#173439 (C++14) No.470 Inverse S+T Problem

提出ソース

結果

問題	No.470 Inverse S+T Problem
ユーザー	koyumeishi
提出日時	2017-05-14 07:57:04
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	16 ms / 2,000 ms
コード長	8,191 bytes
コンパイル時間	1,809 ms
コンパイル使用メモリ	138,556 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-01 22:50:38
合計ジャッジ時間	2,906 ms
ジャッジサーバーID （参考情報）	judge3 / judge4

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	1 ms 6,812 KB
testcase_01	AC	1 ms 6,812 KB
testcase_02	AC	2 ms 6,944 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	1 ms 6,944 KB
testcase_06	AC	16 ms 6,940 KB
testcase_07	AC	16 ms 6,944 KB
testcase_08	AC	16 ms 6,944 KB
testcase_09	AC	1 ms 6,944 KB
testcase_10	AC	1 ms 6,940 KB
testcase_11	AC	1 ms 6,944 KB
testcase_12	AC	1 ms 6,944 KB
testcase_13	AC	2 ms 6,944 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	2 ms 6,944 KB
testcase_16	AC	2 ms 6,944 KB
testcase_17	AC	2 ms 6,940 KB
testcase_18	AC	2 ms 6,940 KB
testcase_19	AC	1 ms 6,940 KB
testcase_20	AC	1 ms 6,944 KB
testcase_21	AC	1 ms 6,940 KB
testcase_22	AC	1 ms 6,940 KB
testcase_23	AC	2 ms 6,940 KB
testcase_24	AC	1 ms 6,940 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	2 ms 6,940 KB
testcase_27	AC	1 ms 6,940 KB
testcase_28	AC	3 ms 6,944 KB
testcase_29	AC	1 ms 6,940 KB
testcase_30	AC	2 ms 6,944 KB

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

raw source code

#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;

void TopologicalSort_dfs(vector<vector<int> > &G, vector<int> &res, int node, vector<bool> &visit){
  if(visit[node] == true) return;
  visit[node] = true;
  for(auto itr = G[node].rbegin(); itr != G[node].rend(); itr++){
    TopologicalSort_dfs(G, res, *itr, visit);
  }
  /*
  for(int i=0; i<G[node].size(); i++){
    TopologicalSort(G, res, G[node][i], visit);
  }
  */
  res.push_back(node);
}

vector<int> TopologicalSort(vector<vector<int>> &G){
  int n = G.size();
  vector<int> ret;
  vector<bool> visit(n,false);
  for(int i=0; i<n; i++){
    if(visit[i]) continue;
    TopologicalSort_dfs(G, ret, i, visit);    
  }
  reverse(ret.begin(), ret.end());
  return ret;
}
class SCC{
  int n;
  vector<vector<int> > G;
  vector<vector<int> > rG;
  
  void dfs(vector<bool> &visit, int pos, vector<int> &result){
    visit[pos] = true;
    for(int i=0; i<G[pos].size(); i++){
      if(visit[ G[pos][i] ]) continue;
      dfs(visit, G[pos][i], result);
    }
    result.push_back(pos);
  }

  void rdfs(vector<bool> &visit, int pos, int k){
    visit[pos] = true;
    component[pos] = k;
    for(int i=0; i<rG[pos].size(); i++){
      if(visit[ rG[pos][i] ]) continue;
      rdfs(visit, rG[pos][i], k);
    }
  }

  void make_rev(vector<vector<int> > &G){
    for(int i=0; i<n; i++){
      for(int j=0; j<G[i].size(); j++){
        rG[ G[i][j] ].push_back(i);
      }
    }
  }

 public:
  int num_components;
  vector<int> component;
  vector< vector<int> > scc_graph;
  
  SCC(int n){
    this->n = n;
    G.resize(n);
    rG.resize(n);
  }

  SCC(vector<vector<int> > &G){
    this->n = G.size();
    this->G = G;
    rG.resize(n);
    make_rev(G);
  }
  
  void strongly_connected_components(){
    vector<bool> visit(n, false);
    vector<int> result;

    for(int i=0; i<n; i++){
      if(visit[i]) continue;
      dfs(visit, i, result);
    }

    
    component.resize(n);
    fill(visit.begin(), visit.end(), false);
    int k=0;
    for(int i=result.size()-1; i>=0; i--){
      if(visit[ result[i] ]) continue;
      rdfs(visit, result[i], k);
      k++;
    }

    num_components = k;
    scc_graph.resize( num_components );
    for(int i=0; i<n; i++){
      int cmp = component[i];
      for(int j=0; j<G[i].size(); j++){
        if(component[ G[i][j] ] == cmp) continue;
        scc_graph[cmp].push_back( component[ G[i][j] ] );
      }
    }
    
    for(int i=0; i<scc_graph.size(); i++){
      sort(scc_graph[i].begin(), scc_graph[i].end());
      scc_graph[i].erase( unique(scc_graph[i].begin(), scc_graph[i].end()), scc_graph[i].end());
    }
    
  }
  
  void add_edge(int from, int to){
    G[from].push_back(to);
    rG[to].push_back(from);
  }
};

class TwoSAT{
  int n;
  vector<pair<int,int>> f;
  vector<vector<int>> G;
 public:
  vector<bool> ans;
  bool has_solution;
  TwoSAT(int num_of_variables) : n(num_of_variables), G(num_of_variables*2), ans(num_of_variables), has_solution(false){
  }

  // 1<=x,y<=num_of_variables
  // (x OR !y) => add(x, -y)
  // (x||y) <=> ( !y=>x && !x=>y )
  void add(int x, int y){
    assert( 1 <= abs(x) && abs(x) <= n);
    assert( 1 <= abs(y) && abs(y) <= n);
    x = (x>0)?x-1:n-x-1;
    y = (y>0)?y-1:n-y-1;
    int not_x = (x+n)%(n+n);
    int not_y = (y+n)%(n+n);
    G[not_x].push_back(y);
    G[not_y].push_back(x);
  }

  // has solution ? true : false
  bool solve(){
    SCC scc(G);
    scc.strongly_connected_components();

    auto d = TopologicalSort(scc.scc_graph);
    auto c = scc.component;
    for(int i=0; i<n; i++){
      if( c[i] == c[i+n] ){ // x and !x in the same scc
        has_solution = false;
        return false;
      }
    }

    has_solution = true;
    vector<int> c_t( d.size() ); // topological order of component x
    for(int i=0; i<d.size(); i++){
      c_t[ d[i] ]  = i;
    }

    for(int i=0; i<n; i++){
      if( c_t[ c[i] ] < c_t[ c[i+n] ] ){
        ans[i] = false;
      }else{
        ans[i] = true;
      }
    }

    return true;
  }
};


int main(){
  int n;
  cin >> n;

  vector<string> s(n);
  cin >> s;

  if(n > 26*2){
    println("Impossible");
    return 0;
  }

  map<string, vector<int>> v;
  for(int i : range(n)){
    v[ s[i].substr(0, 1) ].push_back( i+1 );
    v[ s[i].substr(1, 2) ].push_back( i+1 );

    v[ s[i].substr(0, 2) ].push_back( -(i+1) );
    v[ s[i].substr(2, 1) ].push_back( -(i+1) );
  }

  TwoSAT sat(n);
  for(auto p : v){
    if( p.second.size() < 2 ){
      continue;
    }
    for(int i=0; i<p.second.size(); i++){
      for(int j=i+1; j<p.second.size(); j++){
        sat.add( -p.second[i], -p.second[j] );
      }
    }
  }

  bool ok = sat.solve();
  if(!ok){
    println("Impossible");
    return 0;
  }

  for(int i : range(n)){
    if( sat.ans[i] ){
      println( s[i].substr(0,1), s[i].substr(1,2) );
    }else{
      println( s[i].substr(0,2), s[i].substr(2,1) );
    }
  }


  return 0;
}

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結果

テストケース

ソースコード