红黑树

红黑树是一棵二叉搜索树，它在每个节点上增加了一个存储位来表示节点的颜色，可以是Red或Black。通过对任何一条从根到叶子简单路径上的颜色来约束，红黑树保证最长路径不超过最短路径的两倍，因而近似于平衡。
红黑树是满足下面红黑性质的二叉搜索树

每个节点，不是红色就是黑色的

根节点是黑色的

如果一个节点是红色的，则它的两个子节点是黑色的(没有连续的红节点)

对每个节点，从该节点到其所有后代叶节点的简单路径上，均包含相同数目的黑色节点。（每条路径的黑色节点的数量相等）

每个叶子节点都是黑色的（这里的叶子节点是指的NIL节点（空节点））

插入的几种情况

ps:cur为当前节点，p为父节点，g为祖父节点，u为叔叔节点
1.第一种情况
cur为红，p为红，g为黑，u存在且为红
则将p,u改为黑，g改为红，然后把g当成cur，继续向上调整。



2.第二种情况
cur为红，p为红，g为黑，u不存在/u为黑
p为g的左孩子，cur为p的左孩子，则进行右单旋转；相反，p为g的右孩子，cur为p的右孩子，则进行左单旋转
p、g变色--p变黑，g变红



3.第三种情况
cur为红，p为红，g为黑，u不存在/u为黑
p为g的左孩子，cur为p的右孩子，则针对p做左单旋转；相反，p为g的右孩子，cur为p的左孩子，则针对p做右单旋转
则转换成了情况2



#pragma once
#include<iostream>
using namespace std;

enum Colour
{
RED,
BLACK,
};
template<class K,class V>
struct RBTreeNode
{
RBTreeNode<K, V>* _left;
RBTreeNode<K, V>* _right;
RBTreeNode<K, V>* _parent;
K _key;
V _value;
Colour _col;
RBTreeNode(const K& key, const V& value)
:_key(key)
, _value(value)
, _left(NULL)
, _right(NULL)
, _parent(NULL)
, _col(RED)
{}
};
template<class K, class V>
class RBTree
{
typedef RBTreeNode<K, V> Node;
public:
RBTree()
:_root(NULL)
{}
bool Insert(const K& key, const V& value)
{
if (_root == NULL)
{
_root = new Node(key, value);
_root->_col = BLACK;
return true;
}
Node* parent = NULL;
Node* cur = _root;
while (cur)
{
if (cur->_key > key)
{
parent = cur;
cur = cur->_left;
}
else if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else
{
return false;
}
}
cur = new Node(key, value);
if (parent->_key < key)
{
parent->_right = cur;
cur->_parent = parent;
}
else
{
parent->_left = cur;
cur->_parent = parent;
}
while (cur != _root && parent->_col == RED)//grandfather肯定不为空，根节点的颜色为黑色
{
Node* grandfather = parent->_parent;
if (grandfather->_left == parent)//parent为的grandfather左孩子
{
Node* uncle = grandfather->_right;
if (uncle && uncle->_col == RED)//uncle存在并且为红色的
{
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
cur = grandfather;
parent = cur->_parent;
}
else
{
if (cur = parent->_right)//cur为parent的右孩子，先把它左单旋为左孩子
{
RotateL(parent);
swap(parent, cur);
}
parent->_col = BLACK;
grandfather->_col = RED;
RotateR(grandfather);
break;
}
}
else
{
Node* uncle = grandfather->_left;
if (uncle && uncle->_col == RED)
{
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
cur = grandfather;
parent = cur->_parent;
}
else
{
if (parent->_left == cur)
{
RotateR(parent);
swap(parent, cur);
}
parent->_col = BLACK;
grandfather->_col = RED;
RotateL(grandfather);
break;
}
}
}
_root->_col = BLACK;
}
void Inorder()
{
_Inorder(_root);
cout << endl;
}
bool IsBalance()
{
if (_root == NULL)
{
return true;
}
if (_root->_col == RED)//根节点必须是黑色的
{
return false;
}
Node* cur = _root;
int k = 0;
while (cur)
{
if (cur->_col == BLACK)
{
k++;
}
cur = cur->_left;
}
int count = 0;
return _IsBalance(_root, k, count);
}
Node* Find(const K& key)
{
if (_root == NULL)
{
return NULL;
}
Node* cur = _root;
while (cur)
{
if (cur->_key > key)
{
cur = cur->_left;
}
else if (cur->_key < key)
{
cur = cur->_right;
}
else
{
return cur;
}
}
return NULL;
}
protected:
bool _IsBalance(Node* root, const int k, int count)
{
if (root == NULL)
{
return true;
}
if (root->_col == RED && root->_parent->_col == RED)
{
cout << "出现连续的红色节点" << root->_key << endl;
return false;
}
if (root->_col == BLACK)
{
++count;
}
if (root->_left == NULL && root->_right == NULL && count != k)
{
cout << "黑色节点个数不相等" << root->_key << endl;
return false;
}
return _IsBalance(root->_left, k, count) && _IsBalance(root->_right, k, count);
}
void _Inorder(Node* root)
{
if (root == NULL)
{
return;
}
_Inorder(root->_left);
cout << root->_key << " ";
_Inorder(root->_right);
}
void RotateL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
{
subRL->_parent = parent;
}
Node* ppNode = parent->_parent;
subR->_left = parent;
parent->_parent = subR;
if (ppNode == NULL)
{
_root = subR;
}
else
{
if (ppNode->_left == parent)
{
ppNode->_left = subR;
}
else
{
ppNode->_right = subR;
}
}
subR->_parent = ppNode;
}
void RotateR(Node* parent)
{
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
{
subLR->_parent = parent;
}
Node* ppNode = parent->_parent;
subL->_right = parent;
parent->_parent = subL;
if (ppNode == NULL)
{
_root = subL;
}
else
{
if (ppNode->_left == parent)
{
ppNode->_left = subL;
}
else
{
ppNode->_right = subL;
}
}
subL->_parent = ppNode;
}
protected:
Node* _root;
};