C++: 使用红黑树模拟实现STL中的map和set

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正文开始

1. 红黑树的迭代器

迭代器的好处是可以方便遍历，是数据结构的底层实现与用户透明

打开C++的源码我们可以发现, 其实源码中的底层大概如下图所示:

这里额外增加了一个header指针, 有了这个指针可以更方便的找到根节点, 并且可以比较容易的实现反向遍历, 可以看到set和map都是双向迭代器, 但是缺点就是需要不断的维护begin()这个要返回的节点, 所以我们这里为了也是先正反向迭代器, 也避免过于麻烦, 我们暂且讲_root也一并传过来, 方便我们找到根节点

template<class T,class Ref,class Ptr>
struct RBTreeIterator
{
typedef RBTreeNode<T> Node;
typedef RBTreeIterator<T,Ref,Ptr> self;

Node* _node;
Node* _root;

RBTreeIterator(Node* node,Node* root)
:_node(node)
, _root(root)
{}

Ref operator*()
{
return _node->_data;
}

Ptr operator->()
{
return &_node->_data;
}

bool operator==(const self& s)
{
return _node == s._node;
}

bool operator!=(const self& s)
{
return _node != s._node;
}
};

在BSTree中, 有了模板Ref, 和Ptr当我们需要const迭代器就比较方便

typedef RBTreeIterator<T,T&,T*> Iterator;
typedef RBTreeIterator<T, const T&, const T*> ConstIterator;

Iterator Begin()
{
Node* leftMost = _root;
while (leftMost && leftMost->_left)
{
leftMost = leftMost->_left;
}
return Iterator(leftMost,_root);
}

Iterator End()
{
return Iterator(nullptr,_root);
}

ConstIterator Begin() const
{
Node* leftMost = _root;
while (leftMost && leftMost->_left)
{
leftMost = leftMost->_left;
}
return ConstIterator(leftMost, _root);
}

ConstIterator End() const
{
return ConstIterator(nullptr,_root);
}

++和–

对于++,我们由局部到整体分析,首先如果右不为空, 那么我们要访问下一个节点就是右子树的最左节点.

如果右为空, 我们就需要访问孩子是父亲左的那个祖先,因为中序的遍历的顺序为左 根 右,当前节点访问完了, 说明我这棵树的左根右访问完了, 要去访问上一棵树的根.

self& operator++()
{
if (_node->_right)
{
//右不为空, 右子树的最左节点就是中序的下一个
Node* leftMost = _node->_right;
while (leftMost->_left)
{
leftMost = leftMost->_left;
}
_node = leftMost;
}
else
{
//沿着到根节点的路径查找,孩子是父亲左的那个祖先
//节点就是下一个要访问的节点
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_right)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}

对于–操作,就是按照右 根 左的操作, 和++反着来, 因为我们要模拟实现反向迭代, 所以当节点为空时,也就是end()时, 我们–之后要返回到最后一个节点

self& operator--()
{
if (_node == nullptr)
{
//--end()
Node* rightMost = _root;
while (rightMost && rightMost->_right)
{
rightMost = rightMost->_right;
}
_node = rightMost;
}
else if (_node->_left)
{
Node* rightMost = _node->_left;
while (rightMost->_right)
{
rightMost = rightMost->_right;
}
_node = rightMost;
}
else
{
//找孩子是右的那个父亲
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_left)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}

2. 改造红黑树

对于map和set底层存放的一个是key,一个是key_value, 难道我们需要为此适配不同的红黑树吗, 其实不是, 我们来看一下源码. 这里不管是map还是set都是同一棵树, 只是对它进行了改造.
这里的key就是key, 而value_type如果是set就是key, 如果是map就是pair. 那么为什么不省略第一个key, 既然存在即合理, 因为对于set来说无所谓, 但是对于map来说呢, 如果只有pair, 那么怎么比较呢? 我们需要的比较方式是按照pair中的key来比较, 但是pair的底层比较方法并不是, 还有关于find函数, 我们实现查找难道要传递一个pair查找吗, 那如何实现英汉互译那种场景呢?既然知道pair了那还有什么必要查找呢?

