封装红黑树实现mymap和myset

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一. 源码及其框架分析

SGI-STL30版本源代码，map和set的源代码在map/set/stl_map.h/stl_set.h/stl_tree.h等几个头文件中。map和set的实现结构框架核心部分截取出来如下：

// set
#ifndef __SGI_STL_INTERNAL_TREE_H
#include <stl_tree.h>
#endif
#include <stl_set.h>
#include <stl_multiset.h>
// map
#ifndef __SGI_STL_INTERNAL_TREE_H
#include <stl_tree.h>
#endif
#include <stl_map.h>
#include <stl_multimap.h>
// stl_set.h
template <class Key, class Compare = less<Key>, class Alloc = alloc>
class set {
public:
// typedefs:
typedef Key key_type;
typedef Key value_type;
private:
typedef rb_tree<key_type, value_type,
identity<value_type>, key_compare, Alloc> rep_type;
rep_type t; // red-black tree representing set
};
// stl_map.h
template <class Key, class T, class Compare = less<Key>, class Alloc = alloc>
class map {
public:
// typedefs:
typedef Key key_type;
typedef T mapped_type;
typedef pair<const Key, T> value_type;
private:
typedef rb_tree<key_type, value_type,
select1st<value_type>, key_compare, Alloc> rep_type;
rep_type t; // red-black tree representing map
};
// stl_tree.h
struct __rb_tree_node_base
{
typedef __rb_tree_color_type color_type;
typedef __rb_tree_node_base* base_ptr;
color_type color;
base_ptr parent;
base_ptr left;
base_ptr right;
};
// stl_tree.h
template <class Key, class Value, class KeyOfValue, class Compare, class Alloc
= alloc>
class rb_tree {
protected:
typedef void* void_pointer;
typedef __rb_tree_node_base* base_ptr;
typedef __rb_tree_node<Value> rb_tree_node;
typedef rb_tree_node* link_type;
typedef Key key_type;
typedef Value value_type;
public:
// insert⽤的是第⼆个模板参数左形参
pair<iterator,bool> insert_unique(const value_type& x);
// erase和find⽤第⼀个模板参数做形参
size_type erase(const key_type& x);
iterator find(const key_type& x);
protected:
size_type node_count; // keeps track of size of tree
link_type header;
};
template <class Value>
struct __rb_tree_node : public __rb_tree_node_base
{
typedef __rb_tree_node<Value>* link_type;
Value value_field;
};

通过下图对框架的分析，我们可以看到源码中rb_tree用了一个巧妙的泛型思想实现，rb_tree是实现key的搜索场景，还是key/value的搜索场景不是直接写死的，而是由第⼆个模板参数Value决定_rb_tree_node中存储的数据类型。

set实例化rb_tree时第二个模板参数给的是key，map实例化rb_tree时第2二个模板参数给的是pair<const key, T>，这样⼀颗红黑树既可以实现key搜索场景的set，也可以实现key/value搜索场景的map。

要注意⼀下，源码里面模板参数是用T代表value，而内部写的value_type不是我们我们日常key/value场景中说的value，源码中的value_type反而是红黑树结点中存储的真实的数据的类型。

rb_tree第⼆个模板参数Value已经控制了红黑树结点中存储的数据类型，为什么还要传第⼀个模板参数Key呢？尤其是set，两个模板参数是⼀样的，这是很多同学这时的⼀个疑问。要注意的是对于map和set，find/erase时的函数参数都是Key，所以第一个模板参数是传给find/erase等函数做形参的类型的。对于set而言两个参数是一样的，但是对于map而言就完全不一样了，map insert的是pair对象，但是find和ease的是Key对象。

二.模拟实现map和set

2.1搭建框架并实现插入操作

参考源码框架，map和set复用之前我们实现的红黑树。

我们这里相比源码调整一下，key参数就用K，value参数就用V，红黑树中的数据类型，我们使用T。

 其次因为RBTree实现了泛型不知道T参数导致是K，还是pair<K, V>，那么insert内部进行插入逻辑较时，就没办法进行比较，因为pair的默认支持的是key和value⼀起参与比较，我们需要的是任何时候只比较key，所以我们在map和set层分别实现⼀个MapKeyOfT和SetKeyOfT的仿函数传给RBTree的KeyOfT，然后RBTree中通过KeyOfT仿函数取出T类型对象中的key，再进行比较，具体细节参考如下代码实现。

源码中的实现： 

// 源码中pair⽀持的<重载实现
template <class T1, class T2>
bool operator< (const pair<T1,T2>& lhs, const pair<T1,T2>& rhs)
{ return lhs.first<rhs.first || (!(rhs.first<lhs.first) &&
lhs.second<rhs.second); }

 myset：

// Myset.h
namespace bit
{template<class K>class set{struct SetKeyOfT{const K& operator()(const K& key){return key;}};public:bool insert(const K& key){return _t.Insert(key);}private:RBTree<K, const K, SetKeyOfT> _t;};
}

mymap:

//mymap.h
namespace bit
{template<class K, class V>class map{struct MapKeyOfT{const K& operator()(const pair<K, V>& kv){return kv.first;}};public:bool insert(const pair<K, V>& kv)return _t.Insert(kv);}private:RBTree<K, pair<const K, V>, MapKeyOfT> _t;};
}

 RBTree:

//RBTree.henum Colour
{RED,BLACK
};template<class T>
struct RBTreeNode
{// 这里更新控制平衡也要加入parent指针T _data;RBTreeNode<T>* _left;RBTreeNode<T>* _right;RBTreeNode<T>* _parent;Colour _col;RBTreeNode(const T& data):_data(data), _left(nullptr), _right(nullptr), _parent(nullptr){}
};template<class K, class T, class KeyOfT>
class RBTree
{typedef RBTreeNode<T> Node;
public:bool Insert(const T& data){if (_root == nullptr){_root = new Node(data);_root->_col = BLACK;return 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 false;return { Iterator(cur, _root), false };}}cur = new Node(data);Node* newnode = cur;cur->_col = RED;if (kot(parent->_data) < kot(data)){parent->_right = cur;}else{parent->_left = cur;}// 链接父亲cur->_parent = parent;// 父亲是红色，出现连续的红色节点，需要处理while (parent && parent->_col == RED){Node* grandfather = parent->_parent;if (parent == grandfather->_left){//   g// p   uNode* uncle = grandfather->_right;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{if (cur == parent->_left){//     g//   p    u// cRotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{//      g//   p    u//     cRotateL(parent);RotateR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}else{//   g// u   pNode* 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//       cif (cur == parent->_right){RotateL(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{RotateR(parent);RotateL(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}}_root->_col = BLACK;return true;}};

2.2iterator的实现

iterator核心源代码:

struct __rb_tree_base_iterator
{typedef __rb_tree_node_base::base_ptr base_ptr;base_ptr node;void increment(){if (node->right != 0){node = node->right;while (node->left != 0)node = node->left;}else{base_ptr y = node->parent;while (node == y->right){node = y;y = y->parent;}if (node->right != y)node = y;}}void decrement(){if (node->color == __rb_tree_red && node->parent->parent == node)node = node->right;else if (node->left != 0){base_ptr y = node->left;while (y->right != 0)y = y->right;node = y;}else{base_ptr y = node->parent;while (node == y->left)node = y;y = y->parent;}node = y;}
};template <class Value, class Ref, class Ptr>
struct __rb_tree_iterator : public __rb_tree_base_iterator
{typedef Value value_type;typedef Ref reference;typedef Ptr pointer;typedef __rb_tree_iterator<Value, Value&, Value*> iterator;__rb_tree_iterator() {}__rb_tree_iterator(link_type x){node = x;}__rb_tree_iterator(const iterator& it){node = it.node;}reference operator*() const{return link_type(node)->value_field;}#ifndef __SGI_STL_NO_ARROW_OPERATORpointer operator->() const{return &(operator*());}#endif /* __SGI_STL_NO_ARROW_OPERATOR */self& operator++(){increment(); return *this;}self& operator--(){decrement(); return *this;}inline bool operator==(const __rb_tree_base_iterator& x,const __rb_tree_base_iterator& y){return x.node == y.node;}inline bool operator!=(const __rb_tree_base_iterator& x,const __rb_tree_base_iterator& y){return x.node != y.node;}
};

iterator实现思路分析：

• iterator实现的大框架跟list的iterator思路是一致的，用⼀个类型封装结点的指针，再通过重载运算符实现，迭代器像指针一样访问的行为。

• 这里的难点是operator++和operator--的实现。之前使用部分，我们分析了，map和set的迭代器走的是中序遍历，左子树->根结点->右子树，那么begin()会返回中序第⼀个结点的iterator也就是10所在结点的迭代器。

• 迭代器++的核心逻辑就是不看全局，只看局部，只考虑当前中序局部要访问的下⼀个结点。

• 迭代器++时，如果it指向的结点的右子树不为空，代表当前结点已经访问完了，要访问下⼀个结点是右子树的中序第一个，一棵树中序第一个是最左结点，所以直接找右子树的最左结点即可。

• 迭代器++时，如果it指向的结点的右子树空，代表当前结点已经访问完了且当前结点所在的子树也访问完了，要访问的下一个结点在当前结点的祖先里面，所以要沿着当前结点到根的祖先路径向上找。

• 如果当前结点是父亲的左，根据中序左子树->根结点->右子树，那么下一个访问的结点就是当前结点的父亲；如下图：it指向25，25右为空，25是30的左，所以下⼀个访问的结点就是30。

• 如果当前结点是父亲的右，根据中序左子树->根结点->右子树，当前当前结点所在的子树访问完了，当前结点所在父亲的子树也访问完了，那么下一个访问的需要继续往根的祖先中去找，直到找到孩子是父亲左的那个祖先就是中序要问题的下一个结点。如下图：it指向15，15右为空，15是10的右，15所在⼦树话访问完了，10所在⼦树也访问完了，继续往上找，10是18的左，那么下⼀个访问的结点就是18。

• end()如何表示呢？如下图：当it指向50时，++it时，50是40的右，40是30的右，30是18的右，18到根没有父亲，没有找到孩子是父亲左的那个祖先，这是父亲为空了，那我们就把it中的结点指针置为nullptr，我们用nullptr去充当end。需要注意的是stl源码空，红黑树增加了一个哨兵位头结点做为end()，这哨兵位头结点和根互为父亲，左指向最左结点，右指向最右结点。相比我们用nullptr作为end()，差别不大，他能实现的，我们也能实现。只是--end()判断到结点时空，特殊处理⼀下，让迭代器结点指向最右结点。具体参考迭代器--实现。

• 迭代器--的实现跟++的思路完全类似，逻辑正好反过来即可，因为他访问顺序是右子树->根结点->左子树，当it指向的节点左子树不为空，下一个要访问的节点就是当前节点的左子树的最右节点。

当it所指向的节点左子树为空时， 那么下一个访问的需要继续往根的祖先中去找，直到找到孩子是父亲右的那个祖先就是中序要问题的下一个结点。

• map的iterator不支持修改key但是可以修改value，我们把map的第二个模板参数pair的第一个参数改成const K即可， RBTree<K, pair<const K, V>, MapKeyOfT> _t;

//map.h
namespace bit
{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<const K, V>& kv){return _t.Insert(kv);}private:RBTree<K, pair<const K, V>, MapKeyOfT> _t;};
}

• set的iterator也不支持修改，我们把set的第⼆个模板参数改成const K即可， RBTree<K,const K, SetKeyOfT> _t;

//set.h
namespace bit
{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>::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();}bool insert(const K& key)pair<iterator, bool> insert(const K& key){return _t.Insert(key);}private:RBTree<K, const K, SetKeyOfT> _t;};
}

2.3map[]的实现

map要⽀持[]，通过键值（key）直接访问或插入对应的值（value），如map[key] = value,它也需要修改insert返回值，修改RBtree中的insert返回值为pair<Iterator, bool> Insert(const T& data).

V& operator[](const K& key)
{pair<iterator, bool> ret = insert({ key, V() });return ret.first->second;
}

三.完整代码实现

//set.h
#include"RBTree.h"
namespace bit
{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>::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 K& key){return _t.Insert(key);}iterator find(const K& key){return _t.Find(key);}private:RBTree<K, const K, SetKeyOfT> _t;};}

//map.h
#include"RBTree.h"namespace bit
{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);}V& operator[] (const K& key){pair<iterator, bool> ret = insert({ key,V() });return ret.first->second;}private:RBTree<K, pair<const K, V>, MapKeyofT> _t;};
}

//RBTree.h
enum Colour
{RED,BLACK
};
template<class T>
struct RBTreeNode
{T _data;RBTreeNode<T>*_left;RBTreeNode<T>* _right;RBTreeNode<T>* _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，右⼦树最左结点就是中序第⼀个Node* leftMost = _node->_right;while (leftMost->_left){leftMost = leftMost->_left;} _node = leftMost;} else{// 孩⼦是⽗亲左的那个祖先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(){// --end()，特殊处理，⾛到中序最后⼀个结点，整棵树的最右结点Node* rightMost = _root;while (rightMost && rightMost->_right){rightMost = rightMost->_right;} _node = rightMost;} else if (_node->_left){// 左⼦树不为空，中序左⼦树最后⼀个Node* rightMost = _node->_left;while (rightMost->_right){rightMost = rightMost->_right;} _node = rightMost;} else{// 孩⼦是⽗亲右的那个祖先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) const{return _node != s._node;} bool operator== (const Self& s) const{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;// 新增结点。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 uif (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 pNode * 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// cif (cur == parent->_right){RotateL(grandfather);parent->_col = BLACK;grandfather->_col = RED;} else{// g// u p// cRotateR(parent);RotateL(grandfather);cur->_col = BLACK;grandfather->_col = RED;} break;}}} _root->_col = BLACK;return make_pair(Iterator(newnode, _root), true);}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: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;}
private:Node* _root = nullptr;
};