C++ 红黑树【内含代码】

1. 红黑树

1.1 红黑树的概念

红黑树，是一种二叉搜索树，但在每个节点上增加一个存储为表示节点的颜色，可以使Red或Black。通过对任何一条从根到叶子的路径上各个节点着色方式的限制，红黑树确保没有一条路径会比其他路径长出两倍，因而是接近平衡的。

1.2 红黑树的性质

1.每个节点不是红色就是黑色

2.根节点是黑色的

3.如果一个节点是红色的，则它的两个孩子节点是黑色的

4.对于每个节点，从该节点到其所有后代叶节点的简单路径上，均包含相同数目的黑色节点

5.每个叶子节点都是黑色的（此处的叶子节点指的是空节点）

1.3 红黑树节点的定义

enum Color
{RED,BLACK
};template <class K, class V>
struct RBTreeNode
{pair<K, V> _kv;//节点内的数据采用Key、Value形式RBTreeNode<K, V>* _left;//该节点的左孩子RBTreeNode<K, V>* _right;//该节点的右孩子RBTreeNode<K, V>* _parent;//该节点的双亲Color _col;RBTreeNode(const pair<K, V>& kv):_kv(kv), _left(nullptr), _right(nullptr), _parent(nullptr){}
};

1.4 红黑树的定义（代码不包含删除）

template <class K, class V>
class RBTree
{
public:typedef RBTreeNode<K, V> Node;RBTree() = default;RBTree(const RBTree<K, V>& t){_root = Copy(t._root);}RBTree<K, V>& operator=(RBTree<K, V> t){swap(_root, t._root);return *this;}~RBTree(){Destory(_root);_root = nullptr;}bool insert(const pair<K, V>& kv){if (_root == nullptr){_root = new Node(kv);return true;}Node* parent = nullptr;Node* cur = _root;while (cur){if (cur->_kv.first < kv.first){parent = cur;cur = cur->_right;}else if (cur->_kv.first > kv.first){parent = cur;cur = cur->_left;}else{return false;}}cur = new Node(kv);cur->_col = RED;if (parent->_kv.first < kv.first){parent->_right = cur;}else{parent->_left = cur;}cur->_parent = parent;while (parent && parent->_col == RED){Node* grandfather = parent->_parent;if (parent == grandfather->_left){Node* uncle = grandfather->_right;if (uncle && uncle->_col == RED)//如果叔叔存在且为红{parent->_col = BLACK;uncle->_col = BLACK;grandfather->_col = RED;cur = grandfather;parent = cur->_parent;}else//叔叔不存在或叔叔不存在且为黑{if (cur == parent->_left){RotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{RotateL(parent);RotateR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}}break;}else{Node* uncle = grandfather->_left;if (uncle && uncle->_col == RED){uncle->_col = parent->_col = BLACK;grandfather->_col = RED;cur = grandfather;parent = cur->_parent;}else{if (parent->_right == cur){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;}void InOrder(){_InOrder(_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:Node* Copy(Node* root){if (root == nullptr)return nullptr;Node* newRoot = new Node(root->_kv);//不一样的地方newRoot->_left = Copy(root->_left);newRoot->_right = Copy(root->_right);return newRoot;}void Destory(Node* root){if (root == nullptr)return;Destory(root->_left);Destory(root->_right);delete root;}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;//parent的左孩子Node* sublr = subl->_right;//parent左孩子的右孩子parent->_left = sublr;//30的右孩子作为双亲的左孩子if (sublr)//如果30的左孩子的右孩子存在，更新双亲sublr->_parent = parent;Node* parentParent = parent->_parent;// 因为60可能是棵子树，因此在更新其双亲前必须先保存60的双亲subl->_right = parent;//60作为30的右孩子parent->_parent = subl;//更新60的双亲if (parentParent == nullptr)// 如果60是根节点，根新指向根节点的指针{_root = subl;subl->_parent = nullptr;}else // 如果60是子树，可能是其双亲的左子树，也可能是右子树{if (parent == parentParent->_left){parentParent->_left = subl;}else{parentParent->_right = subl;}subl->_parent = parentParent;//更新30的双亲}}Node* _root = nullptr;
};