結果

問題 No.2447 行列累乗根
コンテスト
ユーザー 👑 p-adic
提出日時 2023-04-08 08:17:52
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 5,038 bytes
コンパイル時間 10,795 ms
コンパイル使用メモリ 276,860 KB
最終ジャッジ日時 2025-02-12 03:48:37
ジャッジサーバーID
（参考情報） 		judge2 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 23 WA * 5
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ソースコード

diff # 

// 誤解法（厳密に0である値の近似誤差を無視した解法）チェック
#pragma GCC optimize ( "O3" )
#pragma GCC optimize( "unroll-loops" )
#pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

#define MAIN main
#define TYPE_OF( VAR ) remove_const<remove_reference<decltype( VAR )>::type >::type
#define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN( LL , A ) LL A; cin >> A
#define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
#define CIN_ASSERT( A , MIN , MAX ) CIN( TYPE_OF( MAX ) , A ); ASSERT( A , MIN , MAX )
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT , 0 , HOW_MANY_TIMES )
#define QUIT return 0
#define COUT( ANSWER ) cout << ( ANSWER ) << "\n"
#define SET_PRECISION( PRECISION ) cout << fixed << setprecision( PRECISION )

template <typename T>
class TwoByTwoMatrix
{

public:
  T m_M00;
  T m_M01;
  T m_M10;
  T m_M11;

public:
  inline TwoByTwoMatrix( const T& M00 , const T& M01 , const T& M10 , const T& M11 ) noexcept;
  TwoByTwoMatrix<T>& operator=( const TwoByTwoMatrix<T>& mat ) noexcept;

  inline TwoByTwoMatrix<T> operator*( const TwoByTwoMatrix<T>& mat );
  
};

template <typename T> inline TwoByTwoMatrix<T>::TwoByTwoMatrix( const T& M00 , const T& M01 , const T& M10 , const T& M11 ) noexcept : m_M00( M00 ) , m_M01( M01 ) , m_M10( M10 ) , m_M11( M11 ) {}

template <typename T>
TwoByTwoMatrix<T>& TwoByTwoMatrix<T>::operator=( const TwoByTwoMatrix<T>& mat ) noexcept
{

  if( &mat != this ){

    m_M00 = mat.m_M00;
    m_M01 = mat.m_M01;
    m_M10 = mat.m_M10;
    m_M11 = mat.m_M11;

  }

  return *this;

}

template <typename T> inline TwoByTwoMatrix<T> TwoByTwoMatrix<T>::operator*( const TwoByTwoMatrix<T>& mat ) { return TwoByTwoMatrix<T>( m_M00 * mat.m_M00 + m_M01 * mat.m_M10 , m_M00 * mat.m_M01 + m_M01 * mat.m_M11 , m_M10 * mat.m_M00 + m_M11 * mat.m_M10 , m_M10 * mat.m_M01 + m_M11 * mat.m_M11 ); }

void stod( const string& s , ll& num , double& answer )
{
  bool negative;
  uint i_start;
  if( s.substr( 0 , 1 ) == "-" ){
    negative = true;
    i_start = 1;
  } else {
    negative = false;
    i_start = 0;
  }
  uint size = s.size();
  uint exponent = 0;
  num = 0;
  FOR( i , i_start , size ){
    string c = s.substr( i , 1 );
    if( c == "." ){
      assert( exponent == 0 );
      assert( i - i_start == 1 );
      exponent = size - 1 - i;
      assert( exponent <= 5 );
    } else {
      num = num * 10 + stoi( c );
    }
  }
  answer = ( negative ? - num : num );
  while( exponent != 0 ){
    answer *= 0.1;
    exponent--;
  }
  return;
}

int MAIN()
{
  UNTIE;
  SET_PRECISION( 5 );
  double M_entry[2][2];
  double ( &M0 )[2] = M_entry[0];
  double ( &M1 )[2] = M_entry[1];
  double& M00 = M0[0];
  double& M01 = M0[1];
  double& M10 = M1[0];
  double& M11 = M1[1];
  ll num[2][2];
  double e[2];
  double& e0 = e[0];
  double& e1 = e[1];
  double U_entry[2][2];
  double ( &U0 )[2] = U_entry[0];
  double ( &U1 )[2] = U_entry[1];
  double& U00 = U0[0];
  double& U01 = U0[1];
  double& U10 = U1[0];
  double& U11 = U1[1];
  double norm[2];
  double& norm0 = norm[0];
  double& norm1 = norm[1];
  CEXPR( int , bound_T , 100000 );
  CIN_ASSERT( T , 1 , bound_T );
  REPEAT( T ){
    FOR( i , 0 , 2 ){
      double ( &Mi )[2] = M_entry[i];
      ll ( &numi )[2] = num[i];
      FOR( j , 0 , 2 ){
	CIN( string, S );
	stod( S , numi[j] , Mi[j] );
      }
    }
    double tr = M00 + M11;
    double det = M00 * M11 - M01 * M10;
    double disc = tr * tr - 4.0 * det;
    double discrt = sqrt( disc ); // ここで0とのズレが生じうる
    e[0] = ( tr + discrt ) / 2.0;
    e[1] = ( tr - discrt ) / 2.0;
    double normsq;
    bool degenerate = false;
    FOR( j , 0 , 2 ){
      double& ej = e[j];
      double& U0j = U0[j];
      double& U1j = U1[j];
      double& normj = norm[j];
      U0j = M10;
      U1j = ej - M00;
      normsq = U0j * U0j + U1j * U1j;
      normj = sqrt( normsq ); // ここで0とのズレが生じうる
      if( normj == 0.0 ){
	U0j = ej - M11;
	U1j = M01;
	normsq = U0j * U0j + U1j * U1j;
	normj = sqrt( normsq ); // ここで0とのズレが生じうる
	if( normj == 0.0 ){
	  degenerate = true;
	  break;
	}
      }
    }
    if( degenerate ){
      e0 = M11;
      e1 = M11;
      U00 = 1.0;
      U10 = 0.0;
      U01 = 0.0;
      U11 = 1.0;
    } else {
      U00 /= norm0;
      U10 /= norm0;
      U01 /= norm1;
      U11 /= norm1;
    }
    TwoByTwoMatrix<double> U{ U00 , U01 , U10 , U11 };
    TwoByTwoMatrix<double> Uinv{ U00 , U10 , U01 , U11 };
    TwoByTwoMatrix<double> Dcbrt{ cbrt( e0 ) , 0.0 , 0.0 , cbrt( e1 ) };
    TwoByTwoMatrix<double> Mcbrt = U * Dcbrt * Uinv;
    cout << Mcbrt.m_M00 << " " << Mcbrt.m_M01 << "\n";
    cout << Mcbrt.m_M10 << " " << Mcbrt.m_M11 << "\n";
  }
  QUIT;
}
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