C++：嵌套类中的运算符<<重载

这个问题在这里有一个详细的答案：重载运算符<<：不能将左值绑定到'std：：basic_ostream&&'

我正在尝试重载嵌套子类，并花了一个小时试图重载operator<<.在这里研究了一点，但仍然无法解决。有什么帮助吗？:)

每当我尝试使用 g++ -std=c++11 -lm -ggdb -g -O0 -Wall p_7_1.cpp -o p_7_1 编译它时，它都会给我一个错误：

Undefined symbols for architecture x86_64:
  "operator<<(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, LinkedBinaryTree<int>::Position const&)", referenced from:
      std::__1::basic_ostream<char, std::__1::char_traits<char> >& operator<<<int>(std::__1::basic_ostream<char, std::__1::char_traits<char> >&, LinkedBinaryTree<int> const&) in p_7_1-9fc2c2.o
ld: symbol(s) not found for architecture x86_64
clang: error: linker command failed with exit code 1 (use -v to see invocation)

p_7_1.cpp：

#include "tree.hpp"
typedef LinkedBinaryTree<int> Tree;

#include <iostream>
using namespace std;

int main() {
  // Test if tree works:
  Tree lbt;
  cout << lbt.empty() << endl;
  lbt.addRoot();
  lbt.addRoot();
  cout << lbt.empty() << endl;
  cout << lbt.size() << endl;
  lbt.expandExternal(lbt.root());
  cout << lbt.empty() << endl;
  cout << lbt.size() << endl;
  *(lbt.root()) = 12;
  cout << lbt;
}

树.hpp：

#ifndef LINKED_BINARY_TREE_HPP
#define LINKED_BINARY_TREE_HPP
#include <list>
template <typename T> class LinkedBinaryTree;
template <typename T> std::ostream& operator<<(std::ostream& os, const LinkedBinaryTree<T>& lbt);
template <typename T> std::ostream& operator<<(std::ostream& os, const typename LinkedBinaryTree<T>::Position& p);
template <typename T>
class LinkedBinaryTree {
protected:
  struct Node {         // a node of the tree
    T    elt;       // element value
    Node*   par;        // parent
    Node*   left;       // left child
    Node*   right;      // right child
    Node() : elt(), par(NULL), left(NULL), right(NULL) { } // constructor
  };
public:
  class Position {      // position in the tree
  private:          // 
    Node* v;            // pointer to the node
  public:
    Position(Node* _v = NULL) : v(_v) { } // constructor
    T& operator*()            // get element
    { return v->elt; }            // 
    Position left() const         // get left child
    { return Position(v->left); }     // 
    Position right() const        // get right child
    { return Position(v->right); }    // 
    Position parent() const       // get parent
    { return Position(v->par); }      // 
    bool isRoot() const           // root of the tree?
    { return v->par == NULL; }        // 
    bool isExternal() const       // an external node?
    { return v->left == NULL && v->right == NULL; } // 
    friend class LinkedBinaryTree; // give tree access
  public:
    friend std::ostream& operator<<(std::ostream& os, const typename LinkedBinaryTree<T>::Position& p);
    friend std::ostream& operator<< <T>(std::ostream& os, const LinkedBinaryTree<T>& lbt);
  };
  typedef std::list<Position> PositionList; // list of positions
public:                     // 
  LinkedBinaryTree();               // constructor
  int size() const;             // number of nodes
  bool empty() const;               // is tree empty?
  Position root() const;            // get the root
  PositionList positions() const;       // list of nodes
  void addRoot();               // add root to empty tree
  void expandExternal(const Position& p);   // expand external node
  Position removeAboveExternal(const Position& p); // remove p and parent
                // housekeeping functions omitted...
protected:          // local utilities
  void preorder(Node* v, PositionList& pl) const; // preorder utility
public:
  friend std::ostream& operator<< <T>(std::ostream& os, const LinkedBinaryTree<T>& lbt);
private:                      // 
  Node* _root;          // pointer to the root
  int n;            // number of nodes
};              // 
template <typename T>
LinkedBinaryTree<T>::LinkedBinaryTree() // constructor
  : _root(NULL), n(0) { }
template <typename T>
int LinkedBinaryTree<T>::size() const // number of nodes
{ return n; }
template <typename T>
bool LinkedBinaryTree<T>::empty() const // is tree empty?
{ return size() == 0; }
template <typename T>
typename LinkedBinaryTree<T>::Position LinkedBinaryTree<T>::root() const // get the root
{ return Position(_root); }
template <typename T>
typename LinkedBinaryTree<T>::PositionList LinkedBinaryTree<T>::positions() const {
  PositionList pl;
  preorder(_root, pl);      // preorder traversal
  return PositionList(pl);  // return resulting list
}
template <typename T>
void LinkedBinaryTree<T>::addRoot() // add root to empty tree
{ _root = new Node; n = 1; }
template <typename T>
void LinkedBinaryTree<T>::expandExternal(const Position& p) {
  Node* v = p.v;        // p's node
  v->left = new Node;       // add a new left child
  v->left->par = v;     // v is its parent
  v->right = new Node;      // and a new right child
  v->right->par = v;        // v is its parent
  n += 2;           // two more nodes
}
template <typename T>
typename LinkedBinaryTree<T>::Position  // remove p and parent
LinkedBinaryTree<T>::removeAboveExternal(const Position& p) {
  Node* w = p.v;  Node* v = w->par; // get p's node and parent
  Node* sib = (w == v->left ?  v->right : v->left);
  if (v == _root) {     // child of root?
    _root = sib;        // ...make sibling root
    sib->par = NULL;
  }
  else {
    Node* gpar = v->par;           // w's grandparent
    if (v == gpar->left) gpar->left = sib; // replace parent by sib
    else gpar->right = sib;
    sib->par = gpar;
  }
  delete w; delete v;       // delete removed nodes
  n -= 2;           // two fewer nodes
  return Position(sib);
}
// preorder traversal
template <typename T>
void LinkedBinaryTree<T>::preorder(Node* v, PositionList& pl) const {
  pl.push_back(Position(v));    // add this node
  if (v->left != NULL)      // traverse left subtree
    preorder(v->left, pl);
  if (v->right != NULL)     // traverse right subtree
    preorder(v->right, pl);
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const LinkedBinaryTree<T>& lbt){
  os << lbt.root();
  // os << *(lbt.root());
  return os;
}
template <typename T>
std::ostream& operator<<(std::ostream& os, const typename  LinkedBinaryTree<T>::Position& p) {
  os << *p;         // Other func stuff will be here later
  return os;
}
#endif

更新：david-rodríguez-dribeas 对嵌套类中的运算符重载进行了解释。他建议最好内联声明operator<<。