【C++】红黑树
目录
一 概念
红黑树，是一种二叉搜索树，但在每个结点上增加一个存储位表示结点的颜色，可以是Red或 Black。 通过对任何一条从根到叶子的路径上各个结点着色方式的限制，红黑树确保没有一条路 径会比其他路径长出俩倍，因而是接近平衡的。
时间复杂度: Log(N)
红黑树是近似的平衡树，没有什么最坏情况，插入的时间复杂度为O(log(N))
红黑树的性质
1. 根节点是黑色的
2. 如果一个节点是红色的，则它的两个孩子结点是黑色的(没有连续的红色节点)
3. 对于每个结点，从该结点到其所有后代叶结点的简单路径上，均包含相同数目的黑色结点
4. 每个叶子结点都是黑色的(此处的叶子结点指的是空结点)
为什么满足上面的性质，红黑树就能保证：其最长路径中节点个数不会超过最短路径节点 个数的两倍？
最短路径: 全黑
最长路径: 一黑一红
二 红黑树的模拟实现
1 节点的设置
插入红色节点树的性质可能不会改变，而插入黑色节点每次都会违反每条路径黑色节点的数量相等的规则
节点需要默认红色, 因为插入红色节点, 路径可能不会变化,
//构建红黑树节点
enum Colour
{
RED,
BLACK
};
template<class K, class V>
struct RBTreeNode
{
RBTreeNode<K, V>* _left;
RBTreeNode<K, V>* _right;
RBTreeNode<K, V>* _parent;
pair<K, V> _kv;
Colour _col;
RBTreeNode(const pair<K, V>& kv)
:_left(nullptr)
, _right(nullptr)
, _parent(nullptr)
, _kv(kv)
, _col(RED)
{}
};
2 基本框架的实现
//构建红黑树节点
enum Colour
{
RED,
BLACK
};
template<class K, class V>
struct RBTreeNode
{
RBTreeNode<K, V>* _left;
RBTreeNode<K, V>* _right;
RBTreeNode<K, V>* _parent;
pair<K, V> _kv;
Colour _col;
RBTreeNode(const pair<K, V>& kv)
:_left(nullptr)
, _right(nullptr)
, _parent(nullptr)
, _kv(kv)
, _col(RED)
{}
};
template<class K, class V>
class RBTree
{
typedef RBTreeNode<K, V> Node;
public:
bool Insert(const pair<K, V>& kv)
{
if (_root == nullptr)
{
_root = new Node(kv);
_root->_col = BLACK;
return true;
}
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (cur->_kv.first < kv.first)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_kv.first > kv.first)
{
parent = cur;
cur = cur->_left;
}
else
{
return false;
}
}
cur = new Node(kv); // 红色的
if (parent->_kv.first < kv.first)
{
parent->_right = cur;
}
else
{
parent->_left = cur;
}
cur->_parent = parent;
//旋转操作
return true;
}
//左旋操作
//右旋操作
void _InOrder(Node* root)
{
if (root == nullptr)
return;
_InOrder(root->_left);
cout << root->_kv.first << endl;
_InOrder(root->_right);
}
void InOrder()
{
_InOrder(_root);
}
size_t Size()
{
return _Size(_root);
}
size_t _Size(Node* root)
{
if (root == NULL)
return 0;
return _Size(root->_left)
+ _Size(root->_right) + 1;
}
Node* Find(const K& key)
{
Node* cur = _root;
while (cur)
{
if (cur->_kv.first < key)
{
cur = cur->_right;
}
else if (cur->_kv.first > key)
{
cur = cur->_left;
}
else
{
return cur;
}
}
return NULL;
}
int _Height(Node* root)
{
if (root == nullptr)
return 0;
int leftHeight = _Height(root->_left);
int rightHeight = _Height(root->_right);
return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;
}
int Height()
{
return _Height(_root);
}
int GetRotateSize()
{
return rotateSize;//统计旋转次数
}
private:
Node* _root = nullptr;
int rotateSize = 0;
};三 插入操作
1 情况一
//旋转操作
while (parent && parent->_col == RED)
{
Node* grandfather = parent->_parent;
if (parent == grandfather->_left)
{
Node* uncle = grandfather->_right;
// 情况一：叔叔存在且为红
if (uncle && uncle->_col == RED)
{
// 变色
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上处理
cur = grandfather;
parent = cur->_parent;
}
else
{
// 情况二：叔叔不存在或者存在且为黑
// 旋转+变色
}
}
else
{
Node* uncle = grandfather->_left;
// 情况一：叔叔存在且为红
if (uncle && uncle->_col == RED)
{
// 变色
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上处理
cur = grandfather;
parent = cur->_parent;
}
else
{
// 情况二：叔叔不存在或者存在且为黑
// 旋转+变色
}
}
}
_root->_col = BLACK;//根节点是黑色2 情况二
bool Insert(const pair<K, V>& kv)
{
if (_root == nullptr)
{
_root = new Node(kv);
_root->_col = BLACK;
return true;
}
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (cur->_kv.first < kv.first)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_kv.first > kv.first)
{
parent = cur;
cur = cur->_left;
}
else
{
return false;
}
}
cur = new Node(kv); // 红色的
if (parent->_kv.first < kv.first)
{
parent->_right = cur;
}
else
{
parent->_left = cur;
}
cur->_parent = parent;
//旋转
while (parent && parent->_col == RED)
{
Node* grandfather = parent->_parent;
if (parent == grandfather->_left)
{
Node* uncle = grandfather->_right;
// 情况一：叔叔存在且为红
if (uncle && uncle->_col == RED)
{
// 变色
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上处理
cur = grandfather;
parent = cur->_parent;
}
else
{
// 情况二：叔叔不存在或者存在且为黑
// 旋转+变色
if (cur == parent->_left)
{
// g
// p u
// c
RotateR(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
}
else
{
// g
// p u
// c
RotateL(parent);
RotateR(grandfather);
cur->_col = BLACK;
grandfather->_col = RED;
}
break;
}
}
else
{
Node* uncle = grandfather->_left;
// 情况一：叔叔存在且为红
if (uncle && uncle->_col == RED)
{
// 变色
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上处理
cur = grandfather;
parent = cur->_parent;
}
else
{
// 情况二：叔叔不存在或者存在且为黑
// 旋转+变色
// g
// u p
// c
if (cur == parent->_right)
{
RotateL(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
}
else
{
// g
// u p
// c
RotateR(parent);
RotateL(grandfather);
cur->_col = BLACK;
grandfather->_col = RED;
}
break;
}
}
}
_root->_col = BLACK;//根节点是黑色
return true;
}3 左右旋操作
//左旋操作
void RotateL(Node* parent)
{
++rotateSize;
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
subRL->_parent = parent;
subR->_left = parent;
Node* ppnode = parent->_parent;
parent->_parent = subR;
if (parent == _root)
{
_root = subR;
subR->_parent = nullptr;
}
else
{
if (ppnode->_left == parent)
{
ppnode->_left = subR;
}
else
{
ppnode->_right = subR;
}
subR->_parent = ppnode;
}
}
//右旋操作
void RotateR(Node* parent)
{
++rotateSize;
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
subLR->_parent = parent;
subL->_right = parent;
Node* ppnode = parent->_parent;
parent->_parent = subL;
if (parent == _root)
{
_root = subL;
subL->_parent = nullptr;
}
else
{
if (ppnode->_left == parent)
{
ppnode->_left = subL;
}
else
{
ppnode->_right = subL;
}
subL->_parent = ppnode;
}
}四 判断是否为红黑树
bool Check(Node* cur, int blackNum, int refBlackNum)
{
if (cur == nullptr)
{
if (refBlackNum != blackNum)
{
cout << "黑色节点的数量不相等" << endl;
return false;
}
return true;
}
if (cur->_col == RED && cur->_parent->_col == RED)
{
cout << cur->_kv.first << "存在连续的红色节点" << endl;
return false;
}
if (cur->_col == BLACK)
++blackNum;
return Check(cur->_left, blackNum, refBlackNum)
&& Check(cur->_right, blackNum, refBlackNum);
}
bool IsBalance()
{
if (_root && _root->_col == RED)
return false;
int refBlackNum = 0;
Node* cur = _root;
while (cur)
{
if (cur->_col == BLACK)
refBlackNum++;
cur = cur->_left;
}
return Check(_root, 0, refBlackNum);
}
总结: 本节主要了解和熟悉红黑树基础结构就行 继续加油!
原文地址：https://blog.csdn.net/yf214wxy/article/details/142918632
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