首页 > 代码库 > 红黑树（rb_tree） 源代码
红黑树（rb_tree） 源代码
#ifndef__SGI_STL_INTERNAL_TREE_H
#define__SGI_STL_INTERNAL_TREE_H
/*
本檔實作Red-black tree（紅-黑樹）class，用以實作 STL 關聯式容器（如set,
multiset,map, multimap）。所用之insertion和deletion演算法係以
Cormen,Leiserson和 Rivest所著之Introduction to Algorithms
(MIT Press,1990)一書為基礎，唯以下兩點不同：
(1) header不僅指向 root，也指向紅黑樹的最左節點，以便實作出常數時間之
begin()；並且也指向紅黑樹的最右節點，以便set相關泛型演算法（如set_union
等等）有線性時間之表現。
(2)當一個即將被刪除之節點擁有兩個子節點時，它的successor node is
relinked into its place, rather than copied,如此一來唯一失效（invalidated）的迭代器就只是那些referring to the deletednode.
*/
#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;// 紅色為 0
const__rb_tree_color_type__rb_tree_black =true; //黑色為 1
struct__rb_tree_node_base
{
typedef __rb_tree_color_type color_type;
typedef __rb_tree_node_base* base_ptr;
color_type color; // 節點顏色，非紅即黑。
base_ptr parent; // RB樹的許多操作，必須知道父節點。
base_ptr left; //指向左節點。
base_ptr right; // 指向右節點。
static base_ptr minimum(base_ptr x)
{
while (x->left != 0) x = x->left; //一直向左走，就會找到最小值，
return x; //這是二元搜尋樹的特性。
}
static base_ptr maximum(base_ptr x)
{
while (x->right != 0) x = x->right; // 一直向右走，就會找到最大值，
return x; //這是二元搜尋樹的特性。
}
};
template <classValue>
struct__rb_tree_node :public __rb_tree_node_base
{
typedef __rb_tree_node<Value>*link_type;
Value value_field; // 節點實值
};
struct__rb_tree_base_iterator
{
typedef __rb_tree_node_base::base_ptr base_ptr;
typedef bidirectional_iterator_tagiterator_category;
typedef ptrdiff_t difference_type;
base_ptr node; // 它用來與容器之間產生一個連結關係（make a reference）
// 以下其實可實作於operator++ 內，因為再無他處會呼叫此函式了。
void increment()
{
if (node->right != 0) { //如果有右子節點。狀況(1)
node = node->right; //就向右走
while (node->left != 0) //然後一直往左子樹走到底
node = node->left; //即是解答
}
else { //沒有右子節點。狀況(2)
base_ptr y = node->parent; //找出父節點
while (node == y->right) { //如果現行節點本身是個右子節點，
node = y; //就一直上溯，直到「不為右子節點」止。
y = y->parent;
}
if (node->right != y) //「若此時的右子節點不等於此時的父節點」。
node = y; //狀況(3)此時的父節點即為解答。
// 否則此時的node為解答。狀況(4)
}
// 注意，以上判斷「若此時的右子節點不等於此時的父節點」，是為了應付一種
// 特殊情況：我們欲尋找根節點的下一節點，而恰巧根節點無右子節點。
// 當然，以上特殊作法必須配合RB-tree 根節點與特殊之header之間的
// 特殊關係。
}
// 以下其實可實作於operator-- 內，因為再無他處會呼叫此函式了。
void decrement()
{
if (node->color == __rb_tree_red&& //如果是紅節點，且
node->parent->parent == node) //父節點的父節點等於自己，
node = node->right; //狀況(1)右子節點即為解答。
// 以上情況發生於node為header時（亦即node 為end() 時）。
// 注意，header之右子節點即 mostright，指向整棵樹的 max 節點。
else if (node->left != 0) { //如果有左子節點。狀況(2)
base_ptr y = node->left; //令y指向左子節點
while (y->right != 0) //當y有右子節點時
y = y->right; //一直往右子節點走到底
node = y; //最後即為答案
}
else { //既非根節點，亦無左子節點。
base_ptr y = node->parent; //狀況(3)找出父節點
while (node == y->left) { //當現行節點身為左子節點
node = y; //一直交替往上走，直到現行節點
y = y->parent; //不為左子節點
}
node = y; //此時之父節點即為答案
}
}
};
template <classValue, 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, constValue&, 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 booloperator==(const __rb_tree_base_iterator& x,
