結果

問題 No.460 裏表ちわーわ
ユーザー koyumeishi
提出日時 2016-12-11 06:04:57
言語 C++14
(gcc 7.2.0)
結果
AC  
実行時間 20 ms
コード長 6659 Byte
コンパイル時間 3196 ms
使用メモリ 1568 KB

テストケース

テストケース表示
入力 結果 実行時間
使用メモリ
0.txt AC 20 ms
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1.txt AC 2 ms
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2.txt AC 5 ms
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3.txt AC 3 ms
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4.txt AC 4 ms
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5.txt AC 3 ms
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6.txt AC 2 ms
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7.txt AC 3 ms
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8.txt AC 9 ms
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9.txt AC 3 ms
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10.txt AC 10 ms
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11.txt AC 4 ms
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12.txt AC 3 ms
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13.txt AC 13 ms
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14.txt AC 13 ms
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15.txt AC 13 ms
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16.txt AC 2 ms
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17.txt AC 14 ms
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18.txt AC 14 ms
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19.txt AC 16 ms
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20.txt AC 3 ms
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21.txt AC 13 ms
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23.txt AC 14 ms
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24.txt AC 9 ms
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25.txt AC 3 ms
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27.txt AC 3 ms
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テストケース一括ダウンロード

ソースコード

diff #
#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 rank_;
vector<int> xx;

// A[n*p] * X[p*m] = B[n*m]
template<class T = long long>
vector<T> gaussian_elimination_binary(vector<T> A, vector<T> B, int n, int p, int m){
  vector<T> M(n);
  for(int i=0; i<n; i++){
    M[i] = A[i] << m;
    M[i] |= B[i];
  }

  int rank = 0;
  vector<int> left_most(n,-1);
  for(int row = 0, col = p+m-1; row<n && col>=m; col--){
    if( ((M[row] >> col) & T(1)) == T(0)){
      int pivot = row;
      for(int row__ = row; row__<n; row__++){
        if( ((M[row__] >> col) & T(1)) != T(0) ){
          pivot = row__;
          break;
        }
      }

      if(pivot == row) continue;
      swap(M[row], M[pivot]);
    }

    rank++;
    left_most[row] = col;

    for(int row__=row+1; row__<n; row__++){
      if( ((M[row__] >> col) & T(1)) != T(0) ) M[row__] ^= M[row];
    }

    row++;
  }

  rank_ = rank;
  xx = left_most;

  // T = long long 
  //T mask_B = ((T)1<<m) - 1;
  //T mask_A = (((T)1<<(m+p)) - 1) ^ mask_B;

  // T = bitset
  T mask_B( string(m, '1') );
  T mask_A( string(m+p, '1') );
  mask_A ^= mask_B;

  bool has_solution = true;
  for(int row=n-1; row>=0; row--){
    if( (M[row] & mask_B) != T(0) && (M[row] & mask_A) == T(0) ) has_solution = false;
    if(left_most[row] == -1) continue;
    int col = left_most[row];
    for(int row__ = row-1; row__>=0; row__--){
      if( ((M[row__] >> col) & T(1)) != T(0) ) M[row__] ^= M[row];
    }
  }

  return has_solution? M : vector<T>(0);
}


int dx[] = {0, 0, 1,-1, 1, 1,-1,-1};
int dy[] = {1,-1, 0, 0, 1,-1, 1,-1};

#include <bitset>
using bits = bitset<65>;

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

  vector<vector<int>> v(n, vector<int>(m));
  cin >> v;

  vector<bits> B(n*m);
  for(int i=0; i<n; i++){
    for(int j=0; j<m; j++){
      if( v[i][j] ) B[i*m+j].set(0);
    }
  }

  //eprintln("B\n", join(B,"\n"));

  vector<bits> A(n*m);
  for(int i=0; i<n; i++){
    for(int j=0; j<m; j++){
      A[i*m + j].set(i*m+j);
      for(int k=0; k<8; k++){
        int y = i+dy[k];
        int x = j+dx[k];
        if(y<0 || y>=n || x<0 || x>=m) continue;
        A[i*m+j].set(y*m+x);
      }
    }
  }

  //eprintln("A\n", join(A,"\n"));

  auto res = gaussian_elimination_binary(A,B, n*m, n*m, 1);

  for(auto& w:xx) w--;

  //eprintln(xx);

  if(res.size()==0){
    println("Impossible");
    return 0;
  }

  //eprintln( "res\n", join(res, "\n"));

  set<int> x; //free
  for(int i=0; i<n*m; i++){
    x.insert(i);
  }
  for(int i : xx){
    x.erase(i);
  }

  int ans = 0;
  for(int i=0; i<m*n; i++){
    ans += res[i][0];
  }

  vector<vector<int>> C;
  for(int i : range(n*m)){
    if(xx[i] < 0) break;
    vector<int> tmp;
    for(int j=n*m; j>0; j--){
      if( res[i][j] ) tmp.push_back(j-1);
    }
    C.push_back(tmp);
  }

  for(int i=0; i<(1<<x.size()); i++){
    vector<int> tmp_x(n*m, -1);
    int k=0;
    for(auto w : x){
      if((i>>k) & 1) tmp_x[w] = 1;
      else tmp_x[w] = 0;
      k++;
    }

    int cnt = __builtin_popcount(i);
    for(int j=0; j<n*m && cnt < ans; j++){
      if(xx[j] < 0) break;
      int val = res[j][0];
      for(int l=1; l<C[j].size(); l++){
        val ^= tmp_x[ C[j][l] ];
      }
      if(val){
        tmp_x[ C[j][0] ] = 1;
        cnt++;
      }else{
        tmp_x[C[j][0]] = 0;
      }
    }

    ans = min(ans, cnt);
  }


  println(ans);


  return 0;
}
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