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Set_Map/Windows_Set_Map/RBTree.hpp

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博客 https://blog.lenyiin.com/set-map/ 的代码仓库
2024-09-24 00:01:11 +08:00
#pragma once
#include <iostream>
namespace Lenyiin
{
enum Colour
{
RED,
BLACK
};
template <class T>
struct RBTreeNode
{
RBTreeNode<T>* _left; // <20><><EFBFBD>ӽڵ<D3BD>
RBTreeNode<T>* _right; // <20><><EFBFBD>ӽڵ<D3BD>
RBTreeNode<T>* _parent; // <20><><EFBFBD>ڵ<EFBFBD>
T _data; // <20>ڵ<EFBFBD><DAB5>洢<EFBFBD><E6B4A2><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Colour _colour; // <20>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD>ɫ<EFBFBD><C9AB>
// <20>ڵ<EFBFBD><DAB5>Ĺ<EFBFBD><C4B9>캯<EFBFBD><ECBAAF><EFBFBD><EFBFBD>Ĭ<EFBFBD><C4AC>Ϊ<EFBFBD><CEAA>ɫ<EFBFBD>ڵ<EFBFBD>
RBTreeNode(const T& data)
: _left(nullptr), _right(nullptr), _parent(nullptr), _data(data), _colour(RED)
{
}
};
template <class T, class Ref, class Ptr>
struct __TreeIterator
{
typedef RBTreeNode<T> Node;
typedef __TreeIterator<T, Ref, Ptr> Self;
Node* _node; // <20><>ǰ<EFBFBD><C7B0><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ָ<EFBFBD><D6B8><EFBFBD>Ľڵ<C4BD>
// <20><><EFBFBD>캯<EFBFBD><ECBAAF>
__TreeIterator(Node* node)
: _node(node)
{
}
// <20><><EFBFBD><EFBFBD><EFBFBD>ò<EFBFBD><C3B2><EFBFBD><EFBFBD><EFBFBD>
Ref operator*()
{
return _node->_data;
}
// <20><><EFBFBD>ʳ<EFBFBD>Ա<EFBFBD><D4B1><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Ptr operator->()
{
return &_node->_data;
}
// ǰ<>õ<EFBFBD><C3B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Self& operator++()
{
// 1. <20><><EFBFBD><EFBFBD><EFBFBD>Ҳ<EFBFBD>Ϊ<EFBFBD><CEAA>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD>
if (_node->_right)
{
Node* subLeft = _node->_right;
while (subLeft->_left)
{
subLeft = subLeft->_left;
}
_node = subLeft;
}
// 2. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA>, <20><>ʾ _node <20><><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ѿ<EFBFBD><D1BE><EFBFBD><EFBFBD><EFBFBD>, <20><>һ<EFBFBD><D2BB><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȥ<EFBFBD><C8A5>, <20><><EFBFBD><EFBFBD>·<EFBFBD><C2B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Һ<EFBFBD><D2BA><EFBFBD>ʹ<EFBFBD><CAB9><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ǹ<EFBFBD><C7B8><EFBFBD><EFBFBD><EFBFBD>
else
{
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_right)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}
// <20><><EFBFBD>õ<EFBFBD><C3B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Self operator++(int)
{
Node* tmp = _node;
++(*this);
return Self(tmp);
}
// ǰ<>õݼ<C3B5><DDBC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Self& operator--()
{
// 1. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ҽڵ<D2BD>
if (_node->_left)
{
Node* subRight = _node->left;
while (subRight->_right)
{
subRight = subRight->_right;
}
_node = subRight;
}
// 2. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA>, <20><>ʾ _node <20><><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ѿ<EFBFBD><D1BE><EFBFBD><EFBFBD><EFBFBD>, <20><>һ<EFBFBD><D2BB><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȥ<EFBFBD><C8A5>, <20><><EFBFBD><EFBFBD>·<EFBFBD><C2B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Һ<EFBFBD><D2BA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ҵ<EFBFBD><D2B5>Ǹ<EFBFBD><C7B8><EFBFBD><EFBFBD><EFBFBD>
