簡単な構文木を書こうとしたがprintするだけならTerm, Factorの概念必要なかったというコード(再帰継承しなくてよかった…)

addition-and-multiplication.cpp

#include <iostream>

class Printable;
class Expression;
class Integer;
class Addition;
class Multiplication;

class Printable
{
protected:
	virtual void print(std::ostream &out) const = 0;
public:
	virtual ~Printable() { }
	friend std::ostream &operator<<(std::ostream &out, const Printable &obj);
};

std::ostream &operator<<(std::ostream &out, const Printable &obj)
{
	obj.print(out);
	return out;
}

class Expression : virtual public Printable
{
};

class Integer : virtual public Expression
{
	int data;
public:
	Integer(int data) { this->data = data; }
	int get() { return data; }
	virtual void print (std::ostream &out) const { out << data; }
};

class Addition : virtual public Expression
{
	Expression *left;
	Expression *right;
public:
	Addition(Expression *left, Expression *right) {
		this->left = left;
		this->right = right;
	}
	virtual void print(std::ostream &out) const {
		out << *left << "+" << *right;
	}
};

class Multiplication : virtual public Expression
{
	Expression *left;
	Expression *right;
public:
	Multiplication(Expression *left, Expression *right) {
		this->left = left;
		this->right = right;
	}
	virtual void print(std::ostream &out) const {
		if (typeid(*left) == typeid(Addition)) out << "(" << *left << ")";
		else out << *left;
		out << "*";
		if (typeid(*right) == typeid(Addition)) out << "(" << *right << ")";
		else out << *right;
	}
};

int main() {
	{
		Integer i(1);
		std::cout << i << std::endl;
	}
	{
		Integer i(12), j(3);
		Addition k(&i, &j);
		std::cout << k << std::endl;
	}
	{
		Integer i(4), j(56);
		Multiplication k(&i, &j);
		std::cout << k << std::endl;
	}
	{
		Integer i(1), j(2), k(3), l(4), m(5), n(6);
		Addition a(&i, &j);
		Multiplication b(&a, &k);
		Multiplication c(&b, &l);
		Multiplication d(&m, &n);
		Addition e(&c, &d);
		std::cout << e << std::endl;
	}
	return 0;
}