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| /////////////////////////////////////////////////////////////////////////////////////////
//Составить описание класса для представления комплексных чисел (в тригонометрической форме).
//Обеспечить перегрузку оператора возведения в степень (^) комплексных чисел.
/////////////////////////////////////////////////////////////////////////////////////////
#include <cmath>
#include <complex>//Функции отсюда в классе T_compl_polar не используются. Используются только в функциях тестирования.
#include <cstdlib>
#include <ctime>
#include <conio.h>
#include <iostream>
#include <string>
#include <utility>
/////////////////////////////////////////////////////////////////////////////////////////
typedef std::string T_str;
typedef double T_scalar;
typedef std::complex< T_scalar > T_complex;
/////////////////////////////////////////////////////////////////////////////////////////
class T_compl_polar
{
//-----------------------------------------------------------------------------------
static const char LEFT_BRACKET_SYMB = '<';
static const char COMMA_SYMB = ',';
static const char RIGHT_BRACKET_SYMB = '>';
//-----------------------------------------------------------------------------------
T_scalar radius_;
T_scalar angle_;
//-----------------------------------------------------------------------------------
friend T_compl_polar operator+
(
T_compl_polar const & a,
T_compl_polar const & b
);
//-----------------------------------------------------------------------------------
friend T_compl_polar operator-
(
T_compl_polar const & a,
T_compl_polar const & b
);
//-----------------------------------------------------------------------------------
friend T_compl_polar operator*
(
T_compl_polar const & a,
T_compl_polar const & b
);
//-----------------------------------------------------------------------------------
friend T_compl_polar operator/
(
T_compl_polar const & a,
T_compl_polar const & b
);
//-----------------------------------------------------------------------------------
friend T_compl_polar operator^
(
T_compl_polar const & a,
T_compl_polar const & b
);
//-----------------------------------------------------------------------------------
friend std::ostream& operator<<
(
std::ostream& os,
const T_compl_polar& c
)
{
os << T_compl_polar::LEFT_BRACKET_SYMB
<< c.radius()
<< T_compl_polar::COMMA_SYMB
<< ' '
<< c.angle()
<< T_compl_polar::RIGHT_BRACKET_SYMB;
return os;
}
//-----------------------------------------------------------------------------------
friend std::istream& operator>>
(
std::istream& strm,
T_compl_polar & compl_polar
)
{
char left_bracket_symb = 0;
char comma_symb = 0;
char right_bracket_symb = 0;
T_scalar radius = 0;
T_scalar angle = 0;
strm >> left_bracket_symb
>> radius
>> comma_symb
>> angle
>> right_bracket_symb;
if (
left_bracket_symb == T_compl_polar::LEFT_BRACKET_SYMB
&& comma_symb == T_compl_polar::COMMA_SYMB
&& right_bracket_symb == T_compl_polar::RIGHT_BRACKET_SYMB
)
{
compl_polar = T_compl_polar
(
radius,
angle
);
}
return strm;
}
//-----------------------------------------------------------------------------------
public:
//-----------------------------------------------------------------------------------
T_compl_polar
(
T_scalar radius = 0,
T_scalar angle = 0
)
:
radius_ ( radius ),
angle_ ( angle )
{
normalize();
}
//-----------------------------------------------------------------------------------
T_compl_polar( T_complex const & complex_val )
:
radius_ (
sqrt (
complex_val.real() * complex_val.real()
+ complex_val.imag() * complex_val.imag()
)
)
{
if( complex_val.real() == 0 )
{
angle_ = PI() / 2;
if( complex_val.imag() < 0 )
{
radius_ *= -1;
}
}
else
{
angle_ = atan (
complex_val.imag()
