(d[node]<=0)continue; bool b=0; for(auto ed:e[node]){ if(!d[node])break; if(-eps<=ed->cost-p[node]+p[ed->to]&&ed->cost-p[node]+p[ed->to]<0){ auto f=std::min(d[node],ed->cap); if(!f)continue; ed->cap-=f; d[node]-=f; d[ed->to]+=f; e[ed->to][ed->rev]->cap+=f; if(d[ed->to]>0)active.emplace(ed->to); b=1; } } if(d[node]>0)active.emplace(node); if(!b)p[node]+=eps; } } for(int i=0;i<v;i++)for(auto ed:e[i]){ if(ed->is_rev)continue; ans+=e[ed->to][ed->rev]->cap*(ed->cost/v); } return ans; } bool ok(std::vector<T>b){ T tmp=0,tmp2=0; for(int i=0;i<v;++i){ if(d[i]+b[i]>=0){ mf.add_edge(v,i,d[i]+b[i]); tmp2+=d[i]+b[i]; } else{ mf.add_edge(i,v+1,-(d[i]+b[i])); tmp+=-(d[i]+b[i]); } } return tmp==tmp2&&mf.run(v,v+1)==tmp; } Res run(int s,int t,T f){ d[s]+=f; d[t]-=f; return flow(); } Res run(std::vector<T>b){ for(int i=0;i<v;++i)d[i]+=b[i]; return flow(); } std::vector<T> flow_result(){ for(int i=0;i<v;i++)for(auto ed:e[i]){ if(ed->is_rev)continue; res[ed->id]=ed->st+e[ed->to][ed->rev]->cap*(ed->edge_rev?-1:1); } return res; } //flow_resultを渡す std::vector<T>potential(const std::vector<T>& f){ std::vector<T>p(v,0); std::vector<tuple<int,int,T>>g; int idx=0; for(auto [from,to,mn,mx,cost]:edges){ if(mn<f[idx])g.emplace_back(to,from,-cost); if(f[idx]<mx)g.emplace_back(from,to,cost); idx++; } for(int i=0;i<v;++i)for(auto [s,t,c]:g){ p[t]=std::min(p[t],p[s]+c); } return p; } };