else
{
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_left)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}
// <20><><EFBFBD>õݼ<C3B5><DDBC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Self operator--(int)
{
Node* tmp = _node;
--(*this);
return Self(tmp);
}
bool operator!=(const Self& n)
{
return _node != n._node;
}
bool operator==(const Self& n)
{
return _node == n._node;
}
};
template <class K, class T, class KOfT>
class RBTree
{
private:
typedef RBTreeNode<T> Node;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
void RotateL(Node* parent)
{
Node* ppNode = parent->_parent;
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
{
subRL->_parent = parent;
}
subR->_left = parent;
parent->_parent = subR;
// 1. ԭ<><D4AD> parent <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ĸ<EFBFBD>, <20><><EFBFBD><EFBFBD> subR <20>Ǹ<EFBFBD>
if (_root == parent)
{
_root = subR;
subR->_parent = nullptr;
}
// 2. parent Ϊ<><CEAA><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֻ<EFBFBD><D6BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>е<EFBFBD><D0B5><EFBFBD><EFBFBD><EFBFBD>, <20>ı<EFBFBD><C4B1><EFBFBD><EFBFBD>ӹ<EFBFBD>ϵ, <20><>ô subR Ҫ<><D2AA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>λ<EFBFBD><CEBB>
else
{
if (ppNode->_left == parent)
{
ppNode->_left = subR;
}
else
{
ppNode->_right = subR;
}
subR->_parent = ppNode;
}
}
// <20>ҵ<EFBFBD><D2B5><EFBFBD>
void RotateR(Node* parent)
{
Node* ppNode = parent->_parent;
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
{
subLR->_parent = parent;
}
subL->_right = parent;
parent->_parent = subL;
if (_root == parent)
{
_root = subL;
subL->_parent = nullptr;
}
else
{
if (ppNode->_left == parent)
{
ppNode->_left = subL;
}
else
{
ppNode->_right = subL;
}
subL->_parent = ppNode;
}
}
// ɾ<><C9BE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
void DeleteTree(Node* root)
{
if (root == nullptr)
{
return;
}
// <20>ݹ<EFBFBD>ɾ<EFBFBD><C9BE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
DeleteTree(root->_left);
// <20>ݹ<EFBFBD>ɾ<EFBFBD><C9BE><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
DeleteTree(root->_right);
// ɾ<><C9BE><EFBFBD><EFBFBD>ǰ<EFBFBD>ڵ<EFBFBD>
delete root;
}
public:
typedef __TreeIterator<T, T&, T*> iterator;
typedef __TreeIterator<T, const T&, const T*> const_iterator;
iterator begin()
{
Node* cur = _root;
while (cur && cur->_left)
{
cur = cur->_left;
}
return iterator(cur);
}
iterator end()
{
return iterator(nullptr);
}
const_iterator begin() const
{
Node* cur = _root;
while (cur && cur->_left)
{
cur = cur->_left;
}
return const_iterator(cur);
}
const_iterator end() const
{
return const_iterator(nullptr);
}
RBTree(Node* root = nullptr)
: _root(root)
{
}
~RBTree()
{
DeleteTree(_root);
}
// <20><><EFBFBD><EFBFBD>
// 1. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڡ<EFBFBD>
