#ifndef __RED_BLACK_TREE_H__
#define __RED_BLACK_TREE_H__ namespace lxf {
template <typename Key, typename Value>
class RedBlackTree {
struct Node {
enum Color { RED, BLACK };
Key key;
Value value;
Node *left;
Node *right;
Node *parent;
Color color;
Node(Key pkey, Value pvalue, Color pcolor) : key(pkey), value(pvalue), left(nullptr), right(nullptr), parent(nullptr), color(pcolor) {}
};
Node *root;
void rotateLeft(Node *x);
void rotateRight(Node *x); Node* deleteMin(Node* head);
Node* min(Node *head);
public:
void insert(Key key, Value value);
void erase(Key key);
RedBlackTree():root(nullptr) {}
}; /*
* 对红黑树的节点(x)进行左旋转
*
* 左旋示意图(对节点x进行左旋)：
* px px
* / /
* x y
* / \ --(左旋)--> / \ #
* lx y x ry
* / \ / \
* ly ry lx ly
*
*
*/
template<typename Key, typename Value>
inline void RedBlackTree<Key, Value>::rotateLeft(Node * x)
{
Node *y = x->right; x->right = y->left;
if (y->left != nullptr)
y->left->parent = x; y->parent = x->parent;
if (x->parent == nullptr)
root = y;
else {
if (x->parent->left == x)
x->parent->left = y;
else
x->parent->right = y;
}
y->left = x;
x->parent = y;
} /*
* 对红黑树的节点(y)进行右旋转
*
* 右旋示意图(对节点y进行左旋)：
* py py
* / /
* y x
* / \ --(右旋)--> / \ #
* x ry lx y
* / \ / \ #
* lx rx rx ry
*
*/
template<typename Key, typename Value>
inline void RedBlackTree<Key, Value>::rotateRight(Node * x)
{
Node *x = y->left;
y->left = x->right;
if (x->right != nullptr)
x->right->parent = y;
x->parent = y->parent;
if (y->parent == nullptr)
root = x;
else {
if (y == y->parent->right)
y->parent->right = x;
else
y->parent->left = x;
}
x->right = y;
y->parent = x;
} template<typename Key, typename Value>
inline typename RedBlackTree<Key, Value>::Node * RedBlackTree<Key, Value>::deleteMin(Node * head)
{
if (head == nullptr)
return nullptr;
Node *node = head;
Node *lastNode = nullptr;
while (node->left != nullptr)
{
lastNode = node;
node = node->left;
}
lastNode->left = node->right;
if (node->right != nullptr)
node->right->parent = lastNode;
return head;
} template<typename Key, typename Value>
inline typename RedBlackTree<Key, Value>::Node * RedBlackTree<Key, Value>::min(Node * head)
{
if (head == nullptr)
return nullptr;
Node *node = head;
while (node->left != nullptr)
node = node->left;
return node;
} template<typename Key, typename Value>
inline void RedBlackTree<Key, Value>::insert(Key key, Value value)
{
Node *parent = nullptr;
Node **ppNode = &root;
while (*ppNode != nullptr)
{
parent = *ppNode;
if (key < (*ppNode)->key)
ppNode = &((*ppNode)->left);
else
ppNode = &((*ppNode)->right);
}
if (*ppNode == nullptr) {
*ppNode = new Node(key, value, RED);
(*ppNode)->parent = parent;
} // 结点是根
if (parent == nullptr) {
root->color = Node::BLACK;
return;
} Node *node = *ppNode;
// 调整
while (node->parent->color == Node::RED)
{
Node *parent = node->parent;
Node *gparent = node->parent->parent;
if (parent == gparent->left)
{
Node *uncle = gparent->right;
if (uncle->color == RED)
{
parent->color = BLACK;
uncle->color = BLACK;
gparent->color = RED;
node = gparent;
}
else if (uncle->color == BLACK)
{
if (node == parent->right)
{
node = parent;
rotateLeft(node);
}
else
{
parent->color = BLACK;
gparent->color = RED;
rotateRight(gparent);
}
}
}
else if (parent == gparent->right)
{
Node *uncle = gparent->left;
