結果

問題 No.470 Inverse S+T Problem
ユーザー koyumeishi
提出日時 2016-12-20 01:47:15
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 19 ms / 2,000 ms
コード長 19,253 bytes
コンパイル時間 3,377 ms
コンパイル使用メモリ 235,760 KB
実行使用メモリ 6,528 KB
最終ジャッジ日時 2024-12-22 13:17:49
合計ジャッジ時間 4,714 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
sample AC * 4
other AC * 27
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ソースコード

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プレゼンテーションモードにする

/************************************************************
MiniSat -- Copyright (c) 2003-2006, Niklas Een, Niklas Sorensson
           Copyright (c) 2007-2010  Niklas Sorensson
Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:
The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 ************************************************************/
#include <bits/stdc++.h>
#include <algorithm>
#include <assert.h>
#include <fstream>
#include <iostream>
#include <list>
#include <queue>
#include <sstream>
#include <stdio.h>
#include <string>
#include <vector>
#include <set>
#include <unordered_map>
#include <unordered_set>
// SAT Solver
// CDCL Solver
// Author togatoga
// https://github.com/togasakih/Togasat
namespace togasat {
using Var = int;
using CRef = int;
using lbool = int;
const CRef CRef_Undef = INT32_MAX;
class Solver {
private:
  const lbool l_True = 0;
  const lbool l_False = 1;
  const lbool l_Undef = 2;
  const int var_Undef = -1;
  // Literal
  struct Lit {
    int x;
    inline bool operator==(Lit p) const { return x == p.x; }
    inline bool operator!=(Lit p) const { return x != p.x; }
    inline bool operator<(Lit p) const { return x < p.x; }
    inline Lit operator~() {
      Lit q;
      q.x = x ^ 1;
      return q;
    }
  };
  inline Lit mkLit(Var var, bool sign) {
    Lit p;
    p.x = var + var + sign;
    return p;
  };
  inline bool sign(Lit p) const { return p.x & 1; }
  inline int var(Lit p) const { return p.x >> 1; }
  inline int toInt(Var v) { return v; }
  inline int toInt(Lit p) { return p.x; }
  inline Lit toLit(int x) {
    Lit p;
    p.x = x;
    return p;
  }
  const Lit lit_Undef = {-2};
  const Lit lit_Error = {-1};
  // lifted boolean
  // VarData
  struct VarData {
    CRef reason;
    int level;
  };
  inline VarData mkVarData(CRef cr, int l) {
    VarData d = {cr, l};
    return d;
  }
  // Watcher
  struct Watcher {
    CRef cref;
    Lit blocker;
    Watcher() {}
    Watcher(CRef cr, Lit p) : cref(cr), blocker(p) {}
    bool operator==(const Watcher &w) const { return cref == w.cref; }
    bool operator!=(const Watcher &w) const { return cref != w.cref; }
  };
  // Clause
  class Clause {
  public:
    struct {
      bool learnt;
      int size;
    } header;
    std::vector<Lit> data; //(x1 v x2 v not x3)
    Clause() {}
    Clause(const std::vector<Lit> &ps, bool learnt) {
      header.learnt = learnt;
      header.size = ps.size();
      for (int i = 0; i < ps.size(); i++) {
        data.push_back(ps[i]);
      }
    }
    int size() const { return header.size; }
    bool learnt() const { return header.learnt; }
    Lit &operator[](int i) { return data[i]; }
    Lit operator[](int i) const { return data[i]; }
  };
  CRef alloc_clause(const std::vector<Lit> &ps, bool learnt = false) {
    static CRef res = 0;
    ca[res] = Clause(ps, learnt);
    return res++;
  }
  Var newVar(bool sign = true, bool dvar = true) {
    int v = nVars();
    assigns.push_back(l_Undef);
    vardata.push_back(mkVarData(CRef_Undef, 0));
    activity.push_back(0.0);
    seen.push_back(false);
    polarity.push_back(sign);
    decision.push_back(0);
    setDecisionVar(v, dvar);
    return v;
  }
  bool addClause_(std::vector<Lit> &ps) {
    std::sort(ps.begin(), ps.end());
    // empty clause
    if (ps.size() == 0) {
      return false;
    } else if (ps.size() == 1) {
      uncheckedEnqueue(ps[0]);
    } else {
      CRef cr = alloc_clause(ps, false);
      clauses.insert(cr);
      attachClause(cr);
    }
    return true;
  }
  void attachClause(CRef cr) {
    const Clause &c = ca[cr];
    assert(c.size() > 1);
    watches[(~c[0]).x].push_back(Watcher(cr, c[1]));
    watches[(~c[1]).x].push_back(Watcher(cr, c[0]));
  }
  // Input
  void readClause(const std::string &line, std::vector<Lit> &lits) {
    lits.clear();
    int parsed_lit, var;
    parsed_lit = var = 0;
    bool neg = false;
    std::stringstream ss(line);
    while (ss) {
      int val;
      ss >> val;
      if (val == 0)
        break;
      var = abs(val) - 1;
      while (var >= nVars()) {
        newVar();
      }
      lits.push_back(val > 0 ? mkLit(var, false) : mkLit(var, true));
    }
  }
  std::unordered_map<CRef, Clause> ca; // store clauses
