#include <iostream>
#include <vector>
#include <string>

const int _binop=1, _number=5, _variable=6;

struct node
{ int kind;
  int value;
  string name;
  vector <node *> sub;

  node(int k, int v=0, string n="")
  { kind=k;
    value=v;
    name=n; }

  node * add(node * p)
  { sub.push_back(p);
    return this; }
};

node * num(int v)
{ return new node(_number, v); }

node * var(string n)
{ return new node(_variable, 0, n); }

node * binop(string o)
{ return new node(_binop, 0, o); }

void print(node *n)
{ if (n==NULL)
    cout << "NULL!!!";
  else if (n->kind == _number)
    cout << n->value;
  else if (n->kind == _variable)
    cout << n->name;
  else if (n->kind == _binop)
  { if (n->sub.size() != 2)
      cout << "ERROR IN +!!!";
    else
    { cout << "(";
      print(n->sub[0]);
      cout << n->name;
      print(n->sub[1]);
      cout << ")"; } }
  else
    cout << "ERROR BAD KIND"; }

void main()
{ // 2*a+4/5/6

  node * root = binop("+")
                   ->add(binop("*")
                            ->add(num(3))
                            ->add(var("cat")))
                   ->add(binop("/")
                            ->add(binop("/")
                                      ->add(num(8))
                                      ->add(num(7)))
                            ->add(num(6)));

  print(root);
  cout << "\n"; }