C++STL底层pair的比较方法

所以我们进行改造, 统一讲key和pair改为模板T

template<class K,class T,class KeyOfT>
class RBTree
{
typedef RBTreeNode<T> Node;
public:
typedef RBTreeIterator<T,T&,T*> Iterator;
typedef RBTreeIterator<T, const T&, const T*> ConstIterator;

pair<Iterator,bool> Insert(const T& data)
{
//
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, _root), false);
}
}
}

Iterator Find(const K& key)
{
//
}
private:
Node* _root = nullptr;
};

对于比较逻辑, 我们可以创建一个仿函数进行实现

map:

template<class K,class V>
class map
{
struct MapKeyOfT
{
const K& operator()(const pair<K, V>& kv) 
{
return kv.first;
}
};

set:

template<class K>
class set
{
struct SetKeyOfT
{
const K& operator()(const K& key)
{
return key;
}
};

3. set的模拟实现

#include"RBTree.h"

namespace my
{
template<class K>
class set
{
struct SetKeyOfT
{
const K& operator()(const K& key)
{
return key;
}
};
public:
typedef typename RBTree<K,const K, SetKeyOfT>::Iterator iterator;
typedef typename RBTree<K,const K, SetKeyOfT>::Iterator const_iterator;
iterator begin()
{
return _t.Begin();
}

iterator end() 
{
return _t.End();
}

const_iterator begin() const
{
return _t.Begin();
}

const_iterator end() const
{
return _t.End();
}

pair<iterator,bool> insert(const K& key)
{
return _t.Insert(key);
} 

iterator find(const K& key)
{
return _t.Find(key);
}
private:
RBTree<K, const K, SetKeyOfT> _t;
};

void Print(const set<int>& s)
{
set<int>::const_iterator it = s.end();
while (it != s.begin())
{
--it;
cout << *it << " ";
}
cout << endl;
}
void test_set()
{
set<int> s;
int a[] = { 4,2,6,1,3,5,15,7,16,14 };
for (auto e : a)
{
s.insert(e);
}
for (auto e : s)
{
cout << e << " ";
}

set<int>::iterator it = s.end();
while (it != s.begin())
{
--it;
cout << *it << " ";
}
cout << endl;

}

}

4. map的模拟实现

#include"RBTree.h"

namespace my
{
template<class K,class V>
class map
{
struct MapKeyOfT
{
const K& operator()(const pair<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>::ConstIterator const_iterator;

iterator begin()
{
return _t.Begin();
}

iterator end()
{
return _t.End();
}

const_iterator begin() const
{
return _t.Begin();
}

const_iterator end() const
{
return _t.End();
}

pair<iterator,bool> Insert(const pair<K, V>& kv)
{
return _t.Insert(kv);
}

iterator find(const K& key)
{
return _t.Find(key);
}

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;
};

void test_map()
{
map<string, string> dict;
dict.Insert({ "sort","排序" });
dict.Insert({ "left","左边" });
dict.Insert({ "right","右边" });
map<string, string>::iterator it = dict.begin();
while (it != dict.end())
{
cout << it->first<<it->second << endl;
++it;
}
dict["left"] = "左边,剩余";
dict["insert"];
dict["string"] = "字符串";
cout << endl;

for (const auto& e : dict)
{
cout << e.first << e.second << endl;
}
}
}

5. RBTree的改造代码

#pragma once
#include<iostream>
#include<vector>
#include<assert.h>
using namespace std;

enum Colour
{
RED,
BLACK
};

template<class T>
struct RBTreeNode
{
T _data;
RBTreeNode* _left;
RBTreeNode* _right;
RBTreeNode* _parent;
Colour _col;

RBTreeNode(const T& data)
: _data(data)
, _left(nullptr)
, _right(nullptr)
, _parent(nullptr)
{}

};

template<class T,class Ref,class Ptr>
struct RBTreeIterator
{
typedef RBTreeNode<T> Node;
typedef RBTreeIterator<T,Ref,Ptr> self;

Node* _node;
Node* _root;

RBTreeIterator(Node* node,Node* root)
:_node(node)
, _root(root)
{}

self& operator++()
{
if (_node->_right)
{
//右不为空, 右子树的最左节点就是中序的下一个
Node* leftMost = _node->_right;
while (leftMost->_left)
{
leftMost = leftMost->_left;
}
_node = leftMost;
}
else
{
//沿着到根节点的路径查找,孩子是父亲左的那个祖先
//节点就是下一个要访问的节点
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_right)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}

self& operator--()
{
if (_node == nullptr)
{
//--end()
Node* rightMost = _root;
while (rightMost && rightMost->_right)
{
rightMost = rightMost->_right;
}
_node = rightMost;
}
else if (_node->_left)
{
Node* rightMost = _node->_left;
while (rightMost->_right)
{
rightMost = rightMost->_right;
}
_node = rightMost;
}
else
{
//找孩子是右的那个父亲
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_left)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}



Ref operator*()
{
return _node->_data;
}

Ptr operator->()
{
return &_node->_data;
}

bool operator==(const self& s)
{
return _node == s._node;
}

bool operator!=(const self& s)
{
return _node != s._node;
}
};

template<class K,class T,class KeyOfT>
class RBTree
{
typedef RBTreeNode<T> Node;
public:
typedef RBTreeIterator<T,T&,T*> Iterator;
typedef RBTreeIterator<T, const T&, const T*> ConstIterator;

Iterator Begin()
{
Node* leftMost = _root;
while (leftMost && leftMost->_left)
{
leftMost = leftMost->_left;
}
return Iterator(leftMost,_root);
}

Iterator End()
{
return Iterator(nullptr,_root);
}

ConstIterator Begin() const
{
Node* leftMost = _root;
while (leftMost && leftMost->_left)
{
leftMost = leftMost->_left;
}
return ConstIterator(leftMost, _root);
}

ConstIterator End() const
{
return ConstIterator(nullptr,_root);
}

RBTree() = default;

RBTree(const RBTree& t)
{
_root = Copy(t._root);
}

RBTree& operator=(RBTree t)
{
swap(_root, t._root);
return *this;
}

~RBTree()
{
Destroy(_root);
_root = nullptr;
}

pair<Iterator,bool> Insert(const T& data)
{
if (_root == nullptr)
{
_root = new Node(data);
_root->_col = BLACK;
return make_pair(Iterator(_root,_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, _root), false);
}
}

cur = new Node(data);
Node* newnode = cur;
// 新增节点。颜色红色给红色
cur->_col = RED;
if (kot(parent->_data) < kot(data))
{
parent->_right = cur;
}
else
{
parent->_left = cur;
}
cur->_parent = parent;

while (parent && parent->_col == RED)
{
Node* grandfather = parent->_parent;
//    g
//  p   u
if (parent == grandfather->_left)
{
Node* uncle = grandfather->_right;
if (uncle && uncle->_col == RED)
{
// u存在且为红 -》变色再继续往上处理
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;

cur = grandfather;
parent = cur->_parent;
}
else
{
// u存在且为黑或不存在 -》旋转+变色
if (cur == parent->_left)
{
//    g
//  p   u
//c
//单旋
RotateR(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
}
else
{
//    g
//  p   u
//    c
//双旋
RotateL(parent);
RotateR(grandfather);

cur->_col = BLACK;
grandfather->_col = RED;
}

break;
}
}
else
{
//    g
//  u   p
Node* uncle = grandfather->_left;
// 叔叔存在且为红，-》变色即可
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 // 叔叔不存在，或者存在且为黑
{
// 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;

return make_pair(Iterator(newnode, _root), true);
}

void InOrder()
{
_InOrder(_root);
cout << endl;
}

int Height()
{
return _Height(_root);
}

int Size()
{
return _Size(_root);
}

bool IsBalance()
{
if (_root == nullptr)
return true;

if (_root->_col == RED)
{
return false;
}

// 参考值
int refNum = 0;
Node* cur = _root;
while (cur)
{
if (cur->_col == BLACK)
{
++refNum;
}

cur = cur->_left;
}

return Check(_root, 0, refNum);
}

Iterator 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 Iterator(cur, _root);
}
}

return End();
}
private:
bool Check(Node* root, int blackNum, const int refNum)
{
if (root == nullptr)
{
//cout << blackNum << endl;
if (refNum != blackNum)
{
cout << "存在黑色节点的数量不相等的路径" << endl;
return false;
}

return true;
}

if (root->_col == RED && root->_parent->_col == RED)
{
cout << root->_kv.first << "存在连续的红色节点" << endl;
return false;
}

if (root->_col == BLACK)
{
blackNum++;
}

return Check(root->_left, blackNum, refNum)
&& Check(root->_right, blackNum, refNum);
}

int _Size(Node* root)
{
return root == nullptr ? 0 : _Size(root->_left) + _Size(root->_right) + 1;
}

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;
}

void _InOrder(Node* root)
{
if (root == nullptr)
{
return;
}

_InOrder(root->_left);
cout << root->_kv.first << ":" << root->_kv.second << endl;
_InOrder(root->_right);
}

void RotateL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;

parent->_right = subRL;
if (subRL)
subRL->_parent = parent;

Node* parentParent = parent->_parent;

subR->_left = parent;
parent->_parent = subR;

if (parentParent == nullptr)
{
_root = subR;
subR->_parent = nullptr;
}
else
{
if (parent == parentParent->_left)
{
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;

Node* parentParent = parent->_parent;

subL->_right = parent;
parent->_parent = subL;

if (parentParent == nullptr)
{
_root = subL;
subL->_parent = nullptr;
}
else
{
if (parent == parentParent->_left)
{
parentParent->_left = subL;
}
else
{
parentParent->_right = subL;
}

subL->_parent = parentParent;
}

}

void Destroy(Node* root)
{
if (root == nullptr)
return;

Destroy(root->_left);
Destroy(root->_right);
delete root;
}

Node* Copy(Node* root)
{
if (root == nullptr)
return nullptr;

Node* newRoot = new Node(root->_kv);
newRoot->_left = Copy(root->_left);
newRoot->_right = Copy(root->_right);

return newRoot;
}
Node* _root = nullptr;
};

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完

原文地址：https://blog.csdn.net/2201_75644377/article/details/142388101

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