STL标准库-容器-rb_tree
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红黑树,关联式容器底层实现(map set),在使用中基本运用不到,但是还是想了解一下他的运作方式
Red_Black tree是平衡二分搜寻树(balanced binary search tree),它是高度平衡的二叉树,这样有利于search和insert.
红黑树提供遍历,如果如果按正常规则(++iter)遍历,便能获得排序状态
如上图,你会发现返回迭代器头的begin()函数指向的是"5"这个点.end()记录着最大点"15",它永远先走左边后走右边.
如果你遍历上面的红黑树就会得到 5,6,7,8,10,11,12,13,15
但是我们不应该使用红黑树的迭代器改变其元素,如果改变就会破坏原树的结构,但是编程的层面没有禁止(是可以改,但是我们不应该改).
因为rb_tree是为了实现set和map,而map允许元素data的改变,但是map的key不能够改变.
rb_tree提供两种insertion操作:insert_unique()[插入的key是第一无二的,否则插入失败]. insert_equal()[允许key重复] .
先说一下红黑数的基本性质
红黑树的性质:
a.每个节点或是红的,或是黑的
b.根节点是黑色的
c.每个叶节点(NULL)是黑色的
d.如果一个节点是红色的,则它的两个子节点都是黑色的
e.对每个节点,从该节点到其所有后代叶节点的简单路径上,均含有相同数目的黑色节点
Source Code
介绍rb_tree的部分源码
一 数据类
先看红黑树的数据类 _Rb_tree_node_base
enum _Rb_tree_color { _S_red = false, _S_black = true };//红黑树的颜色 红色0 黑色1 struct _Rb_tree_node_base { typedef _Rb_tree_node_base* _Base_ptr; //节点指针 typedef const _Rb_tree_node_base* _Const_Base_ptr;//const节点指针 _Rb_tree_color _M_color;//颜色 _Base_ptr _M_parent;//父节点 _Base_ptr _M_left;//左节点 _Base_ptr _M_right;//右节点 static _Base_ptr//最小节点,即最左节点 _S_minimum(_Base_ptr __x) _GLIBCXX_NOEXCEPT { while (__x->_M_left != 0) __x = __x->_M_left;//只要左节点不为空就一直向左走,取得最小节点 return __x; } static _Const_Base_ptr _S_minimum(_Const_Base_ptr __x) _GLIBCXX_NOEXCEPT { while (__x->_M_left != 0) __x = __x->_M_left; return __x; } static _Base_ptr//最大节点,即最右节点 _S_maximum(_Base_ptr __x) _GLIBCXX_NOEXCEPT { while (__x->_M_right != 0) __x = __x->_M_right; return __x; } static _Const_Base_ptr _S_maximum(_Const_Base_ptr __x) _GLIBCXX_NOEXCEPT { while (__x->_M_right != 0) __x = __x->_M_right; return __x; } };
其子类_Rb_tree_node
template<typename _Val>//红黑树的节点结构 struct _Rb_tree_node : public _Rb_tree_node_base { typedef _Rb_tree_node<_Val>* _Link_type;//节点指针 指向数据节点 #if __cplusplus < 201103L _Val _M_value_field;//数据类型 _Val* _M_valptr() { return std::__addressof(_M_value_field); } const _Val* _M_valptr() const { return std::__addressof(_M_value_field); } #else __gnu_cxx::__aligned_buffer<_Val> _M_storage;//对齐处理后数据 _Val* _M_valptr() //返回对应数据的指针 { return _M_storage._M_ptr(); } const _Val* _M_valptr() const { return _M_storage._M_ptr(); } #endif };
std::_addressof()的实现在 move.h中找到其实现 用于取变量和函数的内存地址
template<typename _Tp> inline _Tp* __addressof(_Tp& __r) _GLIBCXX_NOEXCEPT { return reinterpret_cast<_Tp*> (&const_cast<char&>(reinterpret_cast<const volatile char&>(__r))); }
volatitle是一种类型修饰符,用它声明的类型变量表示可以被某些编译器未知的因素更改.
比如:操作系统、硬件或者其它线程等。遇到这个关键字声明的变量,编译器对访问该变量的代码就不再进行优化,从而可以提供对特殊地址的稳定访问。
声明时语法:int volatile vInt; 当要求使用 volatile 声明的变量的值的时候,系统总是重新从它所在的内存读取数据,即使它前面的指令刚刚从该处读取过数据。而且读取的数据立刻被保存
二 迭代器 _Rb_tree_iterator
template<typename _Tp> struct _Rb_tree_iterator { typedef _Tp value_type; typedef _Tp& reference; typedef _Tp* pointer; typedef bidirectional_iterator_tag iterator_category; //迭代器类型 typedef ptrdiff_t difference_type; //两个迭代器间距离 typedef _Rb_tree_iterator<_Tp> _Self; typedef _Rb_tree_node_base::_Base_ptr _Base_ptr;//节点指针 typedef _Rb_tree_node<_Tp>* _Link_type;//节点指针 //ctor _Rb_tree_iterator() _GLIBCXX_NOEXCEPT : _M_node() { } explicit _Rb_tree_iterator(_Link_type __x) _GLIBCXX_NOEXCEPT : _M_node(__x) { } reference operator*() const _GLIBCXX_NOEXCEPT { return *static_cast<_Link_type>(_M_node)->_M_valptr(); } //操作符重载返回节点指针 pointer operator->() const _GLIBCXX_NOEXCEPT { return static_cast<_Link_type> (_M_node)->_M_valptr(); } _Self& operator++() _GLIBCXX_NOEXCEPT { _M_node = _Rb_tree_increment(_M_node);//这个函数的实现在4.9中没有找到 用一下其他版本的 其实现原理基本相似 return *this; } _Self operator++(int) _GLIBCXX_NOEXCEPT { _Self __tmp = *this; _M_node = _Rb_tree_increment(_M_node);//++操作 return __tmp; } _Self& operator--() _GLIBCXX_NOEXCEPT//--也没找到 { _M_node = _Rb_tree_decrement(_M_node); return *this; } _Self operator--(int) _GLIBCXX_NOEXCEPT { _Self __tmp = *this; _M_node = _Rb_tree_decrement(_M_node); return __tmp; } bool operator==(const _Self& __x) const _GLIBCXX_NOEXCEPT { return _M_node == __x._M_node; } bool operator!=(const _Self& __x) const _GLIBCXX_NOEXCEPT { return _M_node != __x._M_node; } _Base_ptr _M_node; };
operator++
