結果

問題 No.470 Inverse S+T Problem
コンテスト
ユーザー Haar
提出日時 2019-04-20 16:43:35
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 35 ms / 2,000 ms
コード長 5,577 bytes
コンパイル時間 2,483 ms
コンパイル使用メモリ 200,448 KB
実行使用メモリ 23,620 KB
最終ジャッジ日時 2024-12-22 13:52:38
合計ジャッジ時間 3,914 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 4
other AC * 27
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
#define FOR(v, a, b) for(int v = (a); v < (b); ++v)
#define FORE(v, a, b) for(int v = (a); v <= (b); ++v)
#define REP(v, n) FOR(v, 0, n)
#define REPE(v, n) FORE(v, 0, n)
#define REV(v, a, b) for(int v = (a); v >= (b); --v)
#define ALL(x) (x).begin(), (x).end()
#define ITR(it, c) for(auto it = (c).begin(); it != (c).end(); ++it)
#define RITR(it, c) for(auto it = (c).rbegin(); it != (c).rend(); ++it)
#define EXIST(c,x) ((c).find(x) != (c).end())
#define LLI long long int
#define fst first
#define snd second

#ifdef DEBUG
#include <misc/C++/Debug.cpp>
#else
#define dump(x) ((void)0)
#endif

#define gcd __gcd

using namespace std;
template <class T> constexpr T lcm(T m, T n){return m/gcd(m,n)*n;}

template <typename I> void join(ostream &ost, I s, I t, string d=" "){for(auto i=s; i!=t; ++i){if(i!=s)ost<<d; ost<<*i;}ost<<endl;}
template <typename T> istream& operator>>(istream &is, vector<T> &v){for(auto &a : v) is >> a; return is;}
template <typename T, typename U> istream& operator>>(istream &is, pair<T,U> &p){is >> p.first >> p.second; return is;}

template <typename T, typename U> bool chmin(T &a, const U &b){return (a>b ? a=b, true : false);}
template <typename T, typename U> bool chmax(T &a, const U &b){return (a<b ? a=b, true : false);}
template <typename T, size_t N, typename U> void fill_array(T (&a)[N], const U &v){fill((U*)a, (U*)(a+N), v);}


template <typename Cost = int> class Edge{
public:
  int from,to;
  Cost cost;
  Edge() {}
  Edge(int from, int to, Cost cost): from(from), to(to), cost(cost){}

  Edge rev() const {return Edge(to,from,cost);}
  
  static bool cmp_to_lt(const Edge &e1, const Edge &e2){return e1.to < e2.to;}
  static bool cmp_cost_lt(const Edge &e1, const Edge &e2){return e1.cost < e2.cost;}
  static bool cmp_to_gt(const Edge &e1, const Edge &e2){return e1.to > e2.to;}
  static bool cmp_cost_gt(const Edge &e1, const Edge &e2){return e1.cost > e2.cost;}
  friend ostream& operator<<(ostream &os, const Edge &e){
    os << "(FROM: " << e.from << "," << "TO: " << e.to << "," << "COST: " << e.cost << ")";
    return os;
  }
};

template <typename T> using Graph = vector<vector<Edge<T>>>;

template <typename T> vector<int> strongly_connected_components(Graph<T> &graph){
  int n = graph.size();
  vector<bool> visit(n);
  vector<int> check;

  function<void(int)> dfs =
    [&](int cur){
      visit[cur] = true;
      for(auto &e : graph[cur]) if(!visit[e.to]) dfs(e.to);
      check.push_back(cur);
    };
  
  REP(i,n) if(!visit[i]) dfs(i);

  Graph<T> rgraph(n);
  REP(i,n) for(auto &e : graph[i]) rgraph[e.to].push_back(e.rev());

  vector<int> ret(n,-1);

  reverse(ALL(check));

  function<void(int,int)> rdfs =
    [&](int cur, int i){
      ret[cur] = i;
      for(auto &e : rgraph[cur]) if(ret[e.to] == -1) rdfs(e.to,i);
    };

  int i = 0;
  for(auto c : check) if(ret[c] == -1) {rdfs(c,i); ++i;}
    
  return ret;
}


bool tsort(const Graph<int> &graph, vector<int> &ret){
  int n = graph.size();
  vector<int> indeg(n);
  REP(i,n){
    for(auto &e : graph[i]){
      ++indeg[e.to];
    }
  }
  
  stack<int> st;
  REV(i,n-1,0){
    if(indeg[i]==0) st.push(i);
  }

  while(!st.empty()){
    int cur = st.top(); st.pop();
    ret.push_back(cur);
    for(auto &e : graph[cur]){
      --indeg[e.to];
      if(indeg[e.to]==0){
	st.push(e.to);
      }
    }
  }
  
  return (int)ret.size() == n;
}


class two_sat{
  int n;
  Graph<int> g;
  
public:
  two_sat(int n): n(n), g(2*n){}

  int inv(int i){ // not
    if(i<n) return i+n;
    else return i-n;
  }

  
  void add(int a, int b){
    if(a == b){ // a ∨ a <=> (!a => a)
      g[inv(a)].push_back(Edge<int>(inv(a), a, 1));
    }else{ // a ∨ b <=> (!a => b) ∧ (!b => a)
      g[inv(a)].push_back(Edge<int>(inv(a), b, 1));
      g[inv(b)].push_back(Edge<int>(inv(b), a, 1));
    }
  }
  
  void not_coexist(int a, int b){ // !(A ∧ B) <=> (!A ∨ !B)
    add(inv(a), inv(b));
  }
  
  bool solve(vector<bool> &ret){
    auto s = strongly_connected_components(g);
    
    REP(i,n) if(s[i] == s[i+n]){
      dump(i);
      return false;
    }


    int m = *max_element(ALL(s)) + 1;
    Graph<int> g2(m);
    vector<int> ts;

    for(auto &v : g){
      for(auto &e : v){
	if(s[e.from] != s[e.to]) g2[s[e.from]].push_back(Edge<int>(s[e.from], s[e.to], 1));
      }
    }
    
    tsort(g2, ts);

    vector<int> r(m);
    REP(i,m) r[ts[i]] = i;

    ret = vector<bool>(n);
    REP(i,n) ret[i] = r[s[i]] > r[s[i+n]];

    return true;
  }
};

int main(){
  cin.tie(0);
  ios::sync_with_stdio(false);

  int N;
  while(cin >> N){
    vector<string> U(N); cin >> U;

    vector<string> S1(N), T1(N), S2(N), T2(N);
    REP(i,N){
      S1[i] = {U[i][0], U[i][1]};
      T1[i] = {U[i][2]};
      S2[i] = {U[i][0]};
      T2[i] = {U[i][1], U[i][2]};
    }

    two_sat sat(N);

    set<char> cnt;
    for(auto &s : U) for(auto &c : s) cnt.insert(c);

    if((int)cnt.size() < N){
      cout << "Impossible" << endl;
      continue;
    }

    REP(i,N){
      FOR(j,i+1,N){
	if(S1[i] == S1[j] or T1[i] == T1[j]) sat.not_coexist(i, j);
	if(S1[i] == T2[j] or T1[i] == S2[j]) sat.not_coexist(i, sat.inv(j));
	if(S2[i] == T1[j] or T2[i] == S1[j]) sat.not_coexist(sat.inv(i), j);
	if(S2[i] == S2[j] or T2[i] == T2[j]) sat.not_coexist(sat.inv(i), sat.inv(j));
      }
    }

    vector<bool> ret;
    bool ans = sat.solve(ret);

    if(ans){
      REP(i,N){
	if(ret[i]) cout << S1[i] << " " << T1[i] << endl;
	else cout << S2[i] << " " << T2[i] << endl;
      }
    }else{
      cout << "Impossible" << endl;
    }
  }
  
  return 0;
}
0