/ complex_val.real()
);
if (
complex_val.real() < 0
)
{
radius_ *= -1;
}
}//else
normalize();
}
//-----------------------------------------------------------------------------------
T_scalar radius() const
{
return radius_;
}
//-----------------------------------------------------------------------------------
T_scalar angle() const
{
return angle_;
}
//-----------------------------------------------------------------------------------
T_scalar real() const
{
return radius_ * cos( angle_ );
}
//-----------------------------------------------------------------------------------
T_scalar image() const
{
return radius_ * sin( angle_ );
}
//-----------------------------------------------------------------------------------
T_complex get_complex() const
{
return T_complex
(
real (),
image ()
);
};
//-----------------------------------------------------------------------------------
T_compl_polar operator-() const
{
return T_compl_polar
(
-radius_,
angle_
);
}
//-----------------------------------------------------------------------------------
T_compl_polar operator=( T_compl_polar const & compl_polar )
{
radius_ = compl_polar.radius_;
angle_ = compl_polar.angle_;
return *this;
}
//-----------------------------------------------------------------------------------
bool operator==( T_compl_polar const & compl_polar ) const
{
return radius_ == compl_polar.radius_
&& angle_ == compl_polar.angle_;
}
//-----------------------------------------------------------------------------------
T_compl_polar ln_for_polar() const
{
return T_compl_polar
(
T_complex
(
log( radius_ ),
angle_
)
);
}
//-----------------------------------------------------------------------------------
T_compl_polar exp_for_polar() const
{
return T_compl_polar
(
exp( real() ),
image()
);
}
//-----------------------------------------------------------------------------------
static T_scalar PI()
{
return acos(-1.0);
}
//-----------------------------------------------------------------------------------
private:
//-----------------------------------------------------------------------------------
void normalize()
{
if( radius_ == 0 )
{
angle_ = 0;
}
if( radius_ < 0 )
{
radius_ *= -1;
angle_ += PI();
}
angle_ = fmod( angle_, PI() * 2 );
if( angle_ > PI() )
{
angle_ -= PI() * 2;
}
}
//-----------------------------------------------------------------------------------
};
/////////////////////////////////////////////////////////////////////////////////////////
T_compl_polar operator+
(
T_compl_polar const & a,
T_compl_polar const & b
)
{
T_scalar res_real = a.real () + b.real ();
T_scalar res_image = a.image () + b.image ();
return T_compl_polar
(
T_complex
(
res_real,
res_image
)
);
}
/////////////////////////////////////////////////////////////////////////////////////////
T_compl_polar operator-
(
T_compl_polar const & a,
T_compl_polar const & b
)
{
return a + -b;
}
/////////////////////////////////////////////////////////////////////////////////////////
T_compl_polar operator*
(
T_compl_polar const & a,
T_compl_polar const & b
)
{
return T_compl_polar
(
a.radius_ * b.radius_,
a.angle_ + b.angle_
);
}
/////////////////////////////////////////////////////////////////////////////////////////
T_compl_polar operator/
(
T_compl_polar const & a,
T_compl_polar const & b
)
{
return T_compl_polar
(
a.radius_ / b.radius_,
a.angle_ - b.angle_
);
}
/////////////////////////////////////////////////////////////////////////////////////////
T_compl_polar operator^
(
T_compl_polar const & a,
T_compl_polar const & b
)
{
return ( a.ln_for_polar() * b ).exp_for_polar();
}
/////////////////////////////////////////////////////////////////////////////////////////
enum T_op_type
{
add_op,
sub_op,
mul_op,
div_op,
pow_op,
op_types_total
};
