C++：map和set类
序列式容器和关联式容器
string、vector、list、deque、array、forward_list，这些容器统称为序列式容器
这些容器存储之间的值一般没有紧密的关联关系，比如交换一下，它依然是序列式容器
map、set这些系列的就是关联式容器，两个位置有紧密的关联关系，交换一下它的结构就被破坏了
map和set的底层是红黑树
set是key搜索场景的结构
map是key/value搜索场景的结构
set类
template < class T, class Compare = less<T>, class Alloc = allocator<T>>
class set
{};T是set底层关键字key的类型
set默认是小于进行比较，如果想按照自己的想法来比较可以给第二个参数传一个仿函数
set底层存储数据的内存是从空间配置器申请的，如果需要可以自己实现内存池传给第三个参数
一般情况下只需要传第一个参数即可
multiset和set的差异
multiset和set的用法基本完全类似，主要的区别就在于multiset支持值冗余，也就是multiset能有多个相同的key，但是set不能有相同的key
map类
template<class Key, class T, class Compare = less<Key>, class Alloc = allocator<pair<const Key, T> >map::allocator_type>
class map
{};Key是map底层关键字的类型
T是map底层value的类型
map和set一样也是默认按key小于比较，如果想按照自己的想法来比较可以给第二个参数传一个仿函数
可以自己实现内存池传给第三个参数
multimap和map的差异
multimap和map的用法基本完全类似，主要的区别就在于multimap支持值冗余，也就是multimap能有多个相同的key，但是map不能有相同的key
map和set类的模拟实现
红黑树结构
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)
{}
};结构里和之前一样，这里的数据写的T是为了适配map和set两种容器
如果是map，则T应该是pair<key, value>，如果是set，则T应该是key
迭代器
template<class T, class Ref, class Ptr>
struct RBTreeIterator
{
typedef RBTreeNode<T> Node;
typedef RBTreeIterator<T, Ref, Ptr> Self;
Node* _node;
Node* _root; // 删除的--end需要根节点
RBTreeIterator(Node* node, Node* root)
:_node(node)
,_root(root)
{}
Self operator++()
{
if (_node->_right)
{
Node* min = _node->_right;
while (min->_left)
{
min = min->_left;
}
_node = min;
}
else
{
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && parent->_right == cur)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}
Self operator--()
{
if (_node == nullptr) // end()
{
// root的最右节点
Node* cur = _root;
while (cur && cur->_right)
{
cur = cur->_right;
}
_node = cur;
}
else if (_node->_left)
{
Node* min = _node->_left;
while (min->_right)
{
min = min->_right;
}
_node = min;
}
else
{
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && parent->_left == cur)
{
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;
}
};operator++
这里的++分为两种情况
若当前节点存在右子树，则应该找右子树的最左节点
若不存在右子树，则需要往上找parent，直到当前节点不再是parent的右节点为止
operator--
和operator++的情况相反
若当前节点存在左子树，则应该找左子树的最右节点
若不存在左子树，则需要往上找parent，直到当前节点不再是parent的左节点为止
map的operator[]
V& operator[](const K& key)
{
pair<iterator, bool> ret = insert({ key, V() });
return ret.first->second;
}map的[]需要支持插入、修改两种功能
RBTree中insert的返回值为pair<iterator, bool>
返回插入节点迭代器里面的second即可
完整代码
RBTree.h
#pragma once
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; // 删除的--end需要根节点
RBTreeIterator(Node* node, Node* root)
:_node(node)
,_root(root)
{}
Self operator++()
{
if (_node->_right)
{
Node* min = _node->_right;
while (min->_left)
{
min = min->_left;
}
_node = min;
}
else
{
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && parent->_right == cur)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}
Self operator--()
{
if (_node == nullptr) // end()
{
// root的最右节点
Node* cur = _root;
while (cur && cur->_right)
{
cur = cur->_right;
}
_node = cur;
}
else if (_node->_left)
{
Node* min = _node->_left;
while (min->_right)
{
min = min->_right;
}
_node = min;
}
else
{
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && parent->_left == cur)
{
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;
public:
Iterator Begin()
{
Node* cur = _root;
while (cur && cur->_left)
{
cur = cur->_left;
}
return Iterator(cur, _root);
}
Iterator End()
{
return Iterator(nullptr, _root);
}
ConstIterator Begin() const
{
Node* cur = _root;
while (cur && cur->_left)
{
cur = cur->_left;
}
return ConstIterator(cur, _root);
}
ConstIterator End() const
{
return ConstIterator(nullptr, _root);
}
pair<Iterator, bool> Insert(const T& data)
{
if (_root == nullptr)
{
_root = new Node(data);
_root->_col = BLACK;
return { 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 { 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;
}
cur->_parent = parent;
while (parent && parent->_col == RED)
{
Node* grandfather = parent->_parent;
if (grandfather->_left == parent)
{
Node* uncle = grandfather->_right;
if (uncle && uncle->_col == RED)
{
// 变色
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
// 继续向上处理
cur = grandfather;
parent = cur->_parent;
}
else
{
if (cur == parent->_left)
{
RotateR(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
}
else
{
RotateL(parent);
RotateR(grandfather);
cur->_col = BLACK;
parent->_col = grandfather->_col = RED; // 1
}
break;
}
}
else
{
Node* uncle = grandfather->_left;
if (uncle && uncle->_col == RED)
{
// 变色
parent->_col = uncle->_col = BLACK;
grandfather->_col = RED;
// 继续向上处理
cur = grandfather;
parent = cur->_parent;
}
else
{
if (cur == parent->_right)
{
RotateL(grandfather);
parent->_col = BLACK;
grandfather->_col = RED;
}
else
{
RotateR(parent);
RotateL(grandfather);
cur->_col = BLACK;
parent->_col = grandfather->_col = RED; // 1
}
break;
}
}
}
// 确保根节点颜色是黑色
_root->_col = BLACK;
return { Iterator(newnode, _root), true };
}
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 (parent == _root)
{
_root = subL;
subL->_parent = nullptr;
}
else
{
if (parentParent->_left == parent)
{
parentParent->_left = subL;
}
else
{
parentParent->_right = subL;
}
subL->_parent = parentParent;
}
}
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;
}
}
int Height()
{
return _Height(_root);
}
int Size()
{
return _Size(_root);
}
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 nullptr;
}
private:
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 _Size(Node* root)
{
if (root == nullptr)
return 0;
return _Size(root->_left) + _Size(root->_right) + 1;
}
private:
Node* _root = nullptr;
};Myset.h
#pragma once
#include "RBTree.h"
namespace lyw
{
template<class K>
class set
{
struct SetOfT
{
K operator()(const K& key)
{
return key;
}
};
public:
typedef typename RBTree<K, const K, SetOfT>::Iterator iterator;
typedef typename RBTree<K, const K, SetOfT>::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);
}
private:
RBTree<K, const K, SetOfT> _t;
};
}Mymap.h
#pragma once
#include "RBTree.h"
namespace lyw
{
template<class K, class V>
class map
{
struct MapOfT
{
const K& operator()(const pair<K, V>& kv)
{
return kv.first;
}
};
public:
typedef typename RBTree<K, pair<const K, V>, MapOfT>::Iterator iterator;
typedef typename RBTree<K, pair<const K, V>, MapOfT>::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>, MapOfT> _t;
};
}