lexicographical cost
(test/aoj/2679.test.cpp)

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• Last update: 2020-10-06 13:10:17+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2679

Depends on

• 最小費用流 (mincostflow/primaldual.cpp)

Code

// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2679

#include<bits/stdc++.h>
using namespace std;

#define call_from_test
#include "../../mincostflow/primaldual.cpp"
#undef call_from_test

const int MAX = 52;
struct ARR{
  array<int, MAX> val;
  ARR(){fill(val.begin(),val.end(),0);}
  ARR(int x){fill(val.begin(),val.end(),x);}
  int& operator[](int k){return val[k];};
  int operator[](int k)const{return val[k];};
  ARR operator+(const ARR &oth) const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=val[i]+oth[i];
    return res;
  }
  ARR operator-(const ARR &oth) const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=val[i]-oth[i];
    return res;
  }
  ARR operator-() const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=-val[i];
    return res;
  }
  ARR operator*(const int &k) const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=val[i]*k;
    return res;
  }
  ARR operator/(const int &k) const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=val[i]/k;
    return res;
  }
  bool operator< (const ARR &oth) const{
    return val< oth.val;
  }
  bool operator> (const ARR &oth) const{
    return val< oth.val;
  }
  bool operator==(const ARR &oth) const{
    return val==oth.val;
  }
};

namespace std {
  template<> class numeric_limits<ARR> {
  public:
    static ARR max() {return ARR(numeric_limits<int>::max());};
  };
}

int main(){
  int n;
  cin>>n;
  vector<string> vs(n);
  for(int i=0;i<n;i++) cin>>vs[i];

  auto enc=[&](char c){
    if(isupper(c)) return c-'A';
    return 26+c-'a';
  };
  auto dec=[&](int d){
    if(d<26) return 'A'+d;
    return 'a'+d-26;
  };

  int S=n*2,T=n*2+1;
  PrimalDual<int, ARR> G(n*2+2);
  for(int i=0;i<n;i++){
    G.add_edge(S,i,1,ARR());
    G.add_edge(n+i,T,1,ARR());
  }

  const int INF = 1e5;
  for(int i=0;i<n;i++){
    for(int j=0;j<n;j++){
      ARR cost(INF);
      cost[enc(vs[i][j])]=INF-1;
      G.add_edge(i,n+j,1,cost);
    }
  }

  assert(G.build(S,T,n));
  auto res=G.get_cost();

  string ans;
  for(int i=0;i<MAX;i++)
    for(int j=0;j<n*INF-res[i];j++)
      ans+=dec(i);

  cout<<ans<<endl;
  return 0;
}

#line 1 "test/aoj/2679.test.cpp"
// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2679

#include<bits/stdc++.h>
using namespace std;

#define call_from_test
#line 1 "mincostflow/primaldual.cpp"

#line 3 "mincostflow/primaldual.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
// O(F E \log V)
template<typename Flow, typename Cost>
struct PrimalDual{
  struct Edge{
    int dst;
    Flow cap;
    Cost cost;
    int rev;
    Edge(int dst,Flow cap,Cost cost,int rev):
      dst(dst),cap(cap),cost(cost),rev(rev){}
  };

  vector<vector<Edge>> G;
  vector<Cost> h,dist;
  vector<int> prevv,preve;

  PrimalDual(int n):G(n),h(n),dist(n),prevv(n),preve(n){}

  void add_edge(int u,int v,Flow cap,Cost cost){
    int e=G[u].size();
    int r=(u==v?e+1:G[v].size());
    G[u].emplace_back(v,cap,cost,r);
    G[v].emplace_back(u,0,-cost,e);
  }