/////////////////////////////////////////////////////////////////////////////////////////
T_scalar generate_scalar()
{
int sign = rand() % 2 * 2 - 1;
T_scalar val = rand() / static_cast< T_scalar >( rand() );
int is_not_zero = rand() % 2;
return sign * val * is_not_zero;
}
/////////////////////////////////////////////////////////////////////////////////////////
T_compl_polar generate_compl_polar()
{
return T_compl_polar
(
generate_scalar(),
generate_scalar()
);
}
/////////////////////////////////////////////////////////////////////////////////////////
T_op_type generate_op_type()
{
return static_cast<T_op_type>
(
rand() % op_types_total
);
}
/////////////////////////////////////////////////////////////////////////////////////////
void input_polar_val_and_test()
{
T_complex z;
std::cout << "Введите обычное комплексное число в виде (1.2, 3.4): z = ";
std::cin >> z;
T_compl_polar z_polar(z);
std::cout << std::endl
<< "Это же число, преобразованное в полярную форму конструктором "
<< std::endl
<< "класса T_compl_polar:"
<< std::endl
<< "z = "
<< z_polar
<< std::endl;
T_complex zz = z_polar.get_complex();
std::cout << std::endl
<< "Это же число, преобразованное обратно в комплексную форму функцией "
<< std::endl
<< "класса get_complex:"
<< std::endl
<< "z = "
<< zz
<< std::endl;
}
/////////////////////////////////////////////////////////////////////////////////////////
void print_op_message
(
char op_symb,
T_compl_polar const LP,
T_compl_polar const RP,
T_compl_polar const CP,
T_complex const L,
T_complex const R,
T_complex const C,
T_compl_polar const CCP
)
{
T_str const ARROW_STR = "\t->\t";
T_str const EQ_STR = "\t=\t";
std::cout << '\t' << LP << std::endl
<< op_symb << '\t' << RP << EQ_STR << CP
<< std::endl
<< std::endl;
std::cout << '\t' << L << std::endl
<< op_symb << '\t' << R << EQ_STR
<< C << std::endl
<< "\t\t\t" << ARROW_STR << CCP
<< std::endl
<< std::endl;
}
/////////////////////////////////////////////////////////////////////////////////////////
void test()
{
T_compl_polar LP = generate_compl_polar();
T_compl_polar RP = generate_compl_polar();
T_compl_polar CP;
T_complex L = LP.get_complex();
T_complex R = RP.get_complex();
T_complex C;
T_compl_polar CCP;
char op_symb = 0;
T_op_type op_type = generate_op_type();
std::cout << "\n\n\n\n\n"
<< "Операция сначала производится над случайными числами в полярной форме, а затем "
<< std::endl
<< "над ними же, но в комплексной форме. Затем результат операции"
<< std::endl
<< "в комплексной форме преобразуется обратно в полярную и ввычисляется "
<< std::endl
<< "разность с первым результатом."
<< std::endl
<< std::endl;
switch( op_type )
{
case add_op:
CP = LP + RP;
C = L + R;
CCP = T_compl_polar(C);
op_symb = '+';
print_op_message
(
op_symb,
LP,
RP,
CP,
L,
R,
C,
CCP
);
break;
case sub_op:
CP = LP - RP;
C = L - R;
CCP = T_compl_polar(C);
op_symb = '-';
print_op_message
(
op_symb,
LP,
RP,
CP,
L,
R,
C,
CCP
);
break;
case mul_op:
CP = LP * RP;
C = L * R;
CCP = T_compl_polar(C);
op_symb = '*';
print_op_message
(
op_symb,
LP,
RP,
CP,
L,
R,
C,
CCP
);
break;
case div_op:
CP = LP / RP;
C = L / R;
CCP = T_compl_polar(C);
op_symb = '/';
print_op_message
(
op_symb,
LP,
RP,
CP,
L,
R,
C,
CCP
);
break;
case pow_op:
CP = LP ^ RP;
C = pow(L, R);
CCP = T_compl_polar(C);
op_symb = '^';
print_op_message
(
op_symb,
LP,
RP,
CP,
L,
R,
C,
CCP
);
break;
}
std::cout << "Совпадает с точностью "
<< ( CP - CCP ).radius()
<< std::endl;
}
/////////////////////////////////////////////////////////////////////////////////////////
int main()
{
std::locale::global(std::locale(""));
srand(unsigned(time(0)));
input_polar_val_and_test();
for(;;)
{
test ();
getch ();
}//for
} |
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Сообщение было отмечено BAOlOEJlbLLlUK как решение
