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RB-tree(红黑树)

#ifndef __SGI_STL_INTERNAL_TREE_H
#define __SGI_STL_INTERNAL_TREE_H


#include <stl_algobase.h>
#include <stl_alloc.h>
#include <stl_construct.h>
#include <stl_function.h>


__STL_BEGIN_NAMESPACE 


typedef bool __rb_tree_color_type;
const __rb_tree_color_type __rb_tree_red = false;  //红色为0
const __rb_tree_color_type __rb_tree_black = true; //黑色为1


struct __rb_tree_node_base
{
  typedef __rb_tree_color_type color_type;
  typedef __rb_tree_node_base* base_ptr;


  color_type color; //节点颜色，非红即黑
  base_ptr parent;  //RB-tree 的各种操作时常需要上溯其你节点，所以要特别在数据结构中安排一个 parent 指针
  base_ptr left;    //指向左节点
  base_ptr right;   //指向右节点


  //一直向左走，就会找到最小值
  static base_ptr minimum(base_ptr x)
  {
    while (x->left != 0) x = x->left;
    return x;
  }
  //一直向右走，就会找到最大值
  static base_ptr maximum(base_ptr x)
  {
    while (x->right != 0) x = x->right;
    return x;
  }
};


template <class Value>
struct __rb_tree_node : public __rb_tree_node_base
{
  typedef __rb_tree_node<Value>* link_type;
  Value value_field; //节点值
};




struct __rb_tree_base_iterator
{
  typedef __rb_tree_node_base::base_ptr base_ptr;
  typedef bidirectional_iterator_tag iterator_category;
  typedef ptrdiff_t difference_type;
  base_ptr node; // 用来与容器之间产生一个连结关系


  void increment() //逻辑有点复杂，画张图看看比较好懂
  {
    if (node->right != 0) {   //如果有右子节点 
      node = node->right;     //就向右走
      while (node->left != 0) //然后一直往左子树走到底
        node = node->left;    //既是解答
    }
    else {					      //没有右子节点  
      base_ptr y = node->parent;  //找到父节点
      while (node == y->right) {  //如果现行节点本身是个右子节点
        node = y;				  //就一直上溯，直到"不为右子节点"止
        y = y->parent;
      }
      if (node->right != y)		  //若此时的右子节点不等于此时的父节点
        node = y;				  //此时的父节点即为解答，否则此时的 node 为解答
    }
  }


  void decrement() //这个的逻辑更复杂。。。
  {
    if (node->color == __rb_tree_red &&  //如果是红节点，且父节点的父节点等于自己，右子节点即为解答 --> 什么情况父节点的父节点等于自己？
        node->parent->parent == node)  
      node = node->right;
    else if (node->left != 0) {
      base_ptr y = node->left;
      while (y->right != 0)
        y = y->right;
      node = y;
    }
    else {
      base_ptr y = node->parent;
      while (node == y->left) {
        node = y;
        y = y->parent;
      }
      node = y;
    }
  }
};


//RB-tree 的正规迭代器
template <class Value, class Ref, class Ptr>
struct __rb_tree_iterator : public __rb_tree_base_iterator
{
  typedef Value value_type;
  typedef Ref reference;
  typedef Ptr pointer;
  typedef __rb_tree_iterator<Value, Value&, Value*>             iterator;
  typedef __rb_tree_iterator<Value, const Value&, const Value*> const_iterator;
  typedef __rb_tree_iterator<Value, Ref, Ptr>                   self;
  typedef __rb_tree_node<Value>* link_type;


  __rb_tree_iterator() {}
  __rb_tree_iterator(link_type x) { node = x; }
  __rb_tree_iterator(const iterator& it) { node = it.node; }


  reference operator*() const { return link_type(node)->value_field; }
#ifndef __SGI_STL_NO_ARROW_OPERATOR
  pointer operator->() const { return &(operator*()); }
#endif /* __SGI_STL_NO_ARROW_OPERATOR */


  self& operator++() { increment(); return *this; }
  self operator++(int) {
    self tmp = *this;
    increment();
    return tmp;
  }
    
  self& operator--() { decrement(); return *this; }
  self operator--(int) {
    self tmp = *this;
    decrement();
    return tmp;
  }
};


inline bool operator==(const __rb_tree_base_iterator& x,
                       const __rb_tree_base_iterator& y) {
  return x.node == y.node;
}


inline bool operator!=(const __rb_tree_base_iterator& x,
                       const __rb_tree_base_iterator& y) {
  return x.node != y.node;
}


