結果

問題 No.1324 Approximate the Matrix
ユーザー tko919
提出日時 2020-12-21 00:47:32
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 100 ms / 2,000 ms
コード長 4,641 bytes
コンパイル時間 2,050 ms
コンパイル使用メモリ 191,548 KB
実行使用メモリ 6,144 KB
最終ジャッジ日時 2024-09-21 12:36:37
合計ジャッジ時間 4,081 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 42
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In member function 'bool MinCostFlow<Flow, Cost, type>::dual(const Flow&)':
main.cpp:40:15: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
   40 |          auto [d,u]=pq.top(); pq.pop();
      |               ^
main.cpp: In function 'int main()':
main.cpp:141:9: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  141 |    auto [tmp,add]=mcf.run<int>();
      |         ^

ソースコード

diff #
プレゼンテーションモードにする

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
//template
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(v) (v).begin(),(v).end()
typedef long long int ll;
const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12;
template<typename T>inline bool chmax(T& a,T b){if(a<b){a=b;return 1;}return 0;}
template<typename T>inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;}
//end
template<typename Flow,typename Cost,int type=1>class MinCostFlow{ //Maximize=-1
   struct ptr{int v_id,e_id;};
   struct edge{
      int from,to; Flow flow,cap; Cost weight; int rev;
      edge(int _f,int _t,Flow _c,Cost _w,int _r)
         :from(_f),to(_t),flow(0),cap(_c),weight(_w),rev(_r){}
      Flow residual_cap()const{return cap-flow;}
   };
   int n; vector<vector<edge>> g;
   vector<Flow> b,pot; vector<ptr> es;
   Cost farthest; vector<Cost> dist; vector<edge*> par;
   vector<int> exc,def;
   void push(edge& e,Flow amount){
      e.flow+=amount; g[e.to][e.rev].flow-=amount;
   }
   Cost residual_cost(int from,int to,edge& e){
      return e.weight+pot[from]-pot[to];
   }
   bool dual(const Flow& delta){
      dist.assign(n,numeric_limits<Cost>::max()); par.assign(n,nullptr);
      exc.erase(remove_if(ALL(exc),[&](int v){return b[v]<delta;}),exc.end());
      def.erase(remove_if(ALL(def),[&](int v){return b[v]>-delta;}),def.end());
      priority_queue<pair<Cost,int>,vector<pair<Cost,int>>,greater<>> pq;
      for(auto& v:exc)pq.push({dist[v]=0,v});
      farthest=0; int def_cnt=0;
      while(!pq.empty()){
         auto [d,u]=pq.top(); pq.pop();
         if(dist[u]<d)continue;
         farthest=d;
         if(b[u]<=-delta)def_cnt++;
         if(def_cnt>=(int)def.size())break;
         for(auto& e:g[u]){
            if(e.residual_cap()<delta)continue;
            int v=e.to; Cost nd=d+residual_cost(u,v,e);
            if(nd>=dist[v])continue;
            pq.push({dist[v]=nd,v}); par[v]=&e;
         }
      }
      rep(v,0,n)pot[v]+=min(dist[v],farthest);
      return def_cnt>0;
   }
   void primal(const Flow& delta){
      for(auto& t:def){
         if(dist[t]>farthest)continue;
         Flow f=-b[t]; int v;
         for(v=t;par[v]!=nullptr;v=par[v]->from){
            chmin(f,par[v]->residual_cap());
         }
         chmin(f,b[v]); f-=f%delta;
         if(f<=0)continue;
         for(v=t;par[v]!=nullptr;){
            auto& e=*par[v];
            push(e,f);
            int u=par[v]->from;
            if(e.residual_cap()<=0)par[v]=nullptr;
            v=u;
         }
         b[t]+=f; b[v]-=f;
      }
   }
public:
   MinCostFlow(int _n):n(_n),g(_n),b(_n),pot(_n){}
   void add_edge(int from,int to,Flow lb,Flow ub,Cost cost){
      int f_id=g[from].size(),t_id=(from==to?f_id+1:g[to].size());
      g[from].push_back(edge(from,to,ub,cost*type,t_id));
      g[to].push_back(edge(to,from,-lb,-cost*type,f_id));
      es.push_back(ptr{from,f_id});
   }
   void add_supply(int v,Flow amount){b[v]+=amount;}
   void add_demand(int v,Flow amount){b[v]-=amount;}
   Flow get_pot(int v){return pot[v];}
   Flow get_flow(int v){return g[es[v].v_id][es[v].e_id].flow;}
   template<typename T>pair<bool,T> run(const Flow& sf=2){
      Flow max_flow=1;
      for(auto& t:b)chmax(max_flow,abs(t));
      for(auto& es:g)for(auto& e:es)chmax(max_flow,abs(e.residual_cap()));
      Flow delta=1;
      while(delta<max_flow)delta*=sf;
      for(;delta;delta/=sf){
         for(auto& es:g)for(auto& e:es){
            Flow rcap=e.residual_cap();
            rcap-=rcap%delta;
            Cost rcost=residual_cost(e.from,e.to,e);
            if(rcost<0 or rcap<0){
               push(e,rcap);
               b[e.from]-=rcap; b[e.to]+=rcap;
            }
         }
         rep(v,0,n)if(b[v]!=0){
            (b[v]>0?exc:def).push_back(v);
         }
         while(dual(delta))primal(delta);
      }
      T res=0;
      for(auto& es:g)for(auto& e:es)res+=T(e.flow)*T(e.weight);
      res>>=1;
      if(exc.empty() and def.empty())return {1,res*type};
      else return {0,res*type};
   }
};
int main(){
   int n,k; cin>>n>>k;
   vector<int> a(n),b(n);
   rep(i,0,n)cin>>a[i];
   rep(i,0,n)cin>>b[i];
   
   MinCostFlow<int,int> mcf(n*2);
   rep(i,0,n){
      mcf.add_supply(i,a[i]);
      mcf.add_demand(i+n,b[i]);
   }
   ll res=0;
   rep(i,0,n)rep(j,0,n){
      int x,lim=min(a[i],b[j]);
      cin>>x;
      res+=x*x;
      int pre=x*x;
      rep(v,1,lim+1){
         mcf.add_edge(i,j+n,0,1,(v-x)*(v-x)-pre);
         pre=(v-x)*(v-x);
      }
   }
   auto [tmp,add]=mcf.run<int>();
   assert(tmp);
   res+=add;
   cout<<res<<endl;
   return 0;
}
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