// 2. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɫ<EFBFBD>ڵ㣬<DAB5><E3A3AC><EFBFBD>ĸ<EFBFBD><C4B8><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ<EFBFBD>ģ<EFBFBD><C4A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// 3. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɫ<EFBFBD>ڵ㣬<DAB5><E3A3AC><EFBFBD>ĸ<EFBFBD><C4B8><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ<EFBFBD>ģ<EFBFBD><C4A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ƶ<EFBFBD><C6B6><EFBFBD><EFBFBD><EFBFBD><EFBFBD>游<EFBFBD><E6B8B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB>Ϊ<EFBFBD><CEAA>ɫ<EFBFBD><C9AB><EFBFBD>ؼ<EFBFBD><D8BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// a. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD>죬<EFBFBD>Ѹ<EFBFBD><D1B8>׺<EFBFBD><D7BA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڣ<EFBFBD><DAA3>游<EFBFBD><E6B8B8><EFBFBD>죬<EFBFBD><ECA3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϴ<EFBFBD><CFB4><EFBFBD><EFBFBD><EFBFBD>
// b. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD>ڣ<EFBFBD><DAA3><EFBFBD><EFBFBD>߲<EFBFBD><DFB2><EFBFBD><EFBFBD>ڡ<EFBFBD><DAA1><EFBFBD>ת<EFBFBD><D7AA><EFBFBD><EFBFBD><EFBFBD><EFBFBD> or ˫<><CBAB><EFBFBD><EFBFBD>+ <20><>ɫ
std::pair<iterator, bool> Insert(const T& data)
{
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ĺ<EFBFBD><C4B9><EFBFBD><EFBFBD><EFBFBD><EFBFBD>в<EFBFBD><D0B2><EFBFBD>
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD>գ<EFBFBD><D5A3>½ڵ<C2BD>ֱ<EFBFBD><D6B1><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA><EFBFBD>ڵ<EFBFBD>
if (_root == nullptr)
{
_root = new Node(data);
_root->_colour = BLACK; // <20><><EFBFBD>ڵ<EFBFBD><DAB5>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>
return std::make_pair(iterator(_root), true);
}
// <20><><EFBFBD><EFBFBD>ʱʹ<CAB1>ñȽ<C3B1><C8BD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƚϼ<C8BD><CFBC>Ĵ<EFBFBD>С<EFBFBD><D0A1><EFBFBD><EFBFBD>֧<EFBFBD>ֲ<EFBFBD>ͬ<EFBFBD><CDAC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
KOfT koft;
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (koft(cur->_data) > koft(data))
{
parent = cur;
cur = cur->_left;
}
else if (koft(cur->_data) < koft(data))
{
parent = cur;
cur = cur->_right;
}
else
{
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ѿ<EFBFBD><D1BE><EFBFBD><EFBFBD><EFBFBD>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ч, <20><><EFBFBD><EFBFBD> false, <20><><EFBFBD>ҷ<EFBFBD><D2B7>ظü<D8B8><C3BC>ĵ<EFBFBD><C4B5><EFBFBD><EFBFBD><EFBFBD>
return std::make_pair(iterator(cur), false);
}
}
// <20>ҵ<EFBFBD>λ<EFBFBD><CEBB>, <20><><EFBFBD>ݸ<EFBFBD><DDB8>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>½ڵ<C2BD>
cur = new Node(data);
Node* newnode = cur;
if (koft(parent->_data) > koft(cur->_data))
{
parent->_left = cur;
cur->_parent = parent;
}
else
{
parent->_right = cur;
cur->_parent = parent;
}
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҫ<EFBFBD>޸<EFBFBD><DEB8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
InsertFixUp(parent, cur);
return std::make_pair(iterator(newnode), true);
}
void InsertFixUp(Node* parent, Node* cur)
{
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɫ
// <20>½<EFBFBD><C2BD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ļ<EFBFBD><C4BB>Ǻڵ<C7BA>? <09><>ɫ
// 1. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڡ<EFBFBD>
// 2. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɫ<EFBFBD>ڵ<EFBFBD>, <20><><EFBFBD>ĸ<EFBFBD><C4B8><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// 3. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɫ<EFBFBD>ڵ<EFBFBD>, <20><><EFBFBD>ĸ<EFBFBD><C4B8><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>, <20><><EFBFBD><EFBFBD><EFBFBD>ƶ<EFBFBD><C6B6><EFBFBD><EFBFBD><EFBFBD><EFBFBD>游<EFBFBD><E6B8B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><D2BB>Ϊ<EFBFBD><CEAA>ɫ<EFBFBD><C9AB><EFBFBD>ؼ<EFBFBD><D8BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// a. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA>, <20>Ѹ<EFBFBD><D1B8>׺<EFBFBD><D7BA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, <20>游<EFBFBD><E6B8B8><EFBFBD><EFBFBD>, <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϴ<EFBFBD><CFB4><EFBFBD><EFBFBD><EFBFBD>
// b. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA>, <20><><EFBFBD>߲<EFBFBD><DFB2><EFBFBD><EFBFBD>ڡ<EFBFBD><DAA1><EFBFBD>ת<EFBFBD><D7AA><EFBFBD><EFBFBD><EFBFBD><EFBFBD> or ˫<><CBAB><EFBFBD><EFBFBD>+ <20><>ɫ
while (parent && parent->_colour == RED)
{
// <20>ؼ<EFBFBD><D8BC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Node* grandfather = parent->_parent;
// <20><><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD>游<EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD>
if (grandfather->_left == parent)
{
Node* uncle = grandfather->_right;
// <20><><EFBFBD><EFBFBD>1: uncle <20><><EFBFBD><EFBFBD>, <20><>Ϊ<EFBFBD><CEAA>
if (uncle && uncle->_colour == RED)
{
parent->_colour = uncle->_colour = BLACK;
grandfather->_colour = RED;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϴ<EFBFBD><CFB4><EFBFBD>
cur = grandfather;
parent = cur->_parent;
}
// <20><><EFBFBD><EFBFBD> 2 or <20><><EFBFBD><EFBFBD> 3 : uncle <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> or uncle <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA>
else
{
// <20><><EFBFBD><EFBFBD> 3 : ˫<><CBAB> -> <20>䵥<EFBFBD><E4B5A5>
if (cur == parent->_right)
{
RotateL(parent);
std::swap(parent, cur);
}
// <20>ڶ<EFBFBD><DAB6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> (ps: <20>п<EFBFBD><D0BF><EFBFBD><EFBFBD>ǵ<EFBFBD><C7B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>)
RotateR(grandfather);
grandfather->_colour = RED;
parent->_colour = BLACK;
break;
}
}
// <20><><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD>游<EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD>
else
{
Node* uncle = grandfather->_left;
// <20><><EFBFBD><EFBFBD>1: uncle <20><><EFBFBD><EFBFBD>, <20><>Ϊ<EFBFBD><CEAA>
if (uncle && uncle->_colour == RED)
{
parent->_colour = uncle->_colour = BLACK;
grandfather->_colour = RED;
// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϵ<EFBFBD><CFB5><EFBFBD>
cur = grandfather;
parent = cur->_parent;
}
// <20><><EFBFBD><EFBFBD> 2 or <20><><EFBFBD><EFBFBD> 3 : uncle <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD> or uncle <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA>
else
{
// <20><><EFBFBD><EFBFBD> 3 : ˫<><CBAB> -> <20>䵥<EFBFBD><E4B5A5>
if (cur == parent->_left)
{
RotateR(parent);
std::swap(parent, cur);
}
// <20>ڶ<EFBFBD><DAB6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> (ps: <20>п<EFBFBD><D0BF><EFBFBD><EFBFBD>ǵ<EFBFBD><C7B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>)
RotateL(grandfather);
grandfather->_colour = RED;
