第十六章:红黑树模拟实现STL中的map与set
第十六章:红黑树模拟实现STL中的map与set
Iterator.h
#pragma once
// 反向迭代器--迭代器适配器
template<class Iterator>
struct ReverseIterator
{
typedef typename Iterator::reference Ref;
typedef typename Iterator::pointer Ptr;
typedef ReverseIterator<Iterator> Self;
Iterator _it;
ReverseIterator(Iterator it)
:_it(it)
{}
Ref operator*()
{
return *_it;
}
Ptr operator->()
{
return _it.operator->();
}
Self& operator++()
{
--_it;
return *this;
}
Self& operator--()
{
++_it;
rteurn *this;
}
bool operator!=(const Self& s) const
{
return _it != s._it;
}
bool operator==(const Self& s) const
{
return _it == s._it;
}
};
RBTree.h
#pragma once
#include <iostream>
using namespace std;
#include "Iterator.h"
enum Colour
{
RED,
BLACK,
};
//red-black
template<class T>
struct RBTreeNode
{
RBTreeNode<T>* _left;
RBTreeNode<T>* _right;
RBTreeNode<T>* _parent;
T _data;
Colour _col;
RBTreeNode(const T& x)
:_left(nullptr)
, _right(nullptr)
, _parent(nullptr)
, _data(x)
, _col(RED)
{}
};
template<class T, class Ref, class Ptr>
struct __TreeIterator
{
typedef Ref reference;
typedef Ptr pointer;
typedef RBTreeNode<T> Node;
typedef __TreeIterator<T, Ref, Ptr> Self;
Node* _node;
__TreeIterator(Node* node)
:_node(node)
{}
Ref operator*()
{
return _node->_data;
}
Ptr operator->()
{
return &_node->_data;
}
bool operator != (const Self& s) const
{
return _node != s._node;
}
bool operator == (const Self& s) const
{
return _node == s._node;
}
Self& operator++()
{
if (_node->_right)
{
// 下一个访问就是右树中,中序的第一个节点
Node* left = _node->_right;
while (left->_left)
{
left = left->_left;
}
_node = left;
}
else
{
// 找祖先里面还是不是父亲的右的那个
// 因为 cur 右为空,说明cur所在的子树已经访问完了
// cur是parent的右的,说明parent也访问完了,继续往上去找
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_right)
{
cur = cur->_parent;
parent = parent->_parent;
}
_node = parent;
}
return *this;
}
Self& operator--()
{
if (_node->_left)
{
// 左子树的最右节点
Node* right = _node->_left;
while (right->_right)
{
right = right->_right;
}
_node = right;
}
else
{
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_left)
{
cur = parent;
parent = parent->_parent;
}
_node = parent;
}
return *this;
}
};
//KeyOfT是仿函数
template<class K, class T, class KeyOfT>
class RBTree
{
typedef RBTreeNode<T> Node;
public:
typedef __TreeIterator < T, T&, T* > iterator;
typedef __TreeIterator < T, const T&, const T* > const_iterator;
typedef ReverseIterator<iterator> reverse_iterator;
reverse_iterator rbegin()
{
Node* right = _root;
while (right && right->_right)
{
right = right->_right;
}
return reverse_iterator(iterator(right));
}
reverse_iterator rend()
{
return reverse_iterator(iterator(nullptr));
}
iterator begin()
{
Node* left = _root;
while (left && left->_left)
{
left = left->_left;
}
return iterator(left);
}
iterator end()
{
return iterator(nullptr);
}
RBTree()
:_root(nullptr)
{}
// 拷贝构造和operator=大家自己去实现一下
void Destory(Node* root)
{
if (root == nullptr)
{
return;
}
Destory(root->_left);
Destory(root->_right);
delete root;
}
~RBTree()
{
Destory(_root);
_root = nullptr;
}
Node* Find(const K& key)
{
KeyOfT kot;
Node* cur = _root;
while (cur)
{
if (kot(cur->_data) > key)
{
cur = cur->_left;
}
else if (kot(cur->_data) < key)
{
cur = cur->_right;
}
else
{
return cur;
}
}
return nullptr;
}
pair<iterator, bool> Insert(const T& data)
{
if (_root == nullptr)
{
_root = new Node(data);
_root->_col = BLACK;
return make_pair(iterator(_root), true);
}
KeyOfT kot;
Node* parent = nullptr;
Node* cur = _root;
while (cur)
{
if (kot(cur->_data) < kot(data))
{
parent = cur;
cur = cur->_right;
}
else if (kot(cur->_data) > kot(data))
{
parent = cur;
cur = cur->_left;
}
else
{
return make_pair(iterator(cur), false);
}
}
Node* newnode = new Node(data);
newnode->_col = RED;
if (kot(parent->_data) < kot(data))
{
parent->_right = newnode;
newnode->_parent = parent;
}
else
{
parent->_left = newnode;
newnode->_parent = parent;
}
cur = newnode;
// 如果父亲存在,且颜色为红色就需要处理
while (parent && parent->_col == RED)
{
Node* grandfather = parent->_parent;
// 关键是看叔叔
if (parent == grandfather->_left)
{
Node* uncle = grandfather->_right;
// 情况1:uncle存在且为红
if (uncle && uncle->_col == RED)
{
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
// 继续往上处理
cur = grandfather;
parent = cur->_parent;
}
else // 情况2+3:uncle不存在 uncle存在且为黑
{
// 情况2:单旋
if (cur == parent->_left)
{
RotateR(grandfather);
grandfather->_col = RED;
parent->_col = BLACK;
}
else // 情况3:双旋
{
RotateL(parent);
RotateR(grandfather);
cur->_col = BLACK;
grandfather->_col = RED;
}
break;
}
}
else // parent == grandfather->_right
{
Node* uncle = grandfather->_left;
// 情况1
if (uncle && uncle->_col == RED)
{
uncle->_col = parent->_col = BLACK;
grandfather->_col = RED;
cur = grandfather;
parent = cur->_parent;
}
else // 情况2 + 情况3
{
if (cur == parent->_right)
{
RotateL(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
}
else // cur == parent->_left
{
RotateR(parent);
RotateL(grandfather);
cur->_col = BLACK;
grandfather->_col = RED;
}
// 插入结束
break;
}
}
}
_root->_col = BLACK;
return make_pair(iterator(newnode), true);
}
void RotateL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
{
subRL->_parent = parent;
}
subR->_left = parent;
Node* parentParent = parent->_parent;
parent->_parent = subR;
if (parent == _root)
{
_root = subR;
_root->_parent = nullptr;
}
else
{
if (parentParent->_left == parent)
{
parentParent->_left = subR;
}
else
{
parentParent->_right = subR;
}
subR->_parent = parentParent;
}
}
void RotateR(Node* parent)
{
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
subLR->_parent = parent;
subL->_right = parent;
Node* parentParent = parent->_parent;
parent->_parent = subL;
if (parent == _root)
{
_root = subL;
_root->_parent = nullptr;
}
else
{
if (parentParent->_left == parent)
parentParent->_left = subL;
else
parentParent->_right = subL;
subL->_parent = parentParent;
}
}
bool _CheckBlance(Node* root, int blackNum, int count)
{
if (root == nullptr)
{
if (count != blackNum)
{
cout << "黑色节点的数量不相等"<<endl;
return false;
}
return true;
}
if (root->_col == RED && root->_parent->_col == RED)
{
cout << "存在连续的红色节点"<<endl;
return false;
}
if (root->_col == BLACK)
{
count++;
}
return _CheckBlance(root->_left, blackNum, count)
&& _CheckBlance(root->_right, blackNum, count);
}
bool CheckBlance()
{
if (_root == nullptr)
{
return true;
}
if (_root->_col == RED)
{
cout << "根节点是红色的" << endl;
return false;
}
// 找最左路径做黑色节点数量参考值
int blackNum = 0;
Node* left = _root;
while (left)
{
if (left->_col == BLACK)
{
blackNum++;
}
left = left->_left;
}
int count = 0;
return _CheckBlance(_root, blackNum, count);
}
/*void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}
_InOrder(root->_left);
cout << root->_kv.first << ":"<<root->_kv.second<<endl;
_InOrder(root->_right);
}*/
/*void InOrder()
{
_InOrder(_root);
cout << endl;
}
*/
private:
Node* _root;
};
Map.h
#pragma once
#include "RBTree.h"
namespace z
{
template<class K, class V>
class map
{
struct MapKeyOfT
{
const K& operator()(const pair<const K, V>& kv)
{
return kv.first;
}
};
public:
typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::iterator iterator;
typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::reverse_iterator reverse_iterator;
reverse_iterator rbegin()
{
return _t.rbegin();
}
reverse_iterator rend()
{
return _t.rend();
}
iterator begin()
{
return _t.begin();
}
iterator end()
{
return _t.end();
}
pair<iterator, bool> insert(const pair<const K, V>& kv)
{
return _t.Insert(kv);
}
V& operator[](const K& key)
{
pair<iterator, bool> ret = insert(make_pair(key, V()));
return ret.first->second;
}
private:
RBTree<K, pair<const K, V>, MapKeyOfT> _t;
};
}
Set.h
#pragma once
#include "RBTree.h"
namespace z
{
template<class K>
class set
{
struct SetKeyOfT
{
const K& operator()(const K& key)
{
return key;
}
};
public:
typedef typename RBTree<K, K, SetKeyOfT>::iterator iterator;
typedef typename RBTree<K, K, SetKeyOfT>::reverse_iterator reverse_iterator;
reverse_iterator rbegin()
{
return _t.rbegin();
}
reverse_iterator rend()
{
return _t.rend();
}
iterator begin()
{
return _t.begin();
}
iterator end()
{
return _t.end();
}
pair<iterator, bool> insert(const K& k)
{
return _t.Insert(k);
}
private:
RBTree<K, K, SetKeyOfT> _t;
};
}
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