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~set.h
SetKeyofpair
仿函数是为了红黑树比较时能够区分map和set，传MapKeyofpair时，用仿函数去比较就能够区分你到底是传Key过来、还是传pair过来
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, K, SetKeyofpair> _t;
};
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~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 K, class T, class KeyOfT>
class RBtree
{
private:
typedef RBTreeNode<T> Node;
Node* _root = nullptr;
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;
}
}
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;
return true;
}
}
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2.2 ⽀持iterator的实现
红黑树的迭代器可不是++就能得到下一个结点的。
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terator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。
2.2.1红黑树迭代器结构
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) const
{
return _node != s._node;
}
bool operator== (const Self& s) const
{
return _node == s._node;
}
};
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2.2.2 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
【说明】:中序走法
------------左结点->根结点->右结点
情况一（右子树不为空）++：如果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。
情况二（右子树为空）++：如果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。
分析：
右子树为空又可以分成两种情况
情况一：结点是父亲的左
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：如果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。
情况二：结点是父亲的右
• 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：如果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。
迭代器end()如何实现呢？
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。这里雨源码不同，我们是用nullptr来实现end()，而源码使用哨兵位头结点实现end()
stl源码实现迭代器end()
end()不为nullptr,为header(头结点)
iterator++代码实现
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 && cur == parent->_right)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}
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2.2.4 iterator–
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，具体参考下⾯代码实现。
特殊处理：
–end()的之后,是走到最后一个结点（最右结点）。
Self operator--()
{
if (_node == nullptr)
{
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
{
Node* cur = _node;
Node* parent = cur->_parent;
while (parent && cur == parent->_left)
{
cur = parent;
parent = cur->_parent;
}
_node = parent;
}
return *this;
}
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3 注意须知 [实现map/set]
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 _t;
• 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, MapKeyOfT> _t;
3.1 map[]实现
map要⽀持[]主要需要修改insert返回值⽀持，修改RBtree中的insert返回值为
V& operator[](const K& key)
{
pair<iterator, bool> ret = insert({ key, V() });
return ret.first->second;
}
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3.2代码实现
template<class K, class V>
class map
{
struct mapKeyofpair
{
const K& operator()(const pair<K,V>& kv)
{
return kv.first;
}
};
public:
typedef typename RBtree<K, pair<const K, V>, mapKeyofpair>::Iterator iterator;
typedef typename RBtree<K, pair<const K, V>, mapKeyofpair>::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);
}
private:
RBtree<K, pair<const K, V>, mapKeyofpair> _t ;
};
template<class K>
class set
{
struct setKeyofpair
{
const K& operator()(const K& key)
{
return key;
}
};
public:
typedef typename RBtree<K, const K, setKeyofpair>::Iterator iterator;
typedef typename RBtree<K, const K, setKeyofpair>::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& data)
{
return _t.insert(data);
}
private:
RBtree<K,const K, setKeyofpair> _t;
};
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)
{
Node* min = _node->_right;
while (min->_left)
{
min = min->_left;
}
_node = min;
}
else
{
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)
{
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
{
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 Keyofpair>
class RBtree
{
typedef RBTreeNode<T> Node;
public:
typedef RBtreeIterator<T, T&, T*> Iterator;
typedef RBtreeIterator<T, const T&, const T*> ConstIterator;
Iterator begin()
{
Node* node = _root;
while (node && node->_left)
{
node = node->_left;
}
return Iterator(node,_root);
}
ConstIterator begin() const
{
Node* node = _root;
while (node && node->_left)
{
node = node->_left;
}
return ConstIterator(node,_root);
}
Iterator end()
{
return Iterator(nullptr,_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 };
}
Keyofpair com;
Node* cur = _root;
Node* parent = nullptr;
while (cur)
{
if (com(cur->_data) < com(data))
{
parent = cur;
cur = cur->_right;
}
else if (com(cur->_data) > com(data))
{
parent = cur;
cur = cur->_left;
}
else
{
return { Iterator(cur, _root), false };
}
}
cur = new Node(data);
Node* newnode = cur;
cur->_col = RED;
if (com(parent->_data) < com(data))
{
parent->_right = cur;
}
else
{
parent->_left = cur;
}
cur->_parent = parent;
while (parent && parent->_col == RED)
{
Node* grandparent = parent->_parent;
if (parent == grandparent->_left)
{
Node* uncle = grandparent->_right;
if (uncle && uncle->_col == RED)
{
parent->_col = uncle->_col = BLACK;
grandparent->_col = RED;
cur = grandparent;
parent = cur->_parent;
}
else
{
if (cur == parent->_left)
{
RotateR(grandparent);
parent->_col = BLACK;
grandparent->_col = RED;
}
else
{
RotateL(parent);
RotateR(grandparent);
cur->_col = BLACK;
grandparent->_col = RED;
}
break;
}
}
else
{
Node* uncle = grandparent->_left;
if (uncle && uncle->_col == RED)
{
parent->_col = uncle->_col = BLACK;
grandparent->_col = RED;
cur = grandparent;
parent = cur->_parent;
}
else
{
if (cur == parent->_right)
{
RotateL(grandparent);
parent->_col = BLACK;
grandparent->_col = RED;
}
else
{
RotateR(parent);
RotateL(grandparent);
cur->_col = BLACK;
grandparent->_col = RED;
}
break;
}
}
}
_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* pParent = parent->_parent;
subL->_right = parent;
parent->_parent = subL;
if (parent == _root)
{
_root = subL;
subL->_parent = nullptr;
}
else
{
if (pParent->_left == parent)
{
pParent->_left = subL;
}
else
{
pParent->_right = subL;
}
subL->_parent = pParent;
}
}
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;
}
}
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;
}
int Height()
{
return _Height(_root);
}
int Size()
{
return _Size(_root);
}
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;
};
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最后在这悠长的叙述即将抵达彼岸之时，愿以一曲未了的旋律，轻拂你心灵的涟漪。我们共同走过的这段旅程，如同繁星点缀的夜空，每一颗星辰都承载着故事，每一缕光芒都映照着心迹。此刻，虽言尽而意未尽，但愿这份文字的余温，能伴你度过未来的每一个静！！！
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