parent->_colour = BLACK;
break;
}
}
}
// <20><>֤<EFBFBD><D6A4><EFBFBD>ڵ<EFBFBD>Ϊ<EFBFBD><CEAA>
_root->_colour = BLACK;
}
// ɾ<><C9BE><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
bool Erase(const K& key)
{
Node* nodeToDelete = _root;
KOfT koft;
// 1. Ѱ<><D1B0>Ҫɾ<D2AA><C9BE><EFBFBD>Ľڵ<C4BD>
while (nodeToDelete)
{
if (koft(nodeToDelete->_data) > key)
{
nodeToDelete = nodeToDelete->_left;
}
else if (koft(nodeToDelete->_data) < key)
{
nodeToDelete = nodeToDelete->_right;
}
else
{
break; // <20>ҵ<EFBFBD><D2B5><EFBFBD>Ҫɾ<D2AA><C9BE><EFBFBD>Ľڵ<C4BD>
}
}
// <20>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, ֱ<>ӷ<EFBFBD><D3B7><EFBFBD> false
if (nodeToDelete == nullptr)
{
return false;
}
// ִ<><D6B4>ɾ<EFBFBD><C9BE><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Node* parent, * child;
// <20><><EFBFBD><EFBFBD>ԭ<EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD>Ա<EFBFBD><D4B1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
Colour originalColour = nodeToDelete->_colour;
// 2. <20><><EFBFBD><EFBFBD>ɾ<EFBFBD><C9BE><EFBFBD>ڵ<EFBFBD><DAB5>ĸ<EFBFBD><C4B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
if (nodeToDelete->_left == nullptr)
{
// <20><><EFBFBD><EFBFBD> 1<><31>û<EFBFBD><C3BB><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD>
child = nodeToDelete->_right;
parent = nodeToDelete->_parent;
Transplant(nodeToDelete, nodeToDelete->_right);
}
else if (nodeToDelete->_right == nullptr)
{
// <20><><EFBFBD><EFBFBD> 2<><32>û<EFBFBD><C3BB><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD>
child = nodeToDelete->_left;
parent = nodeToDelete->_parent;
Transplant(nodeToDelete, nodeToDelete->_left);
}
else
{
// <20><><EFBFBD><EFBFBD> 3<><33><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD>
// <20>ҵ<EFBFBD><D2B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>е<EFBFBD><D0B5><EFBFBD>С<EFBFBD>ڵ㣨<DAB5><E3A3A8><EFBFBD>̽ڵ㣩
Node* successor = Minimum(nodeToDelete->_right);
originalColour = successor->_colour;
child = successor->_right;
if (successor->_parent == nodeToDelete)
{
parent = successor;
}
else
{
// <20><><EFBFBD>̽ڵ<CCBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ӽڵ㣬<DAB5><E3A3AC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD><DAB5>滻<EFBFBD><E6BBBB>
Transplant(successor, successor->_right);
successor->_right = nodeToDelete->_right;
successor->_right->_parent = successor;
parent = successor->_parent;
}
// <20>ú<EFBFBD><C3BA>̽ڵ<CCBD><DAB5>滻ɾ<E6BBBB><C9BE><EFBFBD>ڵ<EFBFBD>
Transplant(nodeToDelete, successor);
successor->_left = nodeToDelete->_left;
successor->_left->_parent = successor;
successor->_colour = nodeToDelete->_colour; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ɫ<EFBFBD><C9AB><EFBFBD><EFBFBD>
}
// ɾ<><C9BE><EFBFBD>ڵ<EFBFBD>
delete nodeToDelete;
// 3. <20>޸<EFBFBD><DEB8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
// <20><><EFBFBD><EFBFBD>ɾ<EFBFBD><C9BE><EFBFBD>Ľڵ<C4BD><DAB5>Ǻ<EFBFBD>ɫ, <20><>Ҫ<EFBFBD><D2AA><EFBFBD>е<EFBFBD><D0B5><EFBFBD>
if (originalColour == BLACK)
{
EraseFixUp(child, parent);
}
return true;
}
Node* Minimum(Node* node)
{
while (node->_left != nullptr)
{
node = node->_left; // һֱ<D2BB><D6B1><EFBFBD><EFBFBD><EFBFBD>ߣ<EFBFBD>ֱ<EFBFBD><D6B1><EFBFBD>ҵ<EFBFBD><D2B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD>
