#pragma GCC optimize ( "O3" ) #pragma GCC optimize( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #include using namespace std; using ll = long long; #define MAIN main #define TYPE_OF( VAR ) remove_const::type >::type #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define CEXPR( LL , BOUND , VALUE ) constexpr const 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 ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define QUIT return 0 #define COUT( ANSWER ) cout << ( ANSWER ) << "\n" #define SET_PRECISION( PRECISION ) cout << fixed << setprecision( PRECISION ) template inline T Absolute( const T& a ){ return a > 0 ? a : -a; } template 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& operator=( const TwoByTwoMatrix& mat ) noexcept; inline TwoByTwoMatrix operator*( const TwoByTwoMatrix& mat ); }; template inline TwoByTwoMatrix::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 TwoByTwoMatrix& TwoByTwoMatrix::operator=( const TwoByTwoMatrix& 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 inline TwoByTwoMatrix TwoByTwoMatrix::operator*( const TwoByTwoMatrix& mat ) { return TwoByTwoMatrix( 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 == 4 ); } 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 cbrt_e[2]; double& cbrt_e0 = cbrt_e[0]; double& cbrt_e1 = cbrt_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]; CEXPR( int , bound_T , 100000 ); CIN_ASSERT( T , 1 , bound_T ); CEXPR( double , llim_M , 0.00005 ); CEXPR( double , llim_det , 0.000000005 ); CEXPR( double , border_e0 , 0.00000001 ); CEXPR( double , llim_disc , 0.000000005 ); CEXPR( double , llim_normsq , 0.000000005 ); 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.substr( 0 , S.size() - 1 ) , numi[j] , Mi[j] ); } } if( Absolute( M01 ) < llim_M && Absolute( M10 ) < llim_M ){ cout << cbrt( M00 ) << " " << 0.0 << "\n"; cout << 0.0 << " " << cbrt( M11 ) << "\n"; } else { double tr = M00 + M11; double det = M00 * M11 - M01 * M10; if( Absolute( det ) < llim_det ){ e0 = cbrt_e[0] = 0.0; e1 = tr; cbrt_e[1] = cbrt( tr ); } else { double disc = tr * tr - 4.0 * det; double discrt = ( disc < llim_disc ? 0.0 : sqrt( disc ) ); e0 = ( tr + discrt ) / 2.0; e1 = ( tr - discrt ) / 2.0; if( Absolute( e0 ) > Absolute( e1 ) ){ swap( e0 , e1 ); } cbrt_e1 = cbrt( e1 ); cbrt_e0 = Absolute( e0 ) < border_e0 ? cbrt( det ) / cbrt_e1 : cbrt( e0 ); } FOR( j , 0 , 2 ){ double& ej = e[j]; double& U0j = U0[j]; double& U1j = U1[j]; U0j = M10; U1j = ej - M00; double normsq = U0j * U0j + U1j * U1j; if( normsq < llim_normsq ){ U0j = ej - M11; U1j = M01; normsq = U0j * U0j + U1j * U1j; } assert( normsq >= llim_normsq ); double norm = sqrt( normsq ); U0j /= norm; U1j /= norm; } TwoByTwoMatrix U{ U00 , U01 , U10 , U11 }; TwoByTwoMatrix Uinv{ U00 , U10 , U01 , U11 }; TwoByTwoMatrix Dcbrt{ cbrt_e0 , 0.0 , 0.0 , cbrt_e1 }; TwoByTwoMatrix Mcbrt = U * Dcbrt * Uinv; cout << Mcbrt.m_M00 << " " << Mcbrt.m_M01 << "\n"; cout << Mcbrt.m_M10 << " " << Mcbrt.m_M11 << "\n"; } } QUIT; }