  std::unordered_set<CRef> clauses;    // original problem;
  std::unordered_set<CRef> learnts;
  std::unordered_map<int, std::vector<Watcher>> watches;
  std::vector<VarData> vardata; // store reason and level for each variable
  std::vector<bool> polarity;   // The preferred polarity of each variable
  std::vector<bool> decision;
  std::vector<bool> seen;
  // Todo
  int qhead;
  std::vector<Lit> trail;
  std::vector<int> trail_lim;
  // Todo rename(not heap)
  std::set<std::pair<double, Var>> order_heap;
  std::vector<double> activity;
  double var_inc;
  std::vector<Lit> model;
  std::vector<Lit> conflict;
  int nVars() const { return vardata.size(); }
  int decisionLevel() const { return trail_lim.size(); }
  void newDecisionLevel() { trail_lim.push_back(trail.size()); }
  inline CRef reason(Var x) const { return vardata[x].reason; }
  inline int level(Var x) const { return vardata[x].level; }
  inline void varBumpActivity(Var v){
    std::pair<double, Var> p = std::make_pair(activity[v], v);
    activity[v] += var_inc;
    if (order_heap.erase(p) == 1){
      order_heap.emplace(std::make_pair(activity[v], v));
    }
    
    if (activity[v] > 1e100){
      //Rescale
      std::set<std::pair<double,Var>> tmp_order;
      tmp_order = order_heap;
      order_heap.clear();
      for (int i = 0; i < nVars(); i++){
  activity[i] *= 1e-100;
      }
      for (auto &val : tmp_order){
  order_heap.emplace(std::make_pair(activity[val.first], val.first));
      }
      var_inc *= 1e-100;
    }
  }
  bool satisfied(const Clause &c) const {
    for (int i = 0; i < c.size(); i++) {
      if (value(c[i]) == l_True) {
        return true;
      }
    }
    return false;
  }
  lbool value(Var p) const { return assigns[p]; }
  lbool value(Lit p) const {
    if (assigns[var(p)] == l_Undef) {
      return l_Undef;
    }
    return assigns[var(p)] ^ sign(p);
  }
  void setDecisionVar(Var v, bool b) {
    decision[v] = b;
    order_heap.emplace(std::make_pair(0.0, v));
  }
  void uncheckedEnqueue(Lit p, CRef from = CRef_Undef) {
    assert(value(p) == l_Undef);
    assigns[var(p)] = sign(p);
    vardata[var(p)] = mkVarData(from, decisionLevel());
    trail.push_back(p);
  }
  // decision
  Lit pickBranchLit() {
    Var next = var_Undef;
    while (next == var_Undef or value(next) != l_Undef) {
      if (order_heap.empty()) {
        next = var_Undef;
        break;
      } else {
  auto p = *order_heap.rbegin();
        next = p.second;
        order_heap.erase(p);
      }
    }
    return next == var_Undef ? lit_Undef : mkLit(next, polarity[next]);
  }
  // clause learning
  void analyze(CRef confl, std::vector<Lit> &out_learnt, int &out_btlevel) {
    int pathC = 0;
    Lit p = lit_Undef;
    int index = trail.size() - 1;
    out_learnt.push_back(mkLit(0, false));
    do {
      assert(confl != CRef_Undef);
      Clause &c = ca[confl];
      for (int j = (p == lit_Undef) ? 0 : 1; j < c.size(); j++) {
        Lit q = c[j];
        if (not seen[var(q)] and level(var(q)) > 0) {
    varBumpActivity(var(q));
          seen[var(q)] = 1;
          if (level(var(q)) >= decisionLevel()) {
            pathC++;
          } else {
            out_learnt.push_back(q);
          }
        }
      }
      while (not seen[var(trail[index--])])
        ;
      p = trail[index + 1];
      confl = reason(var(p));
      seen[var(p)] = 0;
      pathC--;
    } while (pathC > 0);
    out_learnt[0] = ~p;
    // unit clause
    if (out_learnt.size() == 1) {
      out_btlevel = 0;
    } else {
      int max_i = 1;
      for (int i = 2; i < out_learnt.size(); i++) {
        if (level(var(out_learnt[i])) > level(var(out_learnt[max_i]))) {
          max_i = i;
        }
      }
      Lit p = out_learnt[max_i];
      out_learnt[max_i] = out_learnt[1];
      out_learnt[1] = p;
      out_btlevel = level(var(p));
    }
    for (int i = 0; i < out_learnt.size(); i++) {
      seen[var(out_learnt[i])] = false;
    }
  }
  // backtrack
  void cancelUntil(int level) {
    if (decisionLevel() > level) {
      for (int c = trail.size() - 1; c >= trail_lim[level]; c--) {
        Var x = var(trail[c]);
        assigns[x] = l_Undef;
        polarity[x] = sign(trail[c]);
        order_heap.emplace(std::make_pair(activity[x], x));
      }
      qhead = trail_lim[level];
      trail.erase(trail.end() - (trail.size() - trail_lim[level]), trail.end());
      trail_lim.erase(trail_lim.end() - (trail_lim.size() - level),
                      trail_lim.end());
    }
  }
  CRef propagate() {
    CRef confl = CRef_Undef;
    int num_props = 0;
    while (qhead < trail.size()) {
      Lit p = trail[qhead++]; // 'p' is enqueued fact to propagate.
