Trees in C++

Hello all I'm trying to implement a tree in C++ with multiple children. There are compilers errors I'm trying to understand, but most likely it's implementation. I've looked at source codes for trees and most of them use struct to construct a tree node. Why is that?

What I'm doing is using classes for the nodes inside the tree. I'm having problems instantiating/comparing objects to NULL. How would I check if the object is NULL? I can see a fix if I used structs and have a pointer to the nodes instead.

Below is the code for the ".h" and .cpp" files

Code:

//bfTree.h
//This is a best first search tree.
#ifndef BFTREE_H
#define BFTREE_H

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

class bfTree
{
 private:
  class tree_node
  {
    int visited;
    int result;
    double percentage;
    tree_node parent;
    std::vector<bfTree::tree_node> children;
  };

 public:
  bfTree::tree_node root;
      
  bool is_empty();
};
#endif

Code:

//bfTree.cpp
#include <string>
#include <vector>
#include <iostream>

#include "bfTree.h"

bool bfTree::is_empty()
{
  if (root == NULL)
    return true;
  else
    return false;
}

The compiler errors:

Code:

In file included from HexAI.h:9:0,
                 from Game_of_hex.cpp:9:
bfTree.h:17:15: error: field ‘parent’ has incomplete type
Game_of_hex.cpp:60:5: warning: unused parameter ‘argc’
Game_of_hex.cpp:60:5: warning: unused parameter ‘argv’
In file included from HexAI.h:9:0,
                 from HexAI.cpp:6:
bfTree.h:17:15: error: field ‘parent’ has incomplete type
In file included from bfTree.cpp:5:0:
bfTree.h:17:15: error: field ‘parent’ has incomplete type
bfTree.cpp: In member function ‘bool bfTree::is_empty()’:
bfTree.cpp:9:15: error: no match for ‘operator==’ in ‘((bfTree*)this)->bfTree::root == 0l’
bfTree.cpp:13:1: warning: control reaches end of non-void function

I also realized that I might need to overload the "==" for object comparison. Is there any way to instantiate an object to NULL?

> 18 tree_node parent;
This needs to be a POINTER.

You can't instantiate a pointer to "NULL". Either an object exists, or it does not. A pointer works in such a way that it points to something or it does not (NULL).
Regardless, the way you are doing it is wrong. You declare the object to always have a parent, which is not always true. So either you need some pseudo class that can tell if it's valid or not, or you need a pointer.
The compile error comes from that you are trying to put an instance of a class you are currently defining into itself (infinite recursion).
And don't try comparing an object to 0. That makes no sense. 0 is an integer (NULL is a macro that maps to 0) and hence it is WRONG to make a comparison of an existing instance, that is in no way an integer or has any possible integer semantics, to 0. You'd probably want some "is_valid" function.

Think about that.
Oh, and btw, don't use NULL. Use nullptr instead. Again, this only works (and should rightly so!) for pointers.

Think about it, if every tree_node contained a parent which was also a tree_node, then the structures size would be infinite.
You need a pointer partly because you want the parent to either be a tree_node or *nothing*. Also because you want parent to be a link to the parent, not a copy of it.