const__rb_tree_base_iterator& y) {
return x.node == y.node;
// 兩個迭代器相等，意指其所指的節點相等。
}
inline booloperator!=(const __rb_tree_base_iterator& x,
const __rb_tree_base_iterator&y) {
return x.node != y.node;
// 兩個迭代器不等，意指其所指的節點不等。
}
#ifndef __STL_CLASS_PARTIAL_SPECIALIZATION
inlinebidirectional_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 <classValue, class Ref, class Ptr>
inline Value*value_type(const __rb_tree_iterator<Value, Ref, Ptr>&) {
return (Value*) 0;
}
#endif /*__STL_CLASS_PARTIAL_SPECIALIZATION */
//以下都是全域函式：__rb_tree_rotate_left(),__rb_tree_rotate_right(),
// __rb_tree_rebalance(),__rb_tree_rebalance_for_erase()
//新節點必為紅節點。如果安插處之父節點亦為紅節點，就違反紅黑樹規則，此時必須
//做樹形旋轉（及顏色改變，在程式它處）。
inline void
__rb_tree_rotate_left(__rb_tree_node_base*x, __rb_tree_node_base*&root)
{
// x 為旋轉點
__rb_tree_node_base* y = x->right; //令y為旋轉點的右子節點
x->right = y->left;
if (y->left !=0)
y->left->parent = x; //別忘了回馬槍設定父節點
y->parent = x->parent;
// 令y 完全頂替x 的地位（必須將 x對其父節點的關係完全接收過來）
if (x == root) // x為根節點
root = y;
else if (x == x->parent->left) // x為其父節點的左子節點
x->parent->left = y;
else // x為其父節點的右子節點
x->parent->right = y;
y->left = x;
x->parent = y;
}
//新節點必為紅節點。如果安插處之父節點亦為紅節點，就違反紅黑樹規則，此時必須
//做樹形旋轉（及顏色改變，在程式它處）。
inline void
__rb_tree_rotate_right(__rb_tree_node_base*x, __rb_tree_node_base*&root)
{
// x 為旋轉點
__rb_tree_node_base* y = x->left; // y為旋轉點的左子節點
x->left = y->right;
if (y->right != 0)
y->right->parent = x; // 別忘了回馬槍設定父節點
y->parent = x->parent;
// 令y 完全頂替x 的地位（必須將 x對其父節點的關係完全接收過來）
if (x == root) // x為根節點
root = y;
else if (x == x->parent->right) // x為其父節點的右子節點
x->parent->right = y;
else // x為其父節點的左子節點
x->parent->left = y;
y->right = x;
x->parent = y;
}
//重新令樹形平衡（改變顏色及旋轉樹形）
//參數一為新增節點，參數二為root
inline void
__rb_tree_rebalance(__rb_tree_node_base*x, __rb_tree_node_base*&root)
{
x->color = __rb_tree_red; // 新節點必為紅
while (x != root &&x->parent->color == __rb_tree_red) { //父節點為紅
if (x->parent ==x->parent->parent->left) { //父節點為祖父節點之左子節點
__rb_tree_node_base* y =x->parent->parent->right; // 令y為伯父節點
if (y && y->color ==__rb_tree_red) { //伯父節點存在，且為紅
x->parent->color =__rb_tree_black; // 更改父節點為黑
y->color = __rb_tree_black; //更改伯父節點為黑
x->parent->parent->color =__rb_tree_red; // 更改祖父節點為紅
x = x->parent->parent;
}
else { //無伯父節點，或伯父節點為黑
if (x == x->parent->right) { //如果新節點為父節點之右子節點
x = x->parent;
__rb_tree_rotate_left(x, root);// 第一參數為左旋點
}
x->parent->color =__rb_tree_black; //改變顏色
x->parent->parent->color =__rb_tree_red;
__rb_tree_rotate_right(x->parent->parent, root); //第一參數為右旋點
}
}
else { //父節點為祖父節點之右子節點
__rb_tree_node_base* y =x->parent->parent->left; //令y為伯父節點
if (y && y->color ==__rb_tree_red) { //有伯父節點，且為紅
x->parent->color =__rb_tree_black; //更改父節點為黑
y->color = __rb_tree_black; // 更改伯父節點為黑
x->parent->parent->color =__rb_tree_red; // 更改祖父節點為紅
x = x->parent->parent; //準備繼續往上層檢查...
}
else { //無伯父節點，或伯父節點為黑
if (x == x->parent->left) { //如果新節點為父節點之左子節點
x = x->parent;
__rb_tree_rotate_right(x, root);// 第一參數為右旋點
}
x->parent->color =__rb_tree_black; //改變顏色
x->parent->parent->color =__rb_tree_red;
__rb_tree_rotate_left(x->parent->parent, root); //第一參數為左旋點
}
}
} // while結束
root->color = __rb_tree_black; //根節點永遠為黑
}
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 hasat most one non-null child. y == z.
x = y->right; // x mightbe null.
else
if (y->right == 0) // z hasexactly one non-null child. y == z.
x = y->left; // x isnot 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) { // relinky 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 mustbe 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 tonode 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 asabove, 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 <classKey, class Value, class KeyOfValue, class Compare,
class Alloc = alloc>
classrb_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:
// 注意，沒有定義 iterator（喔，不，定義在後面）
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(); // 配置空間
__STL_TRY {
construct(&tmp->value_field, x);// 建構內容
}
__STL_UNWIND(put_node(tmp));
return tmp;
}
link_type clone_node(link_type x) { // 複製一個節點（的值和色）
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); // 解構內容
put_node(p); // 釋還記憶體
}
protected:
// RB-tree 只以三筆資料表現。
size_type node_count;// 追蹤記錄樹的大小（節點數量）
link_type header;
Compare key_compare;// 節點間的鍵值大小比較準則。應該會是個function object。
// 以下三個函式用來方便取得header 的成員
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; }
// 以下六個函式用來方便取得節點x 的成員
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) { returnKeyOfValue()(value(x)); }
static color_type& color(link_type x) { return (color_type&)(x->color); }
// 以下六個函式用來方便取得節點x 的成員
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); }
// 求取極大值和極小值。node class有實作此功能，交給它們完成即可。
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
typedefreverse_iterator<const_iterator> const_reverse_iterator;
typedef reverse_iterator<iterator>reverse_iterator;
#else /*__STL_CLASS_PARTIAL_SPECIALIZATION */
typedefreverse_bidirectional_iterator<iterator, value_type, reference,
difference_type>
reverse_iterator;
typedefreverse_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(); // 產生一個節點空間，令 header指向它
color(header) = __rb_tree_red;// 令header 為紅色，用來區分 header
// 和 root（在 iterator.operator++ 中）
root() = 0;
leftmost() = header; // 令header 的左子節點為自己。
rightmost() = header; // 令header 的右子節點為自己。
}
public:
// allocation/deallocation
rb_tree(const Compare& comp =Compare())
: node_count(0), key_compare(comp) { init(); }
// 以另一個rb_tree 物件x 為初值
rb_tree(const rb_tree<Key, Value, KeyOfValue, Compare, Alloc>&x)
: node_count(0), key_compare(x.key_compare)
{
header = get_node(); // 產生一個節點空間，令 header指向它
color(header) = __rb_tree_red; //令header 為紅色
if (x.root() == 0) { // 如果x 是個空白樹
root() = 0;
leftmost() = header; // 令header 的左子節點為自己。
rightmost() = header; // 令header 的右子節點為自己。
}
else { // x 不是一個空白樹
__STL_TRY {
root() = __copy(x.root(), header); // ???
}
__STL_UNWIND(put_node(header));
leftmost() = minimum(root()); //令header 的左子節點為最小節點
rightmost() = maximum(root()); //令header 的右子節點為最大節點
}
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 { returnkey_compare; }
iterator begin() { returnleftmost(); } // RB樹的起頭為最左（最小）節點處
const_iterator begin() const { returnleftmost(); }
iterator end() { returnheader; } // RB 樹的終點為header所指處
const_iterator end() const { returnheader; }
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 { returnnode_count == 0; }
size_type size() const { returnnode_count; }
size_type max_size() const { returnsize_type(-1); }
void swap(rb_tree<Key, Value, KeyOfValue, Compare, Alloc>&t) {
// RB-tree 只以三個資料成員表現。所以互換兩個 RB-trees時，
// 只需將這三個成員互換即可。
__STD::swap(header, t.header);
__STD::swap(node_count, t.node_count);
__STD::swap(key_compare, t.key_compare);
}
public:
// insert/erase
// 將x 安插到 RB-tree中（保持節點值獨一無二）。
pair<iterator,bool> insert_unique(const value_type& x);
// 將x 安插到 RB-tree中（允許節點值重複）。
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:
// 集合（set）的各種操作行為:
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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
inline booloperator==(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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
inline booloperator<(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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
inline voidswap(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 <classKey, 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 thatKey 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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
typenamerb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator
rb_tree<Key,Value, KeyOfValue, Compare, Alloc>::
__insert(base_ptrx_, base_ptry_, const Value&v) {
//參數x_為新值安插點，參數y_為安插點之父節點，參數v為新值。
link_type x = (link_type) x_;
link_type y = (link_type) y_;
link_type z;
// key_compare 是鍵值大小比較準則。應該會是個function object。
if (y == header || x != 0 || key_compare(KeyOfValue()(v), key(y))){
z = create_node(v); // 產生一個新節點
left(y) = z; //這使得當 y即為 header時，leftmost() = z
if (y == header) {
root() = z;
rightmost() = z;
}
else if (y == leftmost()) //如果y為最左節點
leftmost() = z; //維護leftmost()，使它永遠指向最左節點
}
else {
z = create_node(v); // 產生一個新節點
right(y) = z; // 令新節點成為安插點之父節點y 的右子節點
if (y == rightmost())
rightmost() = z; //維護rightmost()，使它永遠指向最右節點
}
parent(z) = y; //設定新節點的父節點
left(z) = 0; //設定新節點的左子節點
right(z) = 0; //設定新節點的右子節點
// 新節點的顏色將在 __rb_tree_rebalance()設定（並調整）
__rb_tree_rebalance(z, header->parent); // 參數一為新增節點，參數二為root
++node_count; //節點數累加
return iterator(z); // 傳回一個迭代器，指向新增節點
}
//安插新值；節點鍵值允許重複。
//注意，傳回值是一個RB-tree 迭代器，指向新增節點
template <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
typenamerb_tree<Key, Value, KeyOfValue, Compare, Alloc>::iterator
rb_tree<Key,Value, KeyOfValue, Compare, Alloc>::insert_equal(const Value& v)
{
link_type y = header;
link_type x = root(); //從根節點開始
while (x != 0) { //從根節點開始，往下尋找適當的安插點
y = x;
x = key_compare(KeyOfValue()(v), key(x)) ? left(x) : right(x);
// 以上，遇「大」則往左，遇「小於或等於」則往右
}
return __insert(x, y, v);
}
//安插新值；節點鍵值不允許重複，若重複則安插無效。
//注意，傳回值是個pair，第一元素是個RB-tree 迭代器，指向新增節點，
//第二元素表示安插成功與否。
template <classKey, 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(); //從根節點開始
bool comp = true;
while (x != 0) { //從根節點開始，往下尋找適當的安插點
y = x;
comp = key_compare(KeyOfValue()(v),key(x)); // v鍵值小於目前節點之鍵值？
x = comp ? left(x) : right(x); //遇「大」則往左，遇「小於或等於」則往右
}
// 離開while 迴圈之後，y所指即安插點之父節點（此時的它必為葉節點）
iterator j = iterator(y); //令迭代器j指向安插點之父節點y
if (comp) //如果離開while 迴圈時comp 為真（表示遇「大」，將安插於左側）
if (j == begin()) //如果安插點之父節點為最左節點
return pair<iterator,bool>(__insert(x, y, v),true);
// 以上，x為安插點，y為安插點之父節點，v為新值。
else //否則（安插點之父節點不為最左節點）
--j; //調整j，回頭準備測試...
if (key_compare(key(j.node),KeyOfValue()(v)))
// 小於新值（表示遇「小」，將安插於右側）
return pair<iterator,bool>(__insert(x, y, v),true);
// 進行至此，表示新值一定與樹中鍵值重複，那麼就不該插入新值。
return pair<iterator,bool>(j,false);
}
template <classKey, class Val, class KeyOfValue, class Compare, class Alloc>
typenamerb_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 argumentjust 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 argumentjust needs to be non-null
else
return insert_unique(v).first;
}
}
template <classKey, class Val, class KeyOfValue, class Compare, class Alloc>
typenamerb_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 argumentjust 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 argumentjust needs to be non-null
else
return insert_equal(v);
}
}
#ifdef__STL_MEMBER_TEMPLATES
template <classK, 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 <classK, 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 <classK, 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 <classK, class V, class KoV, class Cmp, class Al>
void
rb_tree<K, V,KoV, Cmp, Al>::insert_equal(const_iteratorfirst,
const_iterator last) {
for ( ; first != last; ++first)
insert_equal(*first);
}
template <classK, 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 <classK, class V, class KoV, class Cmp, class A>
void
rb_tree<K, V,KoV, Cmp, A>::insert_unique(const_iteratorfirst,
const_iterator last) {
for ( ; first != last; ++first)
insert_unique(*first);
}
#endif /*__STL_MEMBER_TEMPLATES */
template <classKey, 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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
typenamerb_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 <classK, class V, class KeyOfValue, class Compare, class Alloc>
typenamerb_tree<K, V, KeyOfValue, Compare, Alloc>::link_type
rb_tree<K, V,KeyOfValue, Compare, Alloc>::__copy(link_type x, link_type p) {
// structuralcopy. 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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
voidrb_tree<Key, Value, KeyOfValue, Compare, Alloc>::__erase(link_type x) {
// erasewithout rebalancing
while (x != 0) {
__erase(right(x));
link_type y = left(x);
destroy_node(x);
x = y;
}
}
template <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
voidrb_tree<Key, Value, KeyOfValue, Compare, Alloc>::erase(iterator first,
iterator last) {
if (first == begin() && last ==end())
clear();
else
while (first != last) erase(first++);
}
template <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
voidrb_tree<Key, Value, KeyOfValue, Compare, Alloc>::erase(const Key* first,
const Key* last) {
while (first != last) erase(*first++);
}
//尋找RB 樹中是否有鍵值為k 的節點
template <classKey, 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; // Lastnode which is not less than k.
