#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;
}
};
最小費用流(CostScaling)