Mam pewną gramatykę i kod źródłowy.
Moim zadaniem jest dodanie obsługi nawiasów { } oraz operatora silni który wiąże mocniej niż * i /

Przetestowałem kod i wydaje się że wszystko działa ale nie jestem pewny czy dobrze rozumiem gramatyki i czy gramatyki te odzwierciedlają to co dzieje się w kodzie (gramatyka po modyfikacji).
Rzuci ktoś okiem i sprawdzi czy wszystko jest ok?

Mam również dwa ekstra pytania:

  1. Czy ktoś może wytłumaczyć mi jak obsługiwane są tutaj np. liczby dwucyfrowe?
  2. Dlaczego definicje funkcji składowych klasy znajdują się poza nią?

Gramatyka:

Expression:

  Term
  Expression "+" Term
  Expression "-" Term

Term:

Primary
  Term "*" Primary
  Term "/" Primary

Primary:

  Number
  "(" Expression ")"

Number:

  floating-point-literal

Kod źródłowy:

#include "../../std_lib_facilities.h"

//------------------------------------------------------------------------------

class Token{
public:
	char kind;        // what kind of token
	double value;     // for numbers: a value 
	Token(char ch)    // make a Token from a char
		:kind(ch), value(0) { }
	Token(char ch, double val)     // make a Token from a char and a double
		:kind(ch), value(val) { }
};

//------------------------------------------------------------------------------

class Token_stream {
public:
	Token_stream();   // make a Token_stream that reads from cin
	Token get();      // get a Token (get() is defined elsewhere)
	void putback(Token t);    // put a Token back
private:
	bool full;        // is there a Token in the buffer?
	Token buffer;     // here is where we keep a Token put back using putback()
};

//------------------------------------------------------------------------------

// The constructor just sets full to indicate that the buffer is empty:
Token_stream::Token_stream()
	:full(false), buffer(0)    // no Token in buffer
{
}

//------------------------------------------------------------------------------

// The putback() member function puts its argument back into the Token_stream's buffer:
void Token_stream::putback(Token t)
{
	if (full) error("putback() into a full buffer");
	buffer = t;       // copy t to buffer
	full = true;      // buffer is now full
}

//------------------------------------------------------------------------------

Token Token_stream::get()
{
	if (full) {       // do we already have a Token ready?
					  // remove token from buffer
		full = false;
		return buffer;
	}

	char ch;
	cin >> ch;    // note that >> skips whitespace (space, newline, tab, etc.)

	switch (ch) {
	case ';':    // for "print"
	case 'q':    // for "quit"
	case '(': case ')': case '+': case '-': case '*': case '/':
		return Token(ch);        // let each character represent itself
	case '.':
	case '0': case '1': case '2': case '3': case '4':
	case '5': case '6': case '7': case '8': case '9':
	{
		cin.putback(ch);         // put digit back into the input stream
		double val;
		cin >> val;              // read a floating-point number
		return Token('8', val);   // let '8' represent "a number"
	}
	default:
		error("Bad token");
	}
}

//------------------------------------------------------------------------------

Token_stream ts;        // provides get() and putback() 

						//------------------------------------------------------------------------------

double expression();    // declaration so that primary() can call expression()

						//------------------------------------------------------------------------------

						// deal with numbers and parentheses
double primary()
{
	Token t = ts.get();
	switch (t.kind) {
	case '(':    // handle '(' expression ')'
	{
		double d = expression();
		t = ts.get();
		if (t.kind != ')') error("')' expected");
			return d;
	}
	case '8':            // we use '8' to represent a number
		return t.value;  // return the number's value
	default:
		error("primary expected");
	}
}

//------------------------------------------------------------------------------

// deal with *, /, and %
double term()
{
	double left = primary();
	Token t = ts.get();        // get the next token from token stream

	while (true) {
		switch (t.kind) {
		case '*':
			left *= primary();
			t = ts.get();
			break;
		case '/':
		{
			double d = primary();
			if (d == 0) error("divide by zero");
			left /= d;
			t = ts.get();
			break;
		}
		default:
			ts.putback(t);     // put t back into the token stream
			return left;
		}
	}
}

//------------------------------------------------------------------------------

// deal with + and -
double expression()
{
	double left = term();      // read and evaluate a Term
	Token t = ts.get();        // get the next token from token stream

	while (true) {
		switch (t.kind) {
		case '+':
			left += term();    // evaluate Term and add
			t = ts.get();
			break;
		case '-':
			left -= term();    // evaluate Term and subtract
			t = ts.get();
			break;
		default:
			ts.putback(t);     // put t back into the token stream
			return left;       // finally: no more + or -: return the answer
		}
	}
}

//------------------------------------------------------------------------------

int main()
try
{
	double val;

	while (cin) {
		Token t = ts.get();

		if (t.kind == 'q') break; // 'q' for quit
		if (t.kind == ';')        // ';' for "print now"
			cout << "=" << val << '\n';
		else
			ts.putback(t);
		val = expression();
	}
	keep_window_open();
}
catch (exception& e) {
	cerr << "error: " << e.what() << '\n';
	keep_window_open();
	return 1;
}
catch (...) {
	cerr << "Oops: unknown exception!\n";
	keep_window_open();
	return 2;
}

//------------------------------------------------------------------------------

Gramatyka po dodaniu obsługi nawiasów { } i operatora silni:

Expression:

  Term
  Expression "+" Term
  Expression "-" Term

Term:

  Primary
  Term "*" Primary
  Term "/" Primary

Fac:

  "!" Primary

Primary:

  Number
  "(" Expression ")"
  "{" Expression "}"

Number:

  floating-point-literal

Kod źródłowy po dodaniu obsługi nawiasów { } i operatora silni:

#include "../../std_lib_facilities.h"

//------------------------------------------------------------------------------

class Token {
public:
	char kind;        // what kind of token
	double value;     // for numbers: a value 
	Token(char ch)    // make a Token from a char
		:kind(ch), value(0) { }
	Token(char ch, double val)     // make a Token from a char and a double
		:kind(ch), value(val) { }
};

//------------------------------------------------------------------------------

class Token_stream {
public:
	Token_stream();   // make a Token_stream that reads from cin
	Token get();      // get a Token (get() is defined elsewhere)
	void putback(Token t);    // put a Token back
private:
	bool full;        // is there a Token in the buffer?
	Token buffer;     // here is where we keep a Token put back using putback()
};

//------------------------------------------------------------------------------

// The constructor just sets full to indicate that the buffer is empty:
Token_stream::Token_stream()
	:full(false), buffer(0)    // no Token in buffer
{
}

//------------------------------------------------------------------------------

// The putback() member function puts its argument back into the Token_stream's buffer:
void Token_stream::putback(Token t)
{
	if (full) error("putback() into a full buffer");
	buffer = t;       // copy t to buffer
	full = true;      // buffer is now full
}

//------------------------------------------------------------------------------

Token Token_stream::get()
{
	if (full) {       // do we already have a Token ready?
					  // remove token from buffer
		full = false;
		return buffer;
	}

	char ch;
	cin >> ch;    // note that >> skips whitespace (space, newline, tab, etc.)

	switch (ch) {
	case '=':    // for "print"
	case 'x':    // for "quit"
	case '(': case ')': case '{': case '}': case '+': case '-': case '*': case '/': case '!':
		return Token(ch);        // let each character represent itself
	case '.':
	case '0': case '1': case '2': case '3': case '4':
	case '5': case '6': case '7': case '8': case '9':
	{
		cin.putback(ch);         // put digit back into the input stream
		double val;
		cin >> val;              // read a floating-point number
		return Token('8', val);   // let '8' represent "a number"
	}
	default:
		error("Bad token");
	}
}

double fac(double x)
{
	double fact = 2;

	if (x == 0) return 1;
	else if (x == 1) return 1;
	else if (x == 2) return 2;
	else
		for (int i = 3; i <= x; ++i)
			fact *= i;
	return fact;
}

//------------------------------------------------------------------------------

Token_stream ts;        // provides get() and putback() 

						//------------------------------------------------------------------------------

double expression();    // declaration so that primary() can call expression()

						//------------------------------------------------------------------------------

						// deal with numbers and parentheses
double primary()
{
	Token t = ts.get();
	switch (t.kind) {
	case '(':    // handle '(' expression ')'
	{
		double d = expression();
		t = ts.get();
		if (t.kind != ')') error("')' expected");
		return d;
	}
	case '{':	// handle '{' expression '}'
	{
		double d = expression();
		t = ts.get();
		if (t.kind != '}') error("'}' expected");
		return d;
	}
	case '8':            // we use '8' to represent a number
		return t.value;  // return the number's value
	default:
		error("primary expected");
	}
}

// deal with !
double factorial()
{
	double left = primary();
	Token t = ts.get();

	if (t.kind == '!')
	{
		double d = fac(left);
		return d;
	}
	else {
		ts.putback(t);
		return left;
	}
}

// deal with *, /, and %
double term()
{
	double left = factorial();
	Token t = ts.get();        // get the next token from token stream

	while (true) {
		switch (t.kind) {
		case '*':
			left *= factorial();
			t = ts.get();
			break;
		case '/':
		{
			double d = factorial();
			if (d == 0) error("divide by zero");
			left /= d;
			t = ts.get();
			break;
		}
		default:
			ts.putback(t);     // put t back into the token stream
			return left;
		}
	}
}

//------------------------------------------------------------------------------

// deal with + and -
double expression()
{
	double left = term();      // read and evaluate a Term
	Token t = ts.get();        // get the next token from token stream

	while (true) {
		switch (t.kind) {
		case '+':
			left += term();    // evaluate Term and add
			t = ts.get();
			break;
		case '-':
			left -= term();    // evaluate Term and subtract
			t = ts.get();
			break;
		default:
			ts.putback(t);     // put t back into the token stream
			return left;       // finally: no more + or -: return the answer
		}
	}
}

//------------------------------------------------------------------------------

int main()
try
{
	system("chcp 1250");
	cout << "Witaj w naszym prostym kalkulatorze. W wyrażeniach stosuj liczby zmiennoprzecinkowe.\n"
		"Kalkulator obsługuje operatory + - * / oraz nawiasy ( ).\n"
		"Aby wydrykować wynik wstaw znak = za wyrażeniem.\n"
		"Aby zakończyć działanie programu wstaw znak x.\n";

	double val = 0;
	while (cin) {
		Token t = ts.get();

		if (t.kind == 'x') break; // 'x' for quit
		if (t.kind == '=')        // '=' for "print now"
			cout << "=" << val << '\n';
		else
			ts.putback(t);
		val = expression();
	}
	keep_window_open();
}
catch (exception& e) {
	cerr << "error: " << e.what() << '\n';
	keep_window_open();
	return 1;
}
catch (...) {
	cerr << "Oops: unknown exception!\n";
	keep_window_open();
	return 2;
}

//------------------------------------------------------------------------------