link_type x = root(); // Currentnode.
while (x != 0)
// 以下，key_compare是節點鍵值大小比較準則。應該會是個function object。
if (!key_compare(key(x), k))
// 進行到這裡，表示x 鍵值大於k。遇到大值就向左走。
y = x, x = left(x); //注意語法!
else
// 進行到這裡，表示x 鍵值小於k。遇到小值就向右走。
x = right(x);
iterator j = iterator(y);
return (j == end()|| key_compare(k, key(j.node))) ? end() : j;
}
//尋找RB 樹中是否有鍵值為k 的節點
template <classKey, 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) {
// 以下，key_compare是節點鍵值大小比較準則。應該會是個function object。
if (!key_compare(key(x), k))
// 進行到這裡，表示x 鍵值大於k。遇到大值就向左走。
y = x, x = left(x); //注意語法!
else
// 進行到這裡，表示x 鍵值小於k。遇到小值就向右走。
x = right(x);
}
const_iterator j = const_iterator(y);
return (j == end() || key_compare(k, key(j.node)))? end() : j;
}
//計算RB 樹中鍵值為k 的節點個數
template <classKey, 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 <classKey, 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 isnot 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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
typenamerb_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 isnot 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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
typenamerb_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 isgreater 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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
typenamerb_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 isgreater 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 <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
inlinepair<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 <classKey, class Value, class KoV, class Compare, class Alloc>
inlinepair<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 {
returnpair<const_iterator,const_iterator>(lower_bound(k),upper_bound(k));
}
//計算從node 至root 路徑中的黑節點數量。
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); //累加
}
}
//驗證己身這棵樹是否符合 RB樹的條件
template <classKey, class Value, class KeyOfValue, class Compare, class Alloc>
bool
rb_tree<Key,Value, KeyOfValue, Compare, Alloc>::__rb_verify() const
{
// 空樹，符合RB樹標準
if(node_count == 0 || begin() == end())
return node_count== 0 &&begin() ==end() &&
header->left== header &&header->right== header;
// 最左（葉）節點至root 路徑內的黑節點數
int len = __black_count(leftmost(), root());
// 以下走訪整個RB樹，針對每個節點（從最小到最大）...
for (const_iterator it = begin(); it !=end(); ++it) {
link_type x = (link_type) it.node;//__rb_tree_base_iterator::node
link_type L = left(x); //這是左子節點
link_type R = right(x); // 這是右子節點
if (x->color == __rb_tree_red)
if ((L && L->color ==__rb_tree_red) ||
(R && R->color ==__rb_tree_red))
return false; //父子節點同為紅色，不符合 RB樹的要求。
if (L && key_compare(key(x), key(L)))// 目前節點的鍵值小於左子節點鍵值
return false; //不符合二元搜尋樹的要求。
if (R && key_compare(key(R), key(x))) //目前節點的鍵值大於右子節點鍵值
return false; //不符合二元搜尋樹的要求。
// 「葉節點至root」路徑內的黑節點數，與「最左節點至root」路徑內的黑節點數不同。
// 這不符合 RB樹的要求。
if (!L && !R && __black_count(x, root()) != len)
return false;
}
if (leftmost() != __rb_tree_node_base::minimum(root()))
return false; //最左節點不為最小節點，不符合二元搜尋樹的要求。
if (rightmost() != __rb_tree_node_base::maximum(root()))
return false; //最右節點不為最大節點，不符合二元搜尋樹的要求。
return true;
}
__STL_END_NAMESPACE
#endif /*__SGI_STL_INTERNAL_TREE_H */
// LocalVariables:
// mode:C++
// End: