結果

問題 No.460 裏表ちわーわ
ユーザー koyumeishikoyumeishi
提出日時 2016-12-11 02:41:25
言語 C++14
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 82 ms / 2,000 ms
コード長 7,087 bytes
コンパイル時間 1,587 ms
コンパイル使用メモリ 122,476 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-05-06 18:17:16
合計ジャッジ時間 3,419 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 2 ms
6,812 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 5 ms
6,944 KB
testcase_03 AC 2 ms
6,940 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 2 ms
6,940 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 3 ms
6,944 KB
testcase_08 AC 79 ms
6,940 KB
testcase_09 AC 2 ms
6,940 KB
testcase_10 AC 82 ms
6,944 KB
testcase_11 AC 2 ms
6,944 KB
testcase_12 AC 3 ms
6,940 KB
testcase_13 AC 79 ms
6,940 KB
testcase_14 AC 79 ms
6,944 KB
testcase_15 AC 78 ms
6,940 KB
testcase_16 AC 2 ms
6,944 KB
testcase_17 AC 79 ms
6,944 KB
testcase_18 AC 79 ms
6,940 KB
testcase_19 AC 79 ms
6,940 KB
testcase_20 AC 2 ms
6,940 KB
testcase_21 AC 79 ms
6,944 KB
testcase_22 AC 79 ms
6,944 KB
testcase_23 AC 79 ms
6,944 KB
testcase_24 AC 79 ms
6,940 KB
testcase_25 AC 2 ms
6,940 KB
testcase_26 AC 2 ms
6,944 KB
testcase_27 AC 2 ms
6,940 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

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;

long long extgcd(long long a, long long b, long long &x, long long &y){
  long long d=a;
  if(b!=0){
    d = extgcd(b, a%b, y, x);
    y -= (a/b) * x;
  }else{
    x = 1;
    y = 0;
  }
  return d;
}

long long mod_inverse(long long a, long long m){
  long long x,y;
  extgcd(a,m,x,y);
  return (m+x%m)%m;
}

vector<int> xx;

// A[n*p] * X[p*m] = B[n*m]
template<class T = int>
vector<vector<T>> gaussian_elimination_with_mod(vector<vector<T>>& A, vector<vector<T>>& B, int n, int p, int m, const T mod){
  int R = max(n,p); int C = p+m;
  vector<vector<T>> V( R, vector<T>(C, 0) );
  for(int i=0; i<n; i++)
    for(int j=0; j<p; j++) V[i][j] = A[i][j];
  for(int i=0; i<n; i++)
    for(int j=0; j<m; j++) V[i][j+p] = B[i][j];


  int rank = 0;
  int row = 0;

  vector<int> left(R, -1);

  //foward
  for(int col=0; col<p && row<R; col++){
    //pivot
    T val = abs( V[row][col] );
    int pivot = row;
    for(int j=row+1; j<R; j++){
      if(val < abs( V[j][col] )){
        val = abs( V[j][col] );
        pivot = j;
      }
    }
    if(pivot != row) swap(V[row], V[pivot]);

    if(val == 0) continue;

    T inv = mod_inverse(val, mod);
    for(int j=row+1; j<R; j++){
      T c = (V[j][col] * inv + mod) % mod;
      for(int k=col; k<p+m; k++) V[j][k] = ((V[j][k] - V[row][k] * c) % mod + mod) % mod;
    }

    left[row] = col;
    row++;
    rank++;
  }

  cerr << "rank = " << rank << endl;
  cerr << "free = " << n*m-rank << endl;
  xx = left;
  //return rank;

  //backward
  for(int i=R-1; i>=0; i--){
    bool zero = true;
    bool valid = true;
    for(int col=0; col<p; col++) if(V[i][col] != 0) zero = false;
    for(int col = p; zero && col<C; col++) if(V[i][col] != 0) valid = false;

    if(valid == false) return {}; //no solution

    if(left[i] == -1) continue;

    T inv = mod_inverse(V[i][ left[i] ], mod);
    for(int j=left[i]; j<C; j++) V[i][j] = (V[i][j] * inv) % mod;

    for(int j=i-1; j>=0; j--){
      if(V[j][left[i]] == 0) continue;
      for(int k=0; k<C; k++){
        V[j][k] = ( (V[j][k] - V[i][k]) % mod + mod ) % mod;
      }
    }
  }
  return V;
  //return rank;
}


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


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

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

  vector<vector<int>> B(n*m, vector<int>(1,0));
  for(int i=0; i<n; i++){
    for(int j=0; j<m; j++){
      if( v[i][j] ) B[i*m+j][0] = 1;
    }
  }

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

  vector<vector<int>> A(n*m, vector<int>(n*m, 0));
  for(int i=0; i<n; i++){
    for(int j=0; j<m; j++){
      A[i*m + j][i*m+j] = 1;
      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][y*m+x] = 1;
      }
    }
  }

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


  auto res = gaussian_elimination_with_mod(A,B, n*m, n*m, 1, 2);

  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][n*m];
  }

  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; j++){
      if(xx[j] == -1) break;
      int val = res[j][n*m];
      for(int l=xx[j]+1; l<n*m; l++){
        if(res[j][l]) val ^= tmp_x[l];
      }
      if(val){
        tmp_x[ xx[j] ] = 1;
        cnt++;
      }else{
        tmp_x[xx[j]] = 0;
      }
    }

    ans = min(ans, cnt);
  }




  println(ans);


  return 0;
}
0