  Cost residual_cost(int src,Edge &e){
    return e.cost+h[src]-h[e.dst];
  }

  void dijkstra(int s){
    struct P{
      Cost first;
      int second;
      P(Cost first,int second):first(first),second(second){}
      bool operator<(const P&a) const{return first>a.first;}
    };
    priority_queue<P> pq;

    dist[s]=0;
    pq.emplace(dist[s],s);
    while(!pq.empty()){
      P p=pq.top();pq.pop();
      int v=p.second;
      if(dist[v]<p.first) continue;
      for(int i=0;i<(int)G[v].size();i++){
        Edge &e=G[v][i];
        if(e.cap==0) continue;
        if(!(dist[v]+residual_cost(v,e)<dist[e.dst])) continue;
        dist[e.dst]=dist[v]+e.cost+h[v]-h[e.dst];
        prevv[e.dst]=v;
        preve[e.dst]=i;
        pq.emplace(dist[e.dst],e.dst);
      }
    }
  }

  Cost res;

  bool build(int s,int t,Flow f,
             function<void(decltype(h)&)> init=[](decltype(h) &p){
               fill(p.begin(),p.end(),0);
             }){
    res=0;
    init(h);
    const Cost INF = numeric_limits<Cost>::max();
    while(f>0){
      fill(dist.begin(),dist.end(),INF);
      dijkstra(s);
      if(dist[t]==INF) return false;

      for(int v=0;v<(int)h.size();v++)
        if(dist[v]<INF) h[v]=h[v]+dist[v];

      Flow d=f;
      for(int v=t;v!=s;v=prevv[v])
        d=min(d,G[prevv[v]][preve[v]].cap);

      f-=d;
      res=res+h[t]*d;
      for(int v=t;v!=s;v=prevv[v]){
        Edge &e=G[prevv[v]][preve[v]];
        e.cap-=d;
        G[v][e.rev].cap+=d;
      }
    }
    return true;
  }

  Cost get_cost(){return res;}
};
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
  return 0;
}
#endif
#line 8 "test/aoj/2679.test.cpp"
#undef call_from_test

const int MAX = 52;
struct ARR{
  array<int, MAX> val;
  ARR(){fill(val.begin(),val.end(),0);}
  ARR(int x){fill(val.begin(),val.end(),x);}
  int& operator[](int k){return val[k];};
  int operator[](int k)const{return val[k];};
  ARR operator+(const ARR &oth) const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=val[i]+oth[i];
    return res;
  }
  ARR operator-(const ARR &oth) const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=val[i]-oth[i];
    return res;
  }
  ARR operator-() const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=-val[i];
    return res;
  }
  ARR operator*(const int &k) const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=val[i]*k;
    return res;
  }
  ARR operator/(const int &k) const{
    ARR res;
    for(int i=0;i<MAX;i++)
      res[i]=val[i]/k;
    return res;
  }
  bool operator< (const ARR &oth) const{
    return val< oth.val;
  }
  bool operator> (const ARR &oth) const{
    return val< oth.val;
  }
  bool operator==(const ARR &oth) const{
    return val==oth.val;
  }
};

namespace std {
  template<> class numeric_limits<ARR> {
  public:
    static ARR max() {return ARR(numeric_limits<int>::max());};
  };
}

int main(){
  int n;
  cin>>n;
  vector<string> vs(n);
  for(int i=0;i<n;i++) cin>>vs[i];

  auto enc=[&](char c){
    if(isupper(c)) return c-'A';
    return 26+c-'a';
  };
  auto dec=[&](int d){
    if(d<26) return 'A'+d;
    return 'a'+d-26;
  };

  int S=n*2,T=n*2+1;
  PrimalDual<int, ARR> G(n*2+2);
  for(int i=0;i<n;i++){
    G.add_edge(S,i,1,ARR());
    G.add_edge(n+i,T,1,ARR());
  }

  const int INF = 1e5;
  for(int i=0;i<n;i++){
    for(int j=0;j<n;j++){
      ARR cost(INF);
      cost[enc(vs[i][j])]=INF-1;
      G.add_edge(i,n+j,1,cost);
    }
  }

  assert(G.build(S,T,n));
  auto res=G.get_cost();

  string ans;
  for(int i=0;i<MAX;i++)
    for(int j=0;j<n*INF-res[i];j++)
      ans+=dec(i);

  cout<<ans<<endl;
  return 0;
}

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