数据结构-红黑树（RBTree）

红黑树是一棵二叉搜索树，它在每个节点上增加了一个存储位来表示节点的颜色，可以是Red或Black。

通过对任何一条从根到叶子简单 路径上的颜色来约束，红黑树保证最长路径不超过最短路径的两倍，因而近似于平衡。

红黑树是满足下面红黑性质的二叉搜索树
1. 每个节点，不是红色就是黑色的

2. 根节点是黑色的

3. 如果一个节点是红色的，则它的两个子节点是黑色的

4. 对每个节点，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。

插入的几种情况
ps:cur为当前节点，p为父节点，g为祖父节点，u为叔叔节点

1.第一种情况 cur为红，p为红，g为黑，u存在且为红

则将p,u改为黑，g改为红，然后把g当成cur，继续向上调整。

2.第二种情况 cur为红，p为红，g为黑，u不存在/u为黑

p为g的左孩子，cur为p的左孩子，则进行右单旋转；

相反，p为g的右孩子，cur为p的右孩子，则进行左单旋转

p、g变色--p变黑，g变红

3.第三种情况
cur为红，p为红，g为黑，u不存在/u为黑

p为g的左孩子，cur为p的右孩子，则针对p做左单旋转；

相反，p为g的右孩子，cur为p的左孩子，则针对p做右单旋转

则转换成了情况2

4.第四种情况

   为空树或者只有一个根节点

主要代码：

#pragma onceenum Color{RED,BLACK};template <typename K, typename V>struct RBTreeNode{K _key;V _value;Color _col;RBTreeNode<K, V>* _left;RBTreeNode<K, V>* _right;RBTreeNode<K, V>* _parent;RBTreeNode(const K& key, const V& value):_key(key), _value(value), _left(NULL), _right(NULL), _parent(NULL), _col(RED){}};template<typename K, typename V>class RBTree{typedef RBTreeNode<K,V> Node;public:RBTree():_root(NULL){}pair<Node* ,bool> Insert(const K& key, const V& value){if (_root == NULL){_root = new Node(key, value);_root->_col = BLACK;return make_pair(_root,true);}Node* cur = _root;Node* parent = NULL;while (cur){if (key < cur->_key){parent = cur;cur = cur->_left;}else if (key>cur->_key){parent = cur;cur = cur->_right;}else{return make_pair(cur, false);}}cur = new Node(key, value);if (parent->_key < key){parent->_right = cur;cur->_parent = parent;}else{parent->_left = cur;cur->_parent = parent;}  //到这块表示插入完成，然后进行调整Node* newcur = cur;while (parent && parent->_col == RED){Node* grandparent = parent->_parent;if (grandparent->_left == parent){Node* uncle = grandparent->_right;//1.if (uncle && uncle->_col == RED){uncle->_col = parent->_col = BLACK;grandparent->_col = RED;cur = grandparent;parent = cur->_parent;}else // 2,3  （2为单旋，3为双旋）{if (cur == parent->_left){//右单旋RotateR(grandparent);}else{//左右双旋RotateLR(grandparent);swap(parent, cur);}parent->_col = BLACK;grandparent->_col = RED;break;}}else{Node* uncle = grandparent->_left;if (uncle && uncle->_col == RED){uncle->_col = parent->_col = BLACK;grandparent->_col = RED;cur = grandparent;parent = cur->_parent;}else // 2,3  （2为单旋，3为双旋）{if (cur == parent->_right){//右单旋RotateL(grandparent);}else{//左右双旋RotateRL(grandparent);swap(parent, cur);}parent->_col = BLACK;grandparent->_col = RED;break;}}}_root->_col = BLACK;return make_pair(newcur, true);}V& operator[](const K& key){pair<Node*, bool> ret;ret = Insert(key,V());return ret.first->_value;}bool IsRBTree(){if (_root && _root->_col == RED)return false;size_t k = 0;size_t num = 0;Node* cur = _root;while (cur){if (cur->_col == BLACK)++k;cur = cur->_left;}return CheckColor(_root) && CheckBlackNum(_root, k, num);}protected:bool CheckColor(Node* root){if (root == NULL)return true;if (root->_col == RED && root->_parent->_col == RED)return false;return CheckColor(root->_left) && CheckColor(root->_right);}bool CheckBlackNum(Node* root, const size_t k, size_t num){if (root == NULL){return k == num;}if (root->_col == BLACK)num++;return CheckBlackNum(root->_left, k, num) && CheckBlackNum(root->_right, k, num);}void RotateL(Node* grandparent)  //左单旋{Node* subR = grandparent->_right;Node* subRL = subR->_left;grandparent->_right = subRL;if (subRL)subRL->_parent = grandparent;subR->_left = grandparent;Node* ppNode = grandparent->_parent;grandparent->_parent = subR;subR->_parent = ppNode;if (ppNode == NULL){_root = subR;}else{if (ppNode->_left == grandparent){ppNode->_left = subR;}else{ppNode->_right = subR;}}}void RotateR(Node* grandparent)  //右单旋{Node* subL = grandparent->_left;Node* subLR = subL->_right;grandparent->_left = subLR;if (subLR)subLR->_parent = grandparent;subL->_right = grandparent;Node* ppNode = grandparent->_parent;grandparent->_parent = subL;subL->_parent = ppNode;if (ppNode == NULL){_root = subL;}else{if (ppNode->_left == grandparent){ppNode->_left = subL;}else{ppNode->_right = subL;}}}void RotateRL(Node* grandparent){RotateR(grandparent->_right);RotateL(grandparent);}void RotateLR(Node* grandparent){RotateL(grandparent->_left);RotateR(grandparent);}private:Node* _root;};