//RB-Tree的后继点 void _M_increment() { //the right subtree of node x is not empty //存在右子树,则找出右子树的最小节点 if (_M_node->_M_right != 0) {//如果有右子树 _M_node = _M_node->_M_right;//向右边走 while (_M_node->_M_left != 0)//往右子树中的左边一直走到底 _M_node = _M_node->_M_left;//最左节点就是后继结点 } //the right subtree of node x is empty,and the node of x has a successor node y //没有右子树,但是RB-Tree中节点node存在后继结点 else { _Base_ptr __y = _M_node->_M_parent;//沿其父节点向上查找 while (_M_node == __y->_M_right) { //若节点是其父节点的右孩子,则向上查找, _M_node = __y; //一直向上查找,直到“某节点不是其父节点的右孩子”为止 __y = __y->_M_parent; } if (_M_node->_M_right != __y)//若此时的右子节点不等于此时的父节点 _M_node = __y;//此时的父节点即为解答 //否则此时的node为解答 } }
operator--
//RB-Tree的前驱节点 void _M_decrement() { if (_M_node->_M_color == _S_rb_tree_red &&// 如果是红节点,且 _M_node->_M_parent->_M_parent == _M_node)// 父节点的父节点等于自己 _M_node = _M_node->_M_right; //右子节点即为解答。 /* 以上情况发生于node为header时(亦即node为end()时)。注意,header之右孩子即 mostright,指向整棵树的max节点。 */ else if (_M_node->_M_left != 0) {//若有左孩子节点。左子树的最大值即为前驱节点 _Base_ptr __y = _M_node->_M_left;//向左边走,即令y指向左孩子 while (__y->_M_right != 0)//y存在右孩子, __y = __y->_M_right;//一直往右走到底 _M_node = __y;//最后即为解答 } else {//即非根节点,且没有左孩子节点 _Base_ptr __y = _M_node->_M_parent;//找出父节点 while (_M_node == __y->_M_left) {//node节点是其父节点的左孩子 _M_node = __y;//一直交替上溯 __y = __y->_M_parent;//直到不为左孩子结点 } _M_node = __y;//此时父节点即为解答 } } };
_Rb_tree_impl
template<typename _Key, typename _Val, typename _KeyOfValue, typename _Compare, typename _Alloc = allocator<_Val> > class _Rb_tree { //先说一下说这五个参数
/*
参数1 key key类型
参数2 val value和key的数据包
参数3 在数据包中取key得方法
参数4 key的排序方法
参数5 分配器
*/
... protected: template<typename _Key_compare, bool _Is_pod_comparator = __is_pod(_Key_compare)> struct _Rb_tree_impl : public _Node_allocator { _Key_compare _M_key_compare; _Rb_tree_node_base _M_header; size_type _M_node_count; // Keeps track of size of tree. _Rb_tree_impl() : _Node_allocator(), _M_key_compare(), _M_header(), _M_node_count(0) { _M_initialize(); } _Rb_tree_impl(const _Key_compare& __comp, const _Node_allocator& __a) : _Node_allocator(__a), _M_key_compare(__comp), _M_header(), _M_node_count(0) { _M_initialize(); } #if __cplusplus >= 201103L _Rb_tree_impl(const _Key_compare& __comp, _Node_allocator&& __a) : _Node_allocator(std::move(__a)), _M_key_compare(__comp), _M_header(), _M_node_count(0) { _M_initialize(); } #endif private: void _M_initialize() { this->_M_header._M_color = _S_red; this->_M_header._M_parent = 0; this->_M_header._M_left = &this->_M_header; this->_M_header._M_right = &this->_M_header; } }; _Rb_tree_impl<_Compare> _M_impl; ... }
4.9的红黑树源码封装的比较严密,导致我没找到一些函数的实现,那么下面的源码分析,我就以我的学习笔记代替了
// 以下都是全域函式:__rb_tree_rotate_left(), __rb_tree_rotate_right(), // __rb_tree_rebalance(), __rb_tree_rebalance_for_erase() //新节点必须为红色节点。如果安插处的父节点为红色,就违反了红黑色规则 //此时要旋转和改变颜色 //左旋转 //节点x为左旋转点 inline void _Rb_tree_rotate_left(_Rb_tree_node_base* __x, _Rb_tree_node_base*& __root) { _Rb_tree_node_base* __y = __x->_M_right;//获取左旋转节点x的右孩子y __x->_M_right = __y->_M_left;//把y节点的左孩子作为旋转节点x的右孩子 if (__y->_M_left !=0) __y->_M_left->_M_parent = __x;//更新节点y左孩子父节点指针,指向新的父节点x __y->_M_parent = __x->_M_parent;//y节点替换x节点的位置 //令y完全顶替x的地位(必须将x对其父节点的关系完全接收过来) if (__x == __root)//若原始位置节点x是根节点 __root = __y;//则y为新的根节点 //否则,若x节点是其父节点的左孩子 else if (__x == __x->_M_parent->_M_left) __x->_M_parent->_M_left = __y;//则更新节点y为原始x父节点的左孩子 else//若x节点是其父节点的右孩子 __x->_M_parent->_M_right = __y;//则更新节点y为原始x父节点的右孩子 __y->_M_left = __x;//旋转后旋转节点x作为节点y的左孩子 __x->_M_parent = __y;//更新x节点的父节点指针 } //右旋转 //节点x为右旋转点 inline void _Rb_tree_rotate_right(_Rb_tree_node_base* __x, _Rb_tree_node_base*& __root) { _Rb_tree_node_base* __y = __x->_M_left;//获取右旋转节点x的左孩子y __x->_M_left = __y->_M_right;//把y节点的右孩子作为旋转节点x的左孩子 if (__y->_M_right != 0) __y->_M_right->_M_parent = __x;//更新节点y右孩子父节点指针,指向新的父节点x __y->_M_parent = __x->_M_parent;//y节点替换x节点的位置 //令y完全顶替x的地位(必须将x对其父节点的关系完全接收过来) if (__x == __root)//若原始位置节点x是根节点 __root = __y;//则y为新的根节点 //否则,若x节点是其父节点的右孩子 else if (__x == __x->_M_parent->_M_right) __x->_M_parent->_M_right = __y;//则更新节点y为原始x父节点的右孩子 else//若x节点是其父节点的左孩子 __x->_M_parent->_M_left = __y;//则更新节点y为原始x父节点的左孩子 __y->_M_right = __x;//旋转后旋转节点x作为节点y的右孩子 __x->_M_parent = __y;//更新x节点的父节点指针 } //重新令RB-tree平衡(改变颜色和旋转) //参数一为新增节点x,参数二为root节点 inline void _Rb_tree_rebalance(_Rb_tree_node_base* __x, _Rb_tree_node_base*& __root) { __x->_M_color = _S_rb_tree_red;//新插入的节点必须为红色,这样不会违反性质5. //若新插入节点不是为RB-Tree的根节点,且其父节点color属性也是红色,即违反了性质4. //则进入while循环. //此时根据节点x的父节点x->parent是其祖父节点x->parent->parent的左孩子还是右孩子进行讨论, //但是左右孩子之间是对称的,所以思想是类似的. while (__x != __root && __x->_M_parent->_M_color == _S_rb_tree_red) { //case1:节点x的父节点x->parent是其祖父节点x->parent->parent的左孩子 if (__x->_M_parent == __x->_M_parent->_M_parent->_M_left) { //节点y为x节点的叔叔节点,即是节点x父节点x->parent的兄弟 _Rb_tree_node_base* __y = __x->_M_parent->_M_parent->_M_right; if (__y && __y->_M_color == _S_rb_tree_red) {//情况1:若其叔叔节点y存在,且为红色 /* 此时x->parent和y都是红色的,解决办法是将x的父节点x->parent和叔叔结点y都着为黑色, 而将x的祖父结点x->parent->parent着为红色, 然后从祖父结点x->parent->parent继续向上判断是否破坏红黑树的性质。 */ __x->_M_parent->_M_color = _S_rb_tree_black;//将其父节点x->parent改变成黑色 __y->_M_color = _S_rb_tree_black;//将其叔叔节点y改变成黑色 __x->_M_parent->_M_parent->_M_color = _S_rb_tree_red;//将其祖父节点变成红色 //把祖父节点作为当前节点,一直上溯,继续判断是否破坏RB-Tree性质. __x = __x->_M_parent->_M_parent; } else {//若无叔叔节点或者其叔叔节点y为黑色 /* 情况2:x的叔叔节点y是黑色且x是一个右孩子 情况3:x的叔叔节点y是黑色且x是一个左孩子 情况2和情况3中y都是黑色的,通过x是parent[x]的左孩子还是右孩子进行区分的。 情况2中x是右孩子,可以在parent[x]结点将情况2通过左旋转为情况3,使得x变为左孩子。 无论是间接还是直接的通过情况2进入到情况3,x的叔叔y总是黑色的。 在情况3中,将parent[x]着为黑色,parent[parent[x]]着为红色,然后从parent[parent[x]]处进行一次右旋转。 情况2、3修正了对性质4的违反,修正过程不会导致其他的红黑性质被破坏。 */ if (__x == __x->_M_parent->_M_right) {//若节点x为其父节点x->parent的右孩子 //则以其父节点作为旋转节点 //进行一次左旋转 __x = __x->_M_parent; _Rb_tree_rotate_left(__x, __root); //旋转之后,节点x变成其父节点的左孩子 } __x->_M_parent->_M_color = _S_rb_tree_black;//改变其父节点x->parent颜色 __x->_M_parent->_M_parent->_M_color = _S_rb_tree_red;//改变其祖父节点x->parent->parent颜色 _Rb_tree_rotate_right(__x->_M_parent->_M_parent, __root);//对其祖父节点进行一次右旋转 } } //case2:节点x的父节点x->parent是其祖父节点x->parent->parent的右孩子 //这种情况是跟上面的情况(父节点为其祖父节点的左孩子)是对称的. else { //节点y为x节点的叔叔节点,即是节点x父节点x->parent的兄弟 _Rb_tree_node_base* __y = __x->_M_parent->_M_parent->_M_left; if (__y && __y->_M_color == _S_rb_tree_red) {//若叔叔节点存在,且为红色 __x->_M_parent->_M_color = _S_rb_tree_black;//改变父节点颜色 __y->_M_color = _S_rb_tree_black;//改变叔叔节点颜色 __x->_M_parent->_M_parent->_M_color = _S_rb_tree_red;//改变祖父节点颜色 __x = __x->_M_parent->_M_parent;//上溯祖父节点,判断是否违背RB-Tree的性质 } else {//若叔叔节点不存在或叔叔节点为黑色 if (__x == __x->_M_parent->_M_left) {//新节点x为其父节点的左孩子 //对其父节点进行一次右旋转 __x = __x->_M_parent; _Rb_tree_rotate_right(__x, __root); } __x->_M_parent->_M_color = _S_rb_tree_black;//改变父节点颜色 __x->_M_parent->_M_parent->_M_color = _S_rb_tree_red;//改变祖父节点颜色 _Rb_tree_rotate_left(__x->_M_parent->_M_parent, __root);//进行一次左旋转 } } } //若新插入节点为根节点,则违反性质2 //只需将其重新赋值为黑色即可 __root->_M_color = _S_rb_tree_black; } //删除节点 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->_M_left == 0) // __z has at most one non-null child. y == z. __x = __y->_M_right; // __x might be null. else if (__y->_M_right == 0) // __z has exactly one non-null child. y == z. __x = __y->_M_left; // __x is not null. else { // __z has two non-null children. Set __y to __y = __y->_M_right; // __z's successor. __x might be null. while (__y->_M_left != 0) __y = __y->_M_left; __x = __y->_M_right; } if (__y != __z) { // relink y in place of z. y is z's successor __z->_M_left->_M_parent = __y; __y->_M_left = __z->_M_left; if (__y != __z->_M_right) { __x_parent = __y->_M_parent; if (__x) __x->_M_parent = __y->_M_parent; __y->_M_parent->_M_left = __x; // __y must be a child of _M_left __y->_M_right = __z->_M_right; __z->_M_right->_M_parent = __y; } else __x_parent = __y; if (__root == __z) __root = __y; else if (__z->_M_parent->_M_left == __z) __z->_M_parent->_M_left = __y; else __z->_M_parent->_M_right = __y; __y->_M_parent = __z->_M_parent; __STD::swap(__y->_M_color, __z->_M_color); __y = __z; // __y now points to node to be actually deleted } else { // __y == __z __x_parent = __y->_M_parent; if (__x) __x->_M_parent = __y->_M_parent; if (__root == __z) __root = __x; else if (__z->_M_parent->_M_left == __z) __z->_M_parent->_M_left = __x; else __z->_M_parent->_M_right = __x; if (__leftmost == __z) if (__z->_M_right == 0) // __z->_M_left must be null also __leftmost = __z->_M_parent; // makes __leftmost == _M_header if __z == __root else __leftmost = _Rb_tree_node_base::_S_minimum(__x); if (__rightmost == __z) if (__z->_M_left == 0) // __z->_M_right must be null also __rightmost = __z->_M_parent; // makes __rightmost == _M_header if __z == __root else // __x == __z->_M_left __rightmost = _Rb_tree_node_base::_S_maximum(__x); } if (__y->_M_color != _S_rb_tree_red) { while (__x != __root && (__x == 0 || __x->_M_color == _S_rb_tree_black)) if (__x == __x_parent->_M_left) { _Rb_tree_node_base* __w = __x_parent->_M_right; if (__w->_M_color == _S_rb_tree_red) { __w->_M_color = _S_rb_tree_black; __x_parent->_M_color = _S_rb_tree_red; _Rb_tree_rotate_left(__x_parent, __root); __w = __x_parent->_M_right; } if ((__w->_M_left == 0 || __w->_M_left->_M_color == _S_rb_tree_black) && (__w->_M_right == 0 || __w->_M_right->_M_color == _S_rb_tree_black)) { __w->_M_color = _S_rb_tree_red; __x = __x_parent; __x_parent = __x_parent->_M_parent; } else { if (__w->_M_right == 0 || __w->_M_right->_M_color == _S_rb_tree_black) { if (__w->_M_left) __w->_M_left->_M_color = _S_rb_tree_black; __w->_M_color = _S_rb_tree_red; _Rb_tree_rotate_right(__w, __root); __w = __x_parent->_M_right; } __w->_M_color = __x_parent->_M_color; __x_parent->_M_color = _S_rb_tree_black; if (__w->_M_right) __w->_M_right->_M_color = _S_rb_tree_black; _Rb_tree_rotate_left(__x_parent, __root); break; } } else { // same as above, with _M_right <-> _M_left. _Rb_tree_node_base* __w = __x_parent->_M_left; if (__w->_M_color == _S_rb_tree_red) { __w->_M_color = _S_rb_tree_black; __x_parent->_M_color = _S_rb_tree_red; _Rb_tree_rotate_right(__x_parent, __root); __w = __x_parent->_M_left; } if ((__w->_M_right == 0 || __w->_M_right->_M_color == _S_rb_tree_black) && (__w->_M_left == 0 || __w->_M_left->_M_color == _S_rb_tree_black)) { __w->_M_color = _S_rb_tree_red; __x = __x_parent; __x_parent = __x_parent->_M_parent; } else { if (__w->_M_left == 0 || __w->_M_left->_M_color == _S_rb_tree_black) { if (__w->_M_right) __w->_M_right->_M_color = _S_rb_tree_black; __w->_M_color = _S_rb_tree_red; _Rb_tree_rotate_left(__w, __root); __w = __x_parent->_M_left; } __w->_M_color = __x_parent->_M_color; __x_parent->_M_color = _S_rb_tree_black; if (__w->_M_left) __w->_M_left->_M_color = _S_rb_tree_black; _Rb_tree_rotate_right(__x_parent, __root); break; } } if (__x) __x->_M_color = _S_rb_tree_black; } return __y; } // Base class to encapsulate the differences between old SGI-style // allocators and standard-conforming allocators. In order to avoid // having an empty base class, we arbitrarily move one of rb_tree's // data members into the base class. //以下是对内存分配的管理 #ifdef __STL_USE_STD_ALLOCATORS // _Base for general standard-conforming allocators. template <class _Tp, class _Alloc, bool _S_instanceless> class _Rb_tree_alloc_base { public: typedef typename _Alloc_traits<_Tp, _Alloc>::allocator_type allocator_type; allocator_type get_allocator() const { return _M_node_allocator; }//空间配置器的类型 _Rb_tree_alloc_base(const allocator_type& __a) : _M_node_allocator(__a), _M_header(0) {} protected: typename _Alloc_traits<_Rb_tree_node<_Tp>, _Alloc>::allocator_type _M_node_allocator; _Rb_tree_node<_Tp>* _M_header;//定义头指针,指向Rb_tree的根节点 _Rb_tree_node<_Tp>* _M_get_node() //分配一个节点空间 { return _M_node_allocator.allocate(1); } void _M_put_node(_Rb_tree_node<_Tp>* __p) //释放一个节点空间 { _M_node_allocator.deallocate(__p, 1); } }; // Specialization for instanceless allocators. template <class _Tp, class _Alloc> class _Rb_tree_alloc_base<_Tp, _Alloc, true> { public: typedef typename _Alloc_traits<_Tp, _Alloc>::allocator_type allocator_type; allocator_type get_allocator() const { return allocator_type(); } _Rb_tree_alloc_base(const allocator_type&) : _M_header(0) {} protected: _Rb_tree_node<_Tp>* _M_header; typedef typename _Alloc_traits<_Rb_tree_node<_Tp>, _Alloc>::_Alloc_type _Alloc_type; _Rb_tree_node<_Tp>* _M_get_node() { return _Alloc_type::allocate(1); } void _M_put_node(_Rb_tree_node<_Tp>* __p) { _Alloc_type::deallocate(__p, 1); } }; //RB-Tree基本结构,即基类,继承_Rb_tree_alloc_base template <class _Tp, class _Alloc> struct _Rb_tree_base : public _Rb_tree_alloc_base<_Tp, _Alloc, _Alloc_traits<_Tp, _Alloc>::_S_instanceless> { typedef _Rb_tree_alloc_base<_Tp, _Alloc, _Alloc_traits<_Tp, _Alloc>::_S_instanceless> _Base; typedef typename _Base::allocator_type allocator_type; _Rb_tree_base(const allocator_type& __a) : _Base(__a) { _M_header = _M_get_node(); } ~_Rb_tree_base() { _M_put_node(_M_header); } }; #else /* __STL_USE_STD_ALLOCATORS */ //RB-Tree基本结构,即基类,没有继承_Rb_tree_alloc_base template <class _Tp, class _Alloc> struct _Rb_tree_base { typedef _Alloc allocator_type; allocator_type get_allocator() const { return allocator_type(); } _Rb_tree_base(const allocator_type&) : _M_header(0) { _M_header = _M_get_node(); } ~_Rb_tree_base() { _M_put_node(_M_header); } protected: _Rb_tree_node<_Tp>* _M_header;//定义头指针节点,指向根节点 typedef simple_alloc<_Rb_tree_node<_Tp>, _Alloc> _Alloc_type; _Rb_tree_node<_Tp>* _M_get_node() { return _Alloc_type::allocate(1); } void _M_put_node(_Rb_tree_node<_Tp>* __p) { _Alloc_type::deallocate(__p, 1); } }; #endif /* __STL_USE_STD_ALLOCATORS */ //RB-Tree类的定义,继承基类_Rb_tree_base template <class _Key, class _Value, class _KeyOfValue, class _Compare, class _Alloc = __STL_DEFAULT_ALLOCATOR(_Value) > class _Rb_tree : protected _Rb_tree_base<_Value, _Alloc> { typedef _Rb_tree_base<_Value, _Alloc> _Base; protected: typedef _Rb_tree_node_base* _Base_ptr; typedef _Rb_tree_node<_Value> _Rb_tree_node; 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; typedef typename _Base::allocator_type allocator_type; allocator_type get_allocator() const { return _Base::get_allocator(); } protected: #ifdef __STL_USE_NAMESPACES using _Base::_M_get_node; using _Base::_M_put_node; using _Base::_M_header;//这里是指向根节点的节点指针 #endif /* __STL_USE_NAMESPACES */ protected: //创建节点并对其初始化为x _Link_type _M_create_node(const value_type& __x) { _Link_type __tmp = _M_get_node();//分配一个节点空间 __STL_TRY { construct(&__tmp->_M_value_field, __x);//构造对象 } __STL_UNWIND(_M_put_node(__tmp)); return __tmp; } //复制节点的值和颜色 _Link_type _M_clone_node(_Link_type __x) { _Link_type __tmp = _M_create_node(__x->_M_value_field); __tmp->_M_color = __x->_M_color; __tmp->_M_left = 0; __tmp->_M_right = 0; return __tmp; } //释放节点 void destroy_node(_Link_type __p) { destroy(&__p->_M_value_field);//析构对象 _M_put_node(__p);//释放节点空间 } protected: size_type _M_node_count; // keeps track of size of tree _Compare _M_key_compare; //节点键值比较准则 //下面三个函数是用来获取header的成员 _Link_type& _M_root() const { return (_Link_type&) _M_header->_M_parent; } _Link_type& _M_leftmost() const { return (_Link_type&) _M_header->_M_left; } _Link_type& _M_rightmost() const { return (_Link_type&) _M_header->_M_right; } //下面六个函数获取节点x的成员 static _Link_type& _S_left(_Link_type __x) { return (_Link_type&)(__x->_M_left); } static _Link_type& _S_right(_Link_type __x) { return (_Link_type&)(__x->_M_right); } static _Link_type& _S_parent(_Link_type __x) { return (_Link_type&)(__x->_M_parent); } static reference _S_value(_Link_type __x) { return __x->_M_value_field; } static const _Key& _S_key(_Link_type __x) { return _KeyOfValue()(_S_value(__x)); } static _Color_type& _S_color(_Link_type __x) { return (_Color_type&)(__x->_M_color); } //跟上面六个函数功能相同,不同的是参数类型不同,一个是基类指针,一个是派生类指针 static _Link_type& _S_left(_Base_ptr __x) { return (_Link_type&)(__x->_M_left); } static _Link_type& _S_right(_Base_ptr __x) { return (_Link_type&)(__x->_M_right); } static _Link_type& _S_parent(_Base_ptr __x) { return (_Link_type&)(__x->_M_parent); } static reference _S_value(_Base_ptr __x) { return ((_Link_type)__x)->_M_value_field; } static const _Key& _S_key(_Base_ptr __x) { return _KeyOfValue()(_S_value(_Link_type(__x)));} static _Color_type& _S_color(_Base_ptr __x) { return (_Color_type&)(_Link_type(__x)->_M_color); } //RB-Tree的极小值 static _Link_type _S_minimum(_Link_type __x) { return (_Link_type) _Rb_tree_node_base::_S_minimum(__x); } //RB-Tree的极大值 static _Link_type _S_maximum(_Link_type __x) { return (_Link_type) _Rb_tree_node_base::_S_maximum(__x); } public: //迭代器 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: //类的私有成员函数,在后面定义 iterator _M_insert(_Base_ptr __x, _Base_ptr __y, const value_type& __v); _Link_type _M_copy(_Link_type __x, _Link_type __p); void _M_erase(_Link_type __x); public: // allocation/deallocation _Rb_tree() : _Base(allocator_type()), _M_node_count(0), _M_key_compare() { _M_empty_initialize(); } _Rb_tree(const _Compare& __comp) : _Base(allocator_type()), _M_node_count(0), _M_key_compare(__comp) { _M_empty_initialize(); } _Rb_tree(const _Compare& __comp, const allocator_type& __a) : _Base(__a), _M_node_count(0), _M_key_compare(__comp) { _M_empty_initialize(); } _Rb_tree(const _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>& __x) : _Base(__x.get_allocator()), _M_node_count(0), _M_key_compare(__x._M_key_compare) { if (__x._M_root() == 0) _M_empty_initialize(); else { _S_color(_M_header) = _S_rb_tree_red; _M_root() = _M_copy(__x._M_root(), _M_header); _M_leftmost() = _S_minimum(_M_root()); _M_rightmost() = _S_maximum(_M_root()); } _M_node_count = __x._M_node_count; } ~_Rb_tree() { clear(); } _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>& operator=(const _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>& __x); private: //初始化header void _M_empty_initialize() { _S_color(_M_header) = _S_rb_tree_red; // used to distinguish header from // __root, in iterator.operator++ _M_root() = 0; _M_leftmost() = _M_header; _M_rightmost() = _M_header; } public: // accessors: _Compare key_comp() const { return _M_key_compare; } iterator begin() { return _M_leftmost(); }//RB-Tree的起始迭代器为最小节点 const_iterator begin() const { return _M_leftmost(); } iterator end() { return _M_header; }//RB-Tree的结束迭代器为header const_iterator end() const { return _M_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()); } //RB-Tree是否为空 bool empty() const { return _M_node_count == 0; } //RB-Tree节点数 size_type size() const { return _M_node_count; } size_type max_size() const { return size_type(-1); } //交换两棵RB-Tree的内容 //RB-tree只有三个表现成员,所以两棵RB-Tree交换内容时,只需互换这3个成员 void swap(_Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>& __t) { __STD::swap(_M_header, __t._M_header); __STD::swap(_M_node_count, __t._M_node_count); __STD::swap(_M_key_compare, __t._M_key_compare); } public: // insert/erase //插入节点,但是节点值必须唯一 pair<iterator,bool> insert_unique(const value_type& __x); //插入节点,节点值可以与当前RB-Tree节点值相等 iterator insert_equal(const value_type& __x); //在指定位置插入节点 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 */ //删除节点 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); //清除RB-Tree void clear() { if (_M_node_count != 0) { _M_erase(_M_root()); _M_leftmost() = _M_header; _M_root() = 0; _M_rightmost() = _M_header; _M_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; }; //以下是操作符重载 //重载operator==运算符,使用的是STL泛型算法 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() && //STL的算法equal(__x.begin(), __x.end(), __y.begin()); equal(__x.begin(), __x.end(), __y.begin()); } //重载operator<运算符,使用的是STL泛型算法 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 bool operator!=(const _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>& __x, const _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>& __y) { return !(__x == __y); } 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 __y < __x; } 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 !(__y < __x); } 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 < __y); } 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(); _M_node_count = 0; _M_key_compare = __x._M_key_compare; if (__x._M_root() == 0) { _M_root() = 0; _M_leftmost() = _M_header; _M_rightmost() = _M_header; } else { _M_root() = _M_copy(__x._M_root(), _M_header); _M_leftmost() = _S_minimum(_M_root()); _M_rightmost() = _S_maximum(_M_root()); _M_node_count = __x._M_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> ::_M_insert(_Base_ptr __x_, _Base_ptr __y_, const _Value& __v) {//参数x_为新值插入点,参数y_为插入点之父节点,参数v 为新值 _Link_type __x = (_Link_type) __x_; _Link_type __y = (_Link_type) __y_; _Link_type __z; if (__y == _M_header || __x != 0 || _M_key_compare(_KeyOfValue()(__v), _S_key(__y))) { __z = _M_create_node(__v);//创建值为v的节点z _S_left(__y) = __z; // also makes _M_leftmost() = __z // when __y == _M_header if (__y == _M_header) { _M_root() = __z; _M_rightmost() = __z; } else if (__y == _M_leftmost())//若y为最左节点 _M_leftmost() = __z; // maintain _M_leftmost() pointing to min node } else { __z = _M_create_node(__v); _S_right(__y) = __z; if (__y == _M_rightmost()) _M_rightmost() = __z; // maintain _M_rightmost() pointing to max node } _S_parent(__z) = __y;//设定新节点的父节点 _S_left(__z) = 0;//设定新节点的左孩子 _S_right(__z) = 0;//设定新节点的右孩子 _Rb_tree_rebalance(__z, _M_header->_M_parent);//调整RB-Tree使其满足性质 ++_M_node_count;//节点数增加1 return iterator(__z);//返回新节点迭代器 } 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 = _M_header; _Link_type __x = _M_root();//从根节点开始 while (__x != 0) {//从根节点开始,往下寻找合适插入点 __y = __x; //判断新插入节点值与当前节点x值的大小,以便判断往x的左边走还是往右边走 __x = _M_key_compare(_KeyOfValue()(__v), _S_key(__x)) ? _S_left(__x) : _S_right(__x); } return _M_insert(__x, __y, __v); } // 安插新值;节点键值不允许重复,若重复则安插无效。 // 注意,传回值是个pair,第一元素是个 RB-tree 迭代器,指向新增节点, // 第二元素表示安插成功与否。 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 = _M_header; _Link_type __x = _M_root();//从根节点开始 bool __comp = true; while (__x != 0) {//从根节点开始,往下寻找合适插入点 __y = __x; //判断新插入节点值与当前节点x值的大小,以便判断往x的左边走还是往右边走 __comp = _M_key_compare(_KeyOfValue()(__v), _S_key(__x)); __x = __comp ? _S_left(__x) : _S_right(__x); } //离开while循环之后,y所指即为安插点的父节点,x必为叶子节点 iterator __j = iterator(__y);//令迭代器j指向插入节点之父节点y if (__comp)//若为真 if (__j == begin())//若插入点之父节点为最左节点 return pair<iterator,bool>(_M_insert(__x, __y, __v), true); else//否则(插入点之父节点不在最左节点) --__j;//调整j // 小于新值(表示遇「小」,将安插于右侧) if (_M_key_compare(_S_key(__j._M_node), _KeyOfValue()(__v))) return pair<iterator,bool>(_M_insert(__x, __y, __v), true); //若运行到这里,表示键值有重复,不应该插入 return pair<iterator,bool>(__j, false); } 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._M_node == _M_header->_M_left) { // begin() if (size() > 0 && _M_key_compare(_KeyOfValue()(__v), _S_key(__position._M_node))) return _M_insert(__position._M_node, __position._M_node, __v); // first argument just needs to be non-null else return insert_unique(__v).first; } else if (__position._M_node == _M_header) { // end() if (_M_key_compare(_S_key(_M_rightmost()), _KeyOfValue()(__v))) return _M_insert(0, _M_rightmost(), __v); else return insert_unique(__v).first; } else { iterator __before = __position; --__before; if (_M_key_compare(_S_key(__before._M_node), _KeyOfValue()(__v)) && _M_key_compare(_KeyOfValue()(__v), _S_key(__position._M_node))) { if (_S_right(__before._M_node) == 0) return _M_insert(0, __before._M_node, __v); else return _M_insert(__position._M_node, __position._M_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._M_node == _M_header->_M_left) { // begin() if (size() > 0 && !_M_key_compare(_S_key(__position._M_node), _KeyOfValue()(__v))) return _M_insert(__position._M_node, __position._M_node, __v); // first argument just needs to be non-null else return insert_equal(__v); } else if (__position._M_node == _M_header) {// end() if (!_M_key_compare(_KeyOfValue()(__v), _S_key(_M_rightmost()))) return _M_insert(0, _M_rightmost(), __v); else return insert_equal(__v); } else { iterator __before = __position; --__before; if (!_M_key_compare(_KeyOfValue()(__v), _S_key(__before._M_node)) && !_M_key_compare(_S_key(__position._M_node), _KeyOfValue()(__v))) { if (_S_right(__before._M_node) == 0) return _M_insert(0, __before._M_node, __v); else return _M_insert(__position._M_node, __position._M_node, __v); // first argument just needs to be non-null } else return insert_equal(__v); } } #ifdef __STL_MEMBER_TEMPLATES template <class _Key, class _Val, class _KoV, class _Cmp, class _Alloc> template<class _II> void _Rb_tree<_Key,_Val,_KoV,_Cmp,_Alloc> ::insert_equal(_II __first, _II __last) { for ( ; __first != __last; ++__first) insert_equal(*__first); } template <class _Key, class _Val, class _KoV, class _Cmp, class _Alloc> template<class _II> void _Rb_tree<_Key,_Val,_KoV,_Cmp,_Alloc> ::insert_unique(_II __first, _II __last) { for ( ; __first != __last; ++__first) insert_unique(*__first); } #else /* __STL_MEMBER_TEMPLATES */ template <class _Key, class _Val, class _KoV, class _Cmp, class _Alloc> void _Rb_tree<_Key,_Val,_KoV,_Cmp,_Alloc> ::insert_equal(const _Val* __first, const _Val* __last) { for ( ; __first != __last; ++__first) insert_equal(*__first); } template <class _Key, class _Val, class _KoV, class _Cmp, class _Alloc> void _Rb_tree<_Key,_Val,_KoV,_Cmp,_Alloc> ::insert_equal(const_iterator __first, const_iterator __last) { for ( ; __first != __last; ++__first) insert_equal(*__first); } template <class _Key, class _Val, class _KoV, class _Cmp, class _Alloc> void _Rb_tree<_Key,_Val,_KoV,_Cmp,_Alloc> ::insert_unique(const _Val* __first, const _Val* __last) { for ( ; __first != __last; ++__first) insert_unique(*__first); } template <class _Key, class _Val, class _KoV, class _Cmp, class _Alloc> void _Rb_tree<_Key,_Val,_KoV,_Cmp,_Alloc> ::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._M_node, _M_header->_M_parent, _M_header->_M_left, _M_header->_M_right); destroy_node(__y); --_M_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 _Key, class _Val, class _KoV, class _Compare, class _Alloc> typename _Rb_tree<_Key, _Val, _KoV, _Compare, _Alloc>::_Link_type _Rb_tree<_Key,_Val,_KoV,_Compare,_Alloc> ::_M_copy(_Link_type __x, _Link_type __p) { // structural copy. __x and __p must be non-null. _Link_type __top = _M_clone_node(__x); __top->_M_parent = __p; __STL_TRY { if (__x->_M_right) __top->_M_right = _M_copy(_S_right(__x), __top); __p = __top; __x = _S_left(__x); while (__x != 0) { _Link_type __y = _M_clone_node(__x); __p->_M_left = __y; __y->_M_parent = __p; if (__x->_M_right) __y->_M_right = _M_copy(_S_right(__x), __y); __p = __y; __x = _S_left(__x); } } __STL_UNWIND(_M_erase(__top)); return __top; } template <class _Key, class _Value, class _KeyOfValue, class _Compare, class _Alloc> void _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc> ::_M_erase(_Link_type __x) { // erase without rebalancing while (__x != 0) { _M_erase(_S_right(__x)); _Link_type __y = _S_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 = _M_header; // Last node which is not less than __k. _Link_type __x = _M_root(); // Current node. while (__x != 0) if (!_M_key_compare(_S_key(__x), __k)) __y = __x, __x = _S_left(__x); else __x = _S_right(__x); iterator __j = iterator(__y); return (__j == end() || _M_key_compare(__k, _S_key(__j._M_node))) ? end() : __j; } //查找RB树中是否有键值为k的节点 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 = _M_header; /* Last node which is not less than __k. */ _Link_type __x = _M_root(); /* Current node. */ while (__x != 0) { if (!_M_key_compare(_S_key(__x), __k))//若k比当前节点x键值小 __y = __x, __x = _S_left(__x); else __x = _S_right(__x); } const_iterator __j = const_iterator(__y); return (__j == end() || _M_key_compare(__k, _S_key(__j._M_node))) ? end() : __j; } //计算RB树中键值为k的节点的个数 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 = _M_header; /* Last node which is not less than __k. */ _Link_type __x = _M_root(); /* Current node. */ while (__x != 0) if (!_M_key_compare(_S_key(__x), __k)) __y = __x, __x = _S_left(__x); else __x = _S_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 = _M_header; /* Last node which is not less than __k. */ _Link_type __x = _M_root(); /* Current node. */ while (__x != 0) if (!_M_key_compare(_S_key(__x), __k)) __y = __x, __x = _S_left(__x); else __x = _S_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 = _M_header; /* Last node which is greater than __k. */ _Link_type __x = _M_root(); /* Current node. */ while (__x != 0) if (_M_key_compare(__k, _S_key(__x))) __y = __x, __x = _S_left(__x); else __x = _S_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 = _M_header; /* Last node which is greater than __k. */ _Link_type __x = _M_root(); /* Current node. */ while (__x != 0) if (_M_key_compare(__k, _S_key(__x))) __y = __x, __x = _S_left(__x); else __x = _S_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)); } //计算从 node 至 root路径中的黑节点数量 inline int __black_count(_Rb_tree_node_base* __node, _Rb_tree_node_base* __root) { if (__node == 0) return 0; else { int __bc = __node->_M_color == _S_rb_tree_black ? 1 : 0;//若节点node为黑色,则bc为1 if (__node == __root)//判断node是否为根节点 return __bc; else return __bc + __black_count(__node->_M_parent, __root);//递归调用 } } //验证己生这棵树是否符合RB树条件 template <class _Key, class _Value, class _KeyOfValue, class _Compare, class _Alloc> bool _Rb_tree<_Key,_Value,_KeyOfValue,_Compare,_Alloc>::__rb_verify() const { //空树 if (_M_node_count == 0 || begin() == end()) return _M_node_count == 0 && begin() == end() && _M_header->_M_left == _M_header && _M_header->_M_right == _M_header; //最左节点到根节点的黑色节点数 int __len = __black_count(_M_leftmost(), _M_root()); //一下走访整个RB树,针对每个节点(从最小到最大)…… for (const_iterator __it = begin(); __it != end(); ++__it) { _Link_type __x = (_Link_type) __it._M_node; _Link_type __L = _S_left(__x); _Link_type __R = _S_right(__x); if (__x->_M_color == _S_rb_tree_red)//违背性质4 //如果一个节点是红色的,则它的两个孩子节点都是黑色的。 if ((__L && __L->_M_color == _S_rb_tree_red) || (__R && __R->_M_color == _S_rb_tree_red)) return false; //以下是违背二叉查找树性质 //节点的左孩子节点键值小于该节点键值 //节点的右孩子节点键值大于该节点键值 if (__L && _M_key_compare(_S_key(__x), _S_key(__L))) return false; if (__R && _M_key_compare(_S_key(__R), _S_key(__x))) return false; //[叶子结点到root]路径内的黑色节点数,与[最左节点至root]路径内的黑色节点不同。不符合RB树要求 //违背性质5 if (!__L && !__R && __black_count(__x, _M_root()) != __len) return false; } if (_M_leftmost() != _Rb_tree_node_base::_S_minimum(_M_root())) return false; // 最左节点不为最小节点,不符合二叉查找树的要求 if (_M_rightmost() != _Rb_tree_node_base::_S_maximum(_M_root())) return false;// 最右节点不为最大节点,不符不符合二叉查找树的要求 return true; }
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