#ifndef __STL_CLASS_PARTIAL_SPECIALIZATION


inline bidirectional_iterator_tag
iterator_category(const __rb_tree_base_iterator&) {
  return bidirectional_iterator_tag();
}


inline __rb_tree_base_iterator::difference_type*
distance_type(const __rb_tree_base_iterator&) {
  return (__rb_tree_base_iterator::difference_type*) 0;
}


template <class Value, class Ref, class Ptr>
inline Value* value_type(const __rb_tree_iterator<Value, Ref, Ptr>&) {
  return (Value*) 0;
}


#endif /* __STL_CLASS_PARTIAL_SPECIALIZATION */


inline void 
__rb_tree_rotate_left(__rb_tree_node_base* x, __rb_tree_node_base*& root)
{
  __rb_tree_node_base* y = x->right;
  x->right = y->left;
  if (y->left !=0)
    y->left->parent = x;
  y->parent = x->parent;


  if (x == root)
    root = y;
  else if (x == x->parent->left)
    x->parent->left = y;
  else
    x->parent->right = y;
  y->left = x;
  x->parent = y;
}


inline void 
__rb_tree_rotate_right(__rb_tree_node_base* x, __rb_tree_node_base*& root)
{
  __rb_tree_node_base* y = x->left;
  x->left = y->right;
  if (y->right != 0)
    y->right->parent = x;
  y->parent = x->parent;


  if (x == root)
    root = y;
  else if (x == x->parent->right)
    x->parent->right = y;
  else
    x->parent->left = y;
  y->right = x;
  x->parent = y;
}


//重新令树形平衡(改变颜色及旋转树形)
//参数一为新增节点，参数二为 root
inline void 
__rb_tree_rebalance(__rb_tree_node_base* x, __rb_tree_node_base*& root)
{
  x->color = __rb_tree_red; //新节点为红
  //父节点为红的时候才要令树形平衡
  while (x != root && x->parent->color == __rb_tree_red) {
    //父节点是祖父节点的左子节点
	if (x->parent == x->parent->parent->left) {
      __rb_tree_node_base* y = x->parent->parent->right;
	  //伯父节点存在，且为红 --> 变色即可
      if (y && y->color == __rb_tree_red) {
        x->parent->color = __rb_tree_black;
        y->color = __rb_tree_black;
        x->parent->parent->color = __rb_tree_red;
        x = x->parent->parent;
      }
	  //无伯父节点，或者伯父节点为黑 --> 旋转
      else {
        if (x == x->parent->right) {
          x = x->parent;
          __rb_tree_rotate_left(x, root);
        }
        x->parent->color = __rb_tree_black;
        x->parent->parent->color = __rb_tree_red;
        __rb_tree_rotate_right(x->parent->parent, root);
      }
    }
	//父节点是祖父节点的右子节点 
    else {
      __rb_tree_node_base* y = x->parent->parent->left;
      //伯父节点存在，且为红 --> 变色即可
	  if (y && y->color == __rb_tree_red) {
        x->parent->color = __rb_tree_black;
        y->color = __rb_tree_black;
        x->parent->parent->color = __rb_tree_red;
        x = x->parent->parent;
      }
	  //无伯父节点，或者伯父节点为黑 --> 旋转
      else {
        if (x == x->parent->left) {
          x = x->parent;
          __rb_tree_rotate_right(x, root);
        }
        x->parent->color = __rb_tree_black;
        x->parent->parent->color = __rb_tree_red;
        __rb_tree_rotate_left(x->parent->parent, root);
      }
    }
  }
  root->color = __rb_tree_black; //根节点必须为黑色
}


inline __rb_tree_node_base*
__rb_tree_rebalance_for_erase(__rb_tree_node_base* z,
                              __rb_tree_node_base*& root,
                              __rb_tree_node_base*& leftmost,
                              __rb_tree_node_base*& rightmost)
{
  __rb_tree_node_base* y = z;
  __rb_tree_node_base* x = 0;
  __rb_tree_node_base* x_parent = 0;
  if (y->left == 0)             // z has at most one non-null child. y == z.
    x = y->right;               // x might be null.
  else
    if (y->right == 0)          // z has exactly one non-null child.  y == z.
      x = y->left;              // x is not null.
    else {                      // z has two non-null children.  Set y to
      y = y->right;             //   z's successor.  x might be null.
      while (y->left != 0)
        y = y->left;
      x = y->right;
    }
  if (y != z) {                 // relink y in place of z.  y is z's successor
    z->left->parent = y; 
    y->left = z->left;
    if (y != z->right) {
      x_parent = y->parent;
      if (x) x->parent = y->parent;
      y->parent->left = x;      // y must be a left child
      y->right = z->right;
      z->right->parent = y;
    }
    else
      x_parent = y;  
    if (root == z)
      root = y;
    else if (z->parent->left == z)
      z->parent->left = y;
    else 
      z->parent->right = y;
    y->parent = z->parent;
    __STD::swap(y->color, z->color);
    y = z;
    // y now points to node to be actually deleted
  }
  else {                        // y == z
    x_parent = y->parent;
    if (x) x->parent = y->parent;   
    if (root == z)
      root = x;
    else 
      if (z->parent->left == z)
        z->parent->left = x;
      else
        z->parent->right = x;
    if (leftmost == z) 
      if (z->right == 0)        // z->left must be null also
        leftmost = z->parent;
    // makes leftmost == header if z == root
      else
        leftmost = __rb_tree_node_base::minimum(x);
    if (rightmost == z)  
      if (z->left == 0)         // z->right must be null also
        rightmost = z->parent;  
    // makes rightmost == header if z == root
      else                      // x == z->left
        rightmost = __rb_tree_node_base::maximum(x);
  }
  if (y->color != __rb_tree_red) { 
    while (x != root && (x == 0 || x->color == __rb_tree_black))
      if (x == x_parent->left) {
        __rb_tree_node_base* w = x_parent->right;
        if (w->color == __rb_tree_red) {
          w->color = __rb_tree_black;
          x_parent->color = __rb_tree_red;
          __rb_tree_rotate_left(x_parent, root);
          w = x_parent->right;
        }
        if ((w->left == 0 || w->left->color == __rb_tree_black) &&
            (w->right == 0 || w->right->color == __rb_tree_black)) {
          w->color = __rb_tree_red;
          x = x_parent;
          x_parent = x_parent->parent;
        } else {
          if (w->right == 0 || w->right->color == __rb_tree_black) {
            if (w->left) w->left->color = __rb_tree_black;
            w->color = __rb_tree_red;
            __rb_tree_rotate_right(w, root);
            w = x_parent->right;
          }
          w->color = x_parent->color;
          x_parent->color = __rb_tree_black;
          if (w->right) w->right->color = __rb_tree_black;
          __rb_tree_rotate_left(x_parent, root);
          break;
        }
      } else {                  // same as above, with right <-> left.
        __rb_tree_node_base* w = x_parent->left;
        if (w->color == __rb_tree_red) {
          w->color = __rb_tree_black;
          x_parent->color = __rb_tree_red;
          __rb_tree_rotate_right(x_parent, root);
          w = x_parent->left;
        }
        if ((w->right == 0 || w->right->color == __rb_tree_black) &&
            (w->left == 0 || w->left->color == __rb_tree_black)) {
          w->color = __rb_tree_red;
          x = x_parent;
          x_parent = x_parent->parent;
        } else {
          if (w->left == 0 || w->left->color == __rb_tree_black) {
            if (w->right) w->right->color = __rb_tree_black;
            w->color = __rb_tree_red;
            __rb_tree_rotate_left(w, root);
            w = x_parent->left;
          }
          w->color = x_parent->color;
          x_parent->color = __rb_tree_black;
          if (w->left) w->left->color = __rb_tree_black;
          __rb_tree_rotate_right(x_parent, root);
          break;
        }
      }
    if (x) x->color = __rb_tree_black;
  }
  return y;
}


template <class Key, class Value, class KeyOfValue, class Compare,
          class Alloc = alloc>
class rb_tree {
protected:
  typedef void* void_pointer;
  typedef __rb_tree_node_base* base_ptr;
  typedef __rb_tree_node<Value> rb_tree_node;
  typedef simple_alloc<rb_tree_node, Alloc> rb_tree_node_allocator;
  typedef __rb_tree_color_type color_type;
public:
  typedef Key key_type;
  typedef Value value_type;
  typedef value_type* pointer;
  typedef const value_type* const_pointer;
  typedef value_type& reference;
  typedef const value_type& const_reference;
  typedef rb_tree_node* link_type;
  typedef size_t size_type;
  typedef ptrdiff_t difference_type;
protected:
  link_type get_node() { return rb_tree_node_allocator::allocate(); }
  void put_node(link_type p) { rb_tree_node_allocator::deallocate(p); }


  link_type create_node(const value_type& x) {
    link_type tmp = get_node(); //配置空间
    __STL_TRY {
      construct(&tmp->value_field, x); //构造内容
    }
    __STL_UNWIND(put_node(tmp));
    return tmp;
  }


  link_type clone_node(link_type x) { //复制一个节点
    link_type tmp = create_node(x->value_field);
    tmp->color = x->color;
    tmp->left = 0;
    tmp->right = 0;
    return tmp;
  }


  void destroy_node(link_type p) {
    destroy(&p->value_field); //析构内容
    put_node(p); //释放内存
  }


protected:
  size_type node_count; // 记录树的节点数量
  link_type header;   //? header 是什么 ？--> 
					  // 小技巧：为根节点设计的一个额外父节点
					  // header 的父节点指向根节点，左子节点指向最小节点，右子节点指向最大节点
  Compare key_compare;  //节点间的键值大小比较准则，是个 function object


  // header 的 parent, left, right 分别记录了 根节点、最左节点、最右节点 ??
  link_type& root() const { return (link_type&) header->parent; }
  link_type& leftmost() const { return (link_type&) header->left; }
  link_type& rightmost() const { return (link_type&) header->right; }


  // 取得 x 的成员，x 的类型是 link_type
  static link_type& left(link_type x) { return (link_type&)(x->left); }
  static link_type& right(link_type x) { return (link_type&)(x->right); }
  static link_type& parent(link_type x) { return (link_type&)(x->parent); }
  static reference value(link_type x) { return x->value_field; }
  static const Key& key(link_type x) { return KeyOfValue()(value(x)); } // ? KeyOfValue 是个 function object ? 在哪定义？
  static color_type& color(link_type x) { return (color_type&)(x->color); }


  // 取得 x 的成员，x 的类型是 base_ptr
  static link_type& left(base_ptr x) { return (link_type&)(x->left); }
  static link_type& right(base_ptr x) { return (link_type&)(x->right); }
  static link_type& parent(base_ptr x) { return (link_type&)(x->parent); }
  static reference value(base_ptr x) { return ((link_type)x)->value_field; }
  static const Key& key(base_ptr x) { return KeyOfValue()(value(link_type(x)));} 
  static color_type& color(base_ptr x) { return (color_type&)(link_type(x)->color); }


  //求取极大值和极小值。 node class 有实现此功能，交给它们完成
  static link_type minimum(link_type x) { 
    return (link_type)  __rb_tree_node_base::minimum(x);
  }
  static link_type maximum(link_type x) {
    return (link_type) __rb_tree_node_base::maximum(x);
  }


public:
  typedef __rb_tree_iterator<value_type, reference, pointer> iterator;
  typedef __rb_tree_iterator<value_type, const_reference, const_pointer> 
          const_iterator;


#ifdef __STL_CLASS_PARTIAL_SPECIALIZATION
  typedef reverse_iterator<const_iterator> const_reverse_iterator;
  typedef reverse_iterator<iterator> reverse_iterator;
#else /* __STL_CLASS_PARTIAL_SPECIALIZATION */
  typedef reverse_bidirectional_iterator<iterator, value_type, reference,
                                         difference_type>
          reverse_iterator; 
  typedef reverse_bidirectional_iterator<const_iterator, value_type,
                                         const_reference, difference_type>
          const_reverse_iterator;
#endif /* __STL_CLASS_PARTIAL_SPECIALIZATION */ 
private:
  iterator __insert(base_ptr x, base_ptr y, const value_type& v);
  link_type __copy(link_type x, link_type p);
  void __erase(link_type x);
  void init() {
    header = get_node(); //产生一个节点空间，令 header 指向它
    color(header) = __rb_tree_red; // used to distinguish header from --> 不懂为什么要将 header 设置为红色
                                   // root, in iterator.operator++
    root() = 0; 			//令 header 的父节点为 NULL
    leftmost() = header;    //令 header 的左子节点为自己
    rightmost() = header;   //令 header 的右子节点为自己
  }
public:
                                // allocation/deallocation
  rb_tree(const Compare& comp = Compare())
    : node_count(0), key_compare(comp) { init(); }


  rb_tree(const rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& x) 
    : node_count(0), key_compare(x.key_compare)
  { 
    header = get_node();
    color(header) = __rb_tree_red;
    if (x.root() == 0) {
      root() = 0;
      leftmost() = header;
      rightmost() = header;
    }
    else {
      __STL_TRY {
        root() = __copy(x.root(), header);
      }
      __STL_UNWIND(put_node(header));
      leftmost() = minimum(root());
      rightmost() = maximum(root());
    }
    node_count = x.node_count;
  }
  ~rb_tree() {
    clear();
    put_node(header);
  }
  rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& 
  operator=(const rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& x);


public:    
                                // accessors:
  Compare key_comp() const { return key_compare; }
  iterator begin() { return leftmost(); }              // RB 树的起头为最左节点处
  const_iterator begin() const { return leftmost(); }
  iterator end() { return header; }                    // RB 树的终点为 header 所指处 ？？
  const_iterator end() const { return header; }
  reverse_iterator rbegin() { return reverse_iterator(end()); }
  const_reverse_iterator rbegin() const { 
    return const_reverse_iterator(end()); 
  }
  reverse_iterator rend() { return reverse_iterator(begin()); }
  const_reverse_iterator rend() const { 
    return const_reverse_iterator(begin());
  } 
  bool empty() const { return node_count == 0; }
  size_type size() const { return node_count; }
  size_type max_size() const { return size_type(-1); }


  void swap(rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& t) {
    __STD::swap(header, t.header);
    __STD::swap(node_count, t.node_count);
    __STD::swap(key_compare, t.key_compare);
  }
    
public:
                                // insert/erase
  pair<iterator,bool> insert_unique(const value_type& x);
  iterator insert_equal(const value_type& x);


  iterator insert_unique(iterator position, const value_type& x);
  iterator insert_equal(iterator position, const value_type& x);


#ifdef __STL_MEMBER_TEMPLATES  
  template <class InputIterator>
  void insert_unique(InputIterator first, InputIterator last);
  template <class InputIterator>
  void insert_equal(InputIterator first, InputIterator last);
#else /* __STL_MEMBER_TEMPLATES */
  void insert_unique(const_iterator first, const_iterator last);
  void insert_unique(const value_type* first, const value_type* last);
  void insert_equal(const_iterator first, const_iterator last);
  void insert_equal(const value_type* first, const value_type* last);
#endif /* __STL_MEMBER_TEMPLATES */


  void erase(iterator position);
  size_type erase(const key_type& x);
  void erase(iterator first, iterator last);
  void erase(const key_type* first, const key_type* last);
  void clear() {
    if (node_count != 0) {
      __erase(root());
      leftmost() = header;
      root() = 0;
      rightmost() = header;
      node_count = 0;
    }
  }      


public:
                                // set operations:
  iterator find(const key_type& x);
  const_iterator find(const key_type& x) const;
  size_type count(const key_type& x) const;
  iterator lower_bound(const key_type& x);
  const_iterator lower_bound(const key_type& x) const;
  iterator upper_bound(const key_type& x);
  const_iterator upper_bound(const key_type& x) const;
  pair<iterator,iterator> equal_range(const key_type& x);
  pair<const_iterator, const_iterator> equal_range(const key_type& x) const;


public:
                                // Debugging.
  bool __rb_verify() const;
};


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
inline bool operator==(const rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& x, 
                       const rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& y) {
  return x.size() == y.size() && equal(x.begin(), x.end(), y.begin());
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
inline bool operator<(const rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& x, 
                      const rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& y) {
  return lexicographical_compare(x.begin(), x.end(), y.begin(), y.end());
}


#ifdef __STL_FUNCTION_TMPL_PARTIAL_ORDER


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
inline void swap(rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& x, 
                 rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& y) {
  x.swap(y);
}