}
return node;
}
void Transplant(Node* u, Node* v)
{
// <20><><EFBFBD><EFBFBD>u<EFBFBD>Ǹ<EFBFBD><C7B8>ڵ㣬v<E3A3AC><76>Ϊ<EFBFBD>µĸ<C2B5><C4B8>ڵ<EFBFBD>
if (u->_parent == nullptr)
{
_root = v;
}
// u<><75><EFBFBD><EFBFBD><EFBFBD>ӽڵ㣬<DAB5><E3A3AC>v<EFBFBD>滻<EFBFBD><E6BBBB>
else if (u == u->_parent->_left)
{
u->_parent->_left = v;
}
// u<><75><EFBFBD><EFBFBD><EFBFBD>ӽڵ㣬<DAB5><E3A3AC>v<EFBFBD>滻<EFBFBD><E6BBBB>
else
{
u->_parent->_right = v;
}
// <20><><EFBFBD><EFBFBD>v<EFBFBD><76>u<EFBFBD>ĸ<EFBFBD><C4B8>ڵ<EFBFBD>
if (v != nullptr)
{
v->_parent = u->_parent;
}
}
void EraseFixUp(Node* child, Node* parent)
{
while (child != _root && (child == nullptr || child->_colour == BLACK))
{
if (child == parent->_left)
{
Node* brother = parent->_right;
// <20><><EFBFBD><EFBFBD>1: child <20><><EFBFBD>ֵܽڵ<DCBD> brother <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>
if (brother->_colour == RED)
{
brother->_colour = BLACK;
parent->_colour = RED;
RotateL(parent);
brother = parent->_right;
}
// <20><><EFBFBD><EFBFBD>2: child <20><><EFBFBD>ֵܽڵ<DCBD> brother <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>, <20><> brother <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ㶼<DAB5>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>
if ((brother->_left == nullptr || brother->_left->_colour == BLACK) &&
(brother->_right == nullptr || brother->_right->_colour == BLACK))
{
brother->_colour = RED;
child = parent;
parent = child->_parent;
}
else
{
// <20><><EFBFBD><EFBFBD>3: brother <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>, <20><><EFBFBD><EFBFBD> brother <20><><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD><DAB5>Ǻ<EFBFBD>ɫ, <20><><EFBFBD>ӽڵ<D3BD><DAB5>Ǻ<EFBFBD>ɫ
if (brother->_right == nullptr || brother->_right->_colour == BLACK)
{
if (brother->_left)
{
brother->_left->_colour = BLACK;
}
brother->_colour = RED;
RotateR(brother);
brother = parent->_right;
}
// <20><><EFBFBD><EFBFBD>4: brother <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>, <20><><EFBFBD><EFBFBD> brother <20><><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD><DAB5>Ǻ<EFBFBD>ɫ
if (brother)
{
brother->_colour = parent->_colour;
parent->_colour = BLACK;
if (brother->_right)
{
brother->_right->_colour = BLACK;
}
RotateL(parent);
}
child = _root;
break;
}
}
else
{
Node* brother = parent->_left;
// <20><><EFBFBD><EFBFBD>1: child <20><><EFBFBD>ֵܽڵ<DCBD> brother <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>
if (brother->_colour == RED)
{
brother->_colour = BLACK;
parent->_colour = RED;
RotateR(parent);
brother = parent->_left;
}
// <20><><EFBFBD><EFBFBD>2: child <20><><EFBFBD>ֵܽڵ<DCBD> parent <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>, <20><> brother <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ㶼<DAB5>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>
if ((brother->_left == nullptr || brother->_left->_colour == BLACK) &&
(brother->_right == nullptr || brother->_right->_colour == BLACK))
{
brother->_colour = RED;
child = parent;
parent = child->_parent;
}
else
{
// <20><><EFBFBD><EFBFBD>3: brother <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>, <20><><EFBFBD><EFBFBD> brother <20><><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD><DAB5>Ǻ<EFBFBD>ɫ, <20><><EFBFBD>ӽڵ<D3BD><DAB5>Ǻ<EFBFBD>ɫ
if (brother->_left == nullptr || brother->_left->_colour == BLACK)
{
if (brother->_right)
{
brother->_right->_colour = BLACK;
}
brother->_colour = RED;
RotateL(brother);
brother = parent->_left;
}
// <20><><EFBFBD><EFBFBD>4: brother <20>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>, <20><><EFBFBD><EFBFBD> brother <20><><EFBFBD><EFBFBD><EFBFBD>ӽڵ<D3BD><DAB5>Ǻ<EFBFBD>ɫ
if (brother)
{
brother->_colour = parent->_colour;
parent->_colour = BLACK;
if (brother->_left)
{
brother->_left->_colour = BLACK;
}
RotateR(parent);
}
child = _root;
break;
}
}
}
if (child)
{
child->_colour = BLACK;
}
}
// <20><><EFBFBD>ҽڵ<D2BD>
iterator& Find(const K& key)
{
KOfT koft;
Node* cur = _root;
while (cur)
{
if (koft(cur->_data) > key)
{
cur = cur->_left;
}
else if (koft(cur->_data) < key)
{
cur = cur->_right;
}
else
{
return iterator(cur);
}
}
return iterator(nullptr);
}
// <20>ж<EFBFBD><D0B6>Ƿ<EFBFBD><C7B7>Ǻ<EFBFBD><C7BA><EFBFBD><EFBFBD><EFBFBD>
bool IsRBTree()
{
Node* root = _root;
// <20><><EFBFBD><EFBFBD>Ҳ<EFBFBD>Ǻ<EFBFBD><C7BA><EFBFBD><EFBFBD><EFBFBD>
if (root == nullptr)
{
return true;
}
// 1. <20>жϸ<D0B6><CFB8>Ƿ<EFBFBD><C7B7>Ǻ<EFBFBD>ɫ<EFBFBD><C9AB>
if (root->_colour != BLACK)
{
std::cout << "<EFBFBD><EFBFBD><EFBFBD>ڵ㲻<EFBFBD>Ǻ<EFBFBD>ɫ" << std::endl;
return false;
}
// <20><>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD>һ<EFBFBD><D2BB>·<EFBFBD><C2B7><EFBFBD>Ϻ<EFBFBD>ɫ<EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
size_t blackCount = 0;
Node* cur = _root;
while (cur)
{
if (cur->_colour == BLACK)
{
blackCount++;
}
cur = cur->_left;
}
// <20>ж<EFBFBD><D0B6>Ƿ<EFBFBD><C7B7><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>, k <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>¼·<C2BC><C2B7><EFBFBD>к<EFBFBD>ɫ<EFBFBD>ڵ<EFBFBD><DAB5>ĸ<EFBFBD><C4B8><EFBFBD>
size_t k = 0;
return _IsRBTree(_root, k, blackCount);
}
bool _IsRBTree(Node* root, size_t k, size_t blackCount)
{
// <20>ߵ<EFBFBD> nullptr ֮<><D6AE>, <20>ж<EFBFBD> k <20><> blackCount <20>Ƿ<EFBFBD><C7B7><EFBFBD><EFBFBD><EFBFBD>
if (root == nullptr)
{
// <20><><EFBFBD>պ<EFBFBD>ɫ<EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD>
if (blackCount != k)
{
std::cout << "Υ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>: ÿ<><C3BF>·<EFBFBD><C2B7><EFBFBD>к<EFBFBD>ɫ<EFBFBD>ڵ<EFBFBD><DAB5>ĸ<EFBFBD><C4B8><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>" << std::endl;
return false;
}
return true;
}
// ͳ<>ƺ<EFBFBD>ɫ<EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD>
if (root->_colour == BLACK)
{
k++;
}
// <20><><EFBFBD>⵱ǰ<E2B5B1>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD>丸<EFBFBD>׽ڵ<D7BD><DAB5>Ƿ<EFBFBD><C7B7><EFBFBD>Ϊ<EFBFBD><CEAA>ɫ
Node* parent = root->_parent;
if (parent && parent->_colour == RED && root->_colour == RED)
{
std::cout << "Υ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>: <20><>ɫ<EFBFBD>ڵ<EFBFBD><DAB5>ĺ<EFBFBD><C4BA>ӱ<EFBFBD><D3B1><EFBFBD><EFBFBD>Ǻ<EFBFBD>ɫ" << std::endl;
return false;
}
return _IsRBTree(root->_left, k, blackCount) && _IsRBTree(root->_right, k, blackCount);
}
private:
Node* _root;
};
}
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