      std::vector<Watcher> &ws = watches[p.x];
      std::vector<Watcher>::iterator i, j, end;
      num_props++;
      for (i = j = ws.begin(), end = i + ws.size(); i != end;) {
        // Try to avoid inspecting the clause:
        Lit blocker = i->blocker;
        if (value(blocker) == l_True) {
          *j++ = *i++;
          continue;
        }
        CRef cr = i->cref;
        Clause &c = ca[cr];
        Lit false_lit = ~p;
        if (c[0] == false_lit)
          c[0] = c[1], c[1] = false_lit;
        assert(c[1] == false_lit);
        i++;
        Lit first = c[0];
        Watcher w = Watcher(cr, first);
        if (first != blocker && value(first) == l_True) {
          *j++ = w;
          continue;
        }
        // Look for new watch:
        for (int k = 2; k < c.size(); k++)
          if (value(c[k]) != l_False) {
            c[1] = c[k];
            c[k] = false_lit;
            watches[(~c[1]).x].push_back(w);
            goto NextClause;
          }
        *j++ = w;
        if (value(first) == l_False) { // conflict
          confl = cr;
          qhead = trail.size();
          while (i < end)
            *j++ = *i++;
        } else {
          uncheckedEnqueue(first, cr);
        }
      NextClause:;
      }
      int size = i - j;
      ws.erase(ws.end() - size, ws.end());
    }
    return confl;
  }
  static double luby(double y, int x) {
    // Find the finite subsequence that contains index 'x', and the
    // size of that subsequence:
    int size, seq;
    for (size = 1, seq = 0; size < x + 1; seq++, size = 2 * size + 1)
      ;
    while (size - 1 != x) {
      size = (size - 1) >> 1;
      seq--;
      x = x % size;
    }
    return pow(y, seq);
  }
  lbool search(int nof_conflicts) {
    int backtrack_level;
    std::vector<Lit> learnt_clause;
    learnt_clause.push_back(mkLit(-1, false));
    int conflictC = 0;
    while (true) {
      CRef confl = propagate();
      if (confl != CRef_Undef) {
        // CONFLICT
        conflictC++;
        if (decisionLevel() == 0)
          return l_False;
        learnt_clause.clear();
        analyze(confl, learnt_clause, backtrack_level);
        cancelUntil(backtrack_level);
        if (learnt_clause.size() == 1) {
          uncheckedEnqueue(learnt_clause[0]);
        } else {
          CRef cr = alloc_clause(learnt_clause, true);
          learnts.insert(cr);
          attachClause(cr);
          uncheckedEnqueue(learnt_clause[0], cr);
        }
  //varDecay
  var_inc *= 1.05;
      } else {
        // NO CONFLICT
        if ((nof_conflicts >= 0 and conflictC >= nof_conflicts)) {
          cancelUntil(0);
          return l_Undef;
        }
        Lit next = pickBranchLit();
        if (next == lit_Undef) {
          return l_True;
        }
        newDecisionLevel();
        uncheckedEnqueue(next);
      }
    }
  };
public:
  std::vector<lbool> assigns; // The current assignments (ex assigns[0] = 0 ->
                              // X1 = True, assigns[1] = 1 -> X2 = False)
  lbool answer;               // SATISFIBLE 0 UNSATISFIBLE 1 UNKNOWN 2
  Solver() { qhead = 0; }
  void parse_dimacs_problem(std::string problem_name) {
    std::vector<Lit> lits;
    int vars = 0;
    int clauses = 0;
    std::string line;
    std::ifstream ifs(problem_name, std::ios_base::in);
    while (ifs.good()) {
      getline(ifs, line);
      if (line.size() > 0) {
        if (line[0] == 'p') {
          sscanf(line.c_str(), "p cnf %d %d", &vars, &clauses);
        } else if (line[0] == 'c' or line[0] == 'p') {
          continue;
        } else {
          readClause(line, lits);
          if (lits.size() > 0)
            addClause_(lits);
        }
      }
    }
    ifs.close();
  }
  lbool solve() {
    model.clear();
    conflict.clear();
    lbool status = l_Undef;
    answer = l_Undef;
    var_inc = 1.01;
    int curr_restarts = 0;
    double restart_inc = 2;
    double restart_first = 100;
    while (status == l_Undef) {
      double rest_base = luby(restart_inc, curr_restarts);
      status = search(rest_base * restart_first);
      curr_restarts++;
    }
    answer = status;
    return status;
  };
  void addClause(std::vector<int> &clause) {
    std::vector<Lit> lits;
    for (int i = 0; i < clause.size(); i++) {
      int var = abs(clause[i]) - 1;
      while (var >= nVars())
        newVar();
      lits.push_back(clause[i] > 0 ? mkLit(var, false) : mkLit(var, true));
    }
    addClause_(lits);
  }
  void print_answer() {
    if (answer == 0) {
      std::cout << "SAT" << std::endl;
      for (int i = 0; i < assigns.size(); i++) {
        if (assigns[i] == 0) {
          std::cout << (i + 1) << " ";
        } else {
          std::cout << -(i + 1) << " ";
        }
      }
      std::cout << "0" << std::endl;
    } else {
      std::cout << "UNSAT" << std::endl;
    }
  }
};
}
#include <iostream>
#include <vector>
#include <cstdio>
#include <sstream>
#include <map>
#include <string>
#include <algorithm>
#include <queue>
#include <cmath>
#include <functional>
#include <set>
#include <ctime>
#include <random>
#include <chrono>
#include <cassert>
#include <tuple>
#include <utility>
using namespace std;
namespace {
  using Integer = long long; //__int128;
  template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;}
  template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;}
  template<class T> istream& operator ,  (istream& is, T& val){ return is >> val;}
  template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;}
  template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" 
      "); return os;}
  template<class T> ostream& operator ,  (ostream& os, const T& val){ return os << " " << val;}
  template<class H> void print(const H& head){ cout << head; }
  template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); }
  template<class ... T> void println(const T& ... values){ print(values...); cout << endl; }
  template<class H> void eprint(const H& head){ cerr << head; }
  template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); }
  template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; }
  class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), 
      step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? 
      val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_
      (end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return 
      range_iterator(start_, step_); } range_iterator   end(){ return range_iterator(  end_, step_); } };
  inline string operator "" _s (const char* str, size_t size){ return move(string(str)); }
  constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);}
  constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M
      ) : my_pow_mod(x*x%M,k>>1,M,z);}
  constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); }
  inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed
  mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count());
  template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << 
      v[i]; } return ss.str(); }
  inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; }
}
constexpr long long mod = 9_ten + 7;
int main(){
  int n;
  cin >> n;
  vector<string> u(n);
  cin >> u;
  if(n > 26*2){
    println("Impossible");
    return 0;
  }
  map<string, vector<int>> c;
  for(auto i : range(n) ){
    c[ u[i].substr(0,1) ].push_back( i+1 );
    c[ u[i].substr(  1) ].push_back( i+1 );
    c[ u[i].substr(0,2) ].push_back( -(i+1) );
    c[ u[i].substr(  2) ].push_back( -(i+1) );
  }
  togasat::Solver solver;
  for(int i=0; i<n; i++){
    vector<int> tmp = {(i+1), -(i+1)};
    solver.addClause( tmp );
  }
  for(auto p : c){
    if(p.second.size() > 1){
      for(int i=0; i<p.second.size(); i++){
        for(int j=i+1; j<p.second.size(); j++){
          if(i==j) continue;
          vector<int> clause;
          clause.push_back( -p.second[i] );
          clause.push_back( -p.second[j] );
          solver.addClause(clause);
        }
      }
    }
  }
  int status = solver.solve();
  if(status == 0){
    for(auto i : range(n)){
      if( solver.assigns[i] == 0 ){
        println( u[i].substr(0,1), u[i].substr(1) );
      }else{
        println( u[i].substr(0,2), u[i].substr(2) );
      }
    }
  }else if(status == 1){
    println("Impossible");
    return 0;
  }else{
    cerr << "unko" << endl;
    abort();
  }
  
  return 0;
}
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