#endif /* __STL_FUNCTION_TMPL_PARTIAL_ORDER */




template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::
operator=(const rb_tree<Key, Value, KeyOfValue, Compare, Alloc>& x) {
  if (this != &x) {
                                // Note that Key may be a constant type.
    clear();
    node_count = 0;
    key_compare = x.key_compare;        
    if (x.root() == 0) {
      root() = 0;
      leftmost() = header;
      rightmost() = header;
    }
    else {
      root() = __copy(x.root(), header);
      leftmost() = minimum(root());
      rightmost() = maximum(root());
      node_count = x.node_count;
    }
  }
  return *this;
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::
__insert(base_ptr x_, base_ptr y_, const Value& v) {
  // x 为新值插入点， y 为插入点之父节点，v 为新值
  link_type x = (link_type) x_;
  link_type y = (link_type) y_;
  link_type z;
  // 遇"大"，往左插入新值
  if (y == header || x != 0 || key_compare(KeyOfValue()(v), key(y))) { // x 不是一定等于 0 吗？  
    z = create_node(v);
    left(y) = z;                
    if (y == header) {           //这使得当 y 为 header 时(即此时树为空)， leftmost() = z
      root() = z;
      rightmost() = z;
    }
    else if (y == leftmost())   //当 y 为最左节点时，更新 leftmost() ，使它永远指向最左节点
      leftmost() = z;           
  }
  // 遇"小"，往右插入新值
  else {	
    z = create_node(v);
    right(y) = z;
    if (y == rightmost())      //当 y 为最右节点时，更新 rightmost() ，使它永远指向最右节点
      rightmost() = z;          
  }
  // 新增的 z 节点的父、左、右节点
  parent(z) = y;
  left(z) = 0;
  right(z) = 0;
  //调整 RB-tree (旋转并改变颜色) 
  __rb_tree_rebalance(z, header->parent);
  ++node_count; //节点累计加1
  return iterator(z); //返回指向新节点的迭代器
}


// 将 x 插入到 RB-tree 中(保持节点值独一无二)
template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::insert_equal(const Value& v)
{
  link_type y = header; // y 记录父节点
  link_type x = root(); 
  while (x != 0) {      //从根节点开始，往下寻找适当的插入点
    y = x; 
	//遇"大"往左，遇"小于或等于"则往右
    x = key_compare(KeyOfValue()(v), key(x)) ? left(x) : right(x); //KeyOfValue 是一个重载了 operator() 的类，语句 KeyOfValue() 产生了该类的一个对象，该对象可像函数一样被调用，称为函数对象
  }
  return __insert(x, y, v); // x 为新值插入点， y 为插入点之父节点， v 为新值
}


// 将 x 插入到 RB-tree 中(允许节点值重复)
// 返回一个 pair ，第一元素是个 RB-tree 迭代器，指向新增节点；第二元素表示插入成功与否
template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
pair<typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator, bool>
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::insert_unique(const Value& v)
{
  link_type y = header;
  link_type x = root();  //从根节点开始
  bool comp = true;
  while (x != 0) {		 //从根节点开始，往下寻找适当的插入点
    y = x;	//记录父节点
    comp = key_compare(KeyOfValue()(v), key(x)); 
    x = comp ? left(x) : right(x); //遇"大"则往左，遇"小于或等于"则往右
  }
  iterator j = iterator(y);   
  if (comp)  									 //遇"大"，将插入于左侧
    if (j == begin())     
      return pair<iterator,bool>(__insert(x, y, v), true);
    else
      --j;
  if (key_compare(key(j.node), KeyOfValue()(v))) //遇"小"，将插入于右侧
    return pair<iterator,bool>(__insert(x, y, v), true);
  return pair<iterator,bool>(j, false); 		// 相等的，不插入
}




template <class Key, class Val, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Val, KeyOfValue, Compare, Alloc>::iterator 
rb_tree<Key, Val, KeyOfValue, Compare, Alloc>::insert_unique(iterator position,
                                                             const Val& v) {
  if (position.node == header->left) // begin()
    if (size() > 0 && key_compare(KeyOfValue()(v), key(position.node)))
      return __insert(position.node, position.node, v);
  // first argument just needs to be non-null 
    else
      return insert_unique(v).first;
  else if (position.node == header) // end()
    if (key_compare(key(rightmost()), KeyOfValue()(v)))
      return __insert(0, rightmost(), v);
    else
      return insert_unique(v).first;
  else {
    iterator before = position;
    --before;
    if (key_compare(key(before.node), KeyOfValue()(v))
        && key_compare(KeyOfValue()(v), key(position.node)))
      if (right(before.node) == 0)
        return __insert(0, before.node, v); 
      else
        return __insert(position.node, position.node, v);
    // first argument just needs to be non-null 
    else
      return insert_unique(v).first;
  }
}


template <class Key, class Val, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Val, KeyOfValue, Compare, Alloc>::iterator 
rb_tree<Key, Val, KeyOfValue, Compare, Alloc>::insert_equal(iterator position,
                                                            const Val& v) {
  if (position.node == header->left) // begin()
    if (size() > 0 && key_compare(KeyOfValue()(v), key(position.node)))
      return __insert(position.node, position.node, v);
  // first argument just needs to be non-null 
    else
      return insert_equal(v);
  else if (position.node == header) // end()
    if (!key_compare(KeyOfValue()(v), key(rightmost())))
      return __insert(0, rightmost(), v);
    else
      return insert_equal(v);
  else {
    iterator before = position;
    --before;
    if (!key_compare(KeyOfValue()(v), key(before.node))
        && !key_compare(key(position.node), KeyOfValue()(v)))
      if (right(before.node) == 0)
        return __insert(0, before.node, v); 
      else
        return __insert(position.node, position.node, v);
    // first argument just needs to be non-null 
    else
      return insert_equal(v);
  }
}


#ifdef __STL_MEMBER_TEMPLATES  


template <class K, class V, class KoV, class Cmp, class Al> template<class II>
void rb_tree<K, V, KoV, Cmp, Al>::insert_equal(II first, II last) {
  for ( ; first != last; ++first)
    insert_equal(*first);
}


template <class K, class V, class KoV, class Cmp, class Al> template<class II>
void rb_tree<K, V, KoV, Cmp, Al>::insert_unique(II first, II last) {
  for ( ; first != last; ++first)
    insert_unique(*first);
}


#else /* __STL_MEMBER_TEMPLATES */


template <class K, class V, class KoV, class Cmp, class Al>
void
rb_tree<K, V, KoV, Cmp, Al>::insert_equal(const V* first, const V* last) {
  for ( ; first != last; ++first)
    insert_equal(*first);
}


template <class K, class V, class KoV, class Cmp, class Al>
void
rb_tree<K, V, KoV, Cmp, Al>::insert_equal(const_iterator first,
                                          const_iterator last) {
  for ( ; first != last; ++first)
    insert_equal(*first);
}


template <class K, class V, class KoV, class Cmp, class A>
void 
rb_tree<K, V, KoV, Cmp, A>::insert_unique(const V* first, const V* last) {
  for ( ; first != last; ++first)
    insert_unique(*first);
}


template <class K, class V, class KoV, class Cmp, class A>
void 
rb_tree<K, V, KoV, Cmp, A>::insert_unique(const_iterator first,
                                          const_iterator last) {
  for ( ; first != last; ++first)
    insert_unique(*first);
}


#endif /* __STL_MEMBER_TEMPLATES */
         
template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
inline void
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::erase(iterator position) {
  link_type y = (link_type) __rb_tree_rebalance_for_erase(position.node,
                                                          header->parent,
                                                          header->left,
                                                          header->right);
  destroy_node(y);
  --node_count;
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::size_type 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::erase(const Key& x) {
  pair<iterator,iterator> p = equal_range(x);
  size_type n = 0;
  distance(p.first, p.second, n);
  erase(p.first, p.second);
  return n;
}


template <class K, class V, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<K, V, KeyOfValue, Compare, Alloc>::link_type 
rb_tree<K, V, KeyOfValue, Compare, Alloc>::__copy(link_type x, link_type p) {
                                // structural copy.  x and p must be non-null.
  link_type top = clone_node(x);
  top->parent = p;
 
  __STL_TRY {
    if (x->right)
      top->right = __copy(right(x), top);
    p = top;
    x = left(x);


    while (x != 0) {
      link_type y = clone_node(x);
      p->left = y;
      y->parent = p;
      if (x->right)
        y->right = __copy(right(x), y);
      p = y;
      x = left(x);
    }
  }
  __STL_UNWIND(__erase(top));


  return top;
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
void rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::__erase(link_type x) {
                                // erase without rebalancing
  while (x != 0) {
    __erase(right(x));
    link_type y = left(x);
    destroy_node(x);
    x = y;
  }
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
void rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::erase(iterator first, 
                                                            iterator last) {
  if (first == begin() && last == end())
    clear();
  else
    while (first != last) erase(first++);
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
void rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::erase(const Key* first, 
                                                            const Key* last) {
  while (first != last) erase(*first++);
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::find(const Key& k) {
  link_type y = header;        // Last node which is not less than k. 
  link_type x = root();        // Current node. 


  while (x != 0) 
	//如果当前键值大于搜索键值，往左走
    if (!key_compare(key(x), k))
      y = x, x = left(x);
	//如果当前键值小于等于搜索键值，往右走
    else
      x = right(x);


  iterator j = iterator(y);   
  return (j == end() || key_compare(k, key(j.node))) ? end() : j;
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::const_iterator 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::find(const Key& k) const {
  link_type y = header; /* Last node which is not less than k. */
  link_type x = root(); /* Current node. */


  while (x != 0) {
    if (!key_compare(key(x), k))
      y = x, x = left(x);
    else
      x = right(x);
  }
  const_iterator j = const_iterator(y);   
  return (j == end() || key_compare(k, key(j.node))) ? end() : j;
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::size_type 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::count(const Key& k) const {
  pair<const_iterator, const_iterator> p = equal_range(k);
  size_type n = 0;
  distance(p.first, p.second, n);
  return n;
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::lower_bound(const Key& k) {
  link_type y = header; /* Last node which is not less than k. */
  link_type x = root(); /* Current node. */


  while (x != 0) 
    if (!key_compare(key(x), k))
      y = x, x = left(x);
    else
      x = right(x);


  return iterator(y);
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::const_iterator 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::lower_bound(const Key& k) const {
  link_type y = header; /* Last node which is not less than k. */
  link_type x = root(); /* Current node. */


  while (x != 0) 
    if (!key_compare(key(x), k))
      y = x, x = left(x);
    else
      x = right(x);


  return const_iterator(y);
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::upper_bound(const Key& k) {
  link_type y = header; /* Last node which is greater than k. */
  link_type x = root(); /* Current node. */


   while (x != 0) 
     if (key_compare(k, key(x)))
       y = x, x = left(x);
     else
       x = right(x);


   return iterator(y);
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::const_iterator 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::upper_bound(const Key& k) const {
  link_type y = header; /* Last node which is greater than k. */
  link_type x = root(); /* Current node. */


   while (x != 0) 
     if (key_compare(k, key(x)))
       y = x, x = left(x);
     else
       x = right(x);


   return const_iterator(y);
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
inline pair<typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator,
            typename rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator>
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::equal_range(const Key& k) {
  return pair<iterator, iterator>(lower_bound(k), upper_bound(k));
}


template <class Key, class Value, class KoV, class Compare, class Alloc>
inline pair<typename rb_tree<Key, Value, KoV, Compare, Alloc>::const_iterator,
            typename rb_tree<Key, Value, KoV, Compare, Alloc>::const_iterator>
rb_tree<Key, Value, KoV, Compare, Alloc>::equal_range(const Key& k) const {
  return pair<const_iterator,const_iterator>(lower_bound(k), upper_bound(k));
}


inline int __black_count(__rb_tree_node_base* node, __rb_tree_node_base* root)
{
  if (node == 0)
    return 0;
  else {
    int bc = node->color == __rb_tree_black ? 1 : 0;
    if (node == root)
      return bc;
    else
      return bc + __black_count(node->parent, root);
  }
}


template <class Key, class Value, class KeyOfValue, class Compare, class Alloc>
bool 
rb_tree<Key, Value, KeyOfValue, Compare, Alloc>::__rb_verify() const
{
  if (node_count == 0 || begin() == end())
    return node_count == 0 && begin() == end() &&
      header->left == header && header->right == header;
  
  int len = __black_count(leftmost(), root());
  for (const_iterator it = begin(); it != end(); ++it) {
    link_type x = (link_type) it.node;
    link_type L = left(x);
    link_type R = right(x);


    if (x->color == __rb_tree_red)
      if ((L && L->color == __rb_tree_red) ||
          (R && R->color == __rb_tree_red))
        return false;


    if (L && key_compare(key(x), key(L)))
      return false;
    if (R && key_compare(key(R), key(x)))
      return false;


    if (!L && !R && __black_count(x, root()) != len)
      return false;
  }


  if (leftmost() != __rb_tree_node_base::minimum(root()))
    return false;
  if (rightmost() != __rb_tree_node_base::maximum(root()))
    return false;


  return true;
}


__STL_END_NAMESPACE 


#endif /* __SGI_STL_INTERNAL_TREE_H */


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