if (uncle->color == RED)
{
parent->color = BLACK;
uncle->color = BLACK;
gparent->color = RED;
node = gparent;
}
else if (uncle->color == BLACK)
{
if (node == parent->left)
{
node = parent;
rotateRight(node);
}
else
{
parent->color = BLACK;
gparent->color = RED;
rotateLeft(gparent);
}
}
}
}
} template<typename Key, typename Value>
inline void RedBlackTree<Key, Value>::erase(Key key)
{
Node *lastNode = nullptr;
Node *node = root;
while (node != nullptr)
{
if (key < node->key) {
lastNode = node;
node = node->left;
}
else if (key > node->key) {
lastNode = node;
node = node->right;
}
else {
Node **plastNode = nullptr;
// 注意树根
if (lastNode == nullptr)
plastNode = &root;
else
plastNode = &lastNode;
// 无节点的情况
if (node->left == nullptr && node->right == nullptr)
{
if ((*plastNode)->left == node)
{
(*plastNode)->left = nullptr;
delete node;
}
else if ((*plastNode)->right == node)
{
(*plastNode)->right = nullptr;
delete node;
}
}
// 两个节点的情况
else if (node->left != nullptr && node->right != nullptr) {
Node *star = min(node->right);
star->right = deleteMin(node->right);
if (star->right != nullptr)
star->right->parent = star;
star->left = node->left;
if (star->left != nullptr)
star->left->parent = star;
delete node;
}
// 只有一个节点的情况
else if (node->left == nullptr) {
if ((*plastNode)->left == node) {
(*plastNode)->left = node->right;
if (node->right != nullptr)
node->right->parent = *plastNode;
delete node;
}
else if ((*plastNode)->right == node) {
(*plastNode)->right = node->right;
if (node->right != nullptr)
node->right->parent = *plastNode;
delete node;
}
}
else if (node->right == nullptr) {
if ((*plastNode)->right == node) {
(*plastNode)->right = node->left;
if (node->left != nullptr)
node->left->parent = *plastNode;
delete node;
}
else if ((*plastNode)->left == node) {
(*plastNode)->left = node->left;
if (node->left != nullptr)
node->left->parent = *plastNode;
delete node;
}
} }
} while (node != root && node->color == BLACK)
{
if (node == node->parent->left)
{
Node* brother = node->parent->right;
if (brother->color == RED)
{
brother->color = BLACK;
node->parent->color = RED;
rotateLeft(node->parent);
}
else
{
if (brother->left->color == BLACK && brother->right->color == BLACK)
{
brother->color = RED;
node = node->parent;
}
else if (brother->right->color == BLACK)
{
brother->color = RED;
brother->left->color = BLACK;
RotateRight(brother);
}
else if (brother->right->color == RED)
{
brother->color = node->parent->color;
node->parent->color = BLACK;
brother->right->color = BLACK;
rotateLeft(node->parent);
node = root;
}
}
}
else
{
Node* brother = node->parent->left;
if (brother->color == RED)
{
brother->color = BLACK;
node->parent->color = RED;
rotateRight(node->parent);
}
else
{
if (brother->left->color == BLACK && brother->right->color == BLACK)
{
brother->color = RED;
node = node->parent;
}
else if (brother->left->color == BLACK)
{
brother->color = RED;
brother->right->color = BLACK;
rotateLeft(brother);
}
else if (brother->left->color == RED)
{
brother->color = node->parent->color;
node->parent->color = BLACK;
brother->left->color = BLACK;
rotateRight(node->parent);
node = root;
}
}
}
}
node->parent = root; //最后将node置为根结点，
node->color = BLACK; //并改为黑色。
}
} #endif /*__RED_BLACK_TREE_H__*/