【C++】红黑树

小小小汐- 2024-06-12 14:35:08 阅读 70

红黑树 

目录

a. 红黑树的概念

b. 红黑树的性质

c. 红黑树的实现


a. 红黑树的概念

红黑树,是一种二叉搜索树,但在每个结点上增加一个存储位表示结点的颜色,可以是Red或

Black。 通过对任何一条从根到叶子的路径上各个结点着色方式的限制,红黑树确保没有一条路

径会比其他路径长出俩倍,因而是接近平衡的

b. 红黑树的性质

每个结点不是红色就是黑色根节点是黑色的如果一个节点是红色的,则它的两个孩子结点是黑色的对于每个结点,从该结点到其所有后代叶结点的简单路径上,均包含相同数目的黑色结点空结点都是黑色的

c. 红黑树的实现

(一)红黑树节点的构建

代码

enum Colour{RED,BLACK};template<class K, class V>struct RBTreeNode{RBTreeNode<K, V>* _left;RBTreeNode<K, V>* _right;RBTreeNode<K, V>* _parent;pair<K, V> _kv;Colour _col;RBTreeNode(const pair<K, V>& kv):_left(nullptr), _right(nullptr), _parent(nullptr), _kv(kv), _col(RED) //默认为红节点,对于性质四,黑节点数不好控制,先默认红节点,后期再变颜色{}};

(二)红黑树的插入

实现思路

如果插入的是第一个节点(即根节点),由于性质二,我们需要把它变成黑色

除了上述情况,还有一种可能需要变色(回到性质三)

如图:

而面对这种情况,也分不同的做法

对于第一种情况(左图):

做法是把 parent 变成黑色的 , grandparent 变成红色的 ,uncle 变成黑色的 ,

然后 cur = grandparent , parent = cur->_parent , grandparent = parent->_parent ,uncle 也有变节点 ,直到不满足两个红节点连在一起的前提 或者 是 parent 为空(循环结束的条件)

注意:

根节点的颜色可能会在过程中更改(如上述右图),一定要在最后改回成黑色

对于第二种情况

parent 变成黑色 , grandparent 变成红色 ,再发生旋转(跟 AVL树 的旋转情况一样),完成 break即可

 

 代码

enum Colour{RED,BLACK};template<class K, class V>struct RBTreeNode{RBTreeNode<K, V>* _left;RBTreeNode<K, V>* _right;RBTreeNode<K, V>* _parent;pair<K, V> _kv;Colour _col;RBTreeNode(const pair<K, V>& kv):_left(nullptr), _right(nullptr), _parent(nullptr), _kv(kv), _col(RED){}};template<class K, class V>class RBTree{typedef RBTreeNode<K, V> Node;public:bool Insert(const pair<K, V>& kv){if (_root == nullptr){_root = new Node(kv);_root->_col = BLACK;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->_parent = parent;if (parent->_kv.first > cur->_kv.first){parent->_left = cur;}else{parent->_right = cur;}while (parent && parent->_col == RED){Node* grandparent = parent->_parent;if (parent == grandparent->_left){Node* uncle = grandparent->_right;if (uncle && uncle->_col == RED){parent->_col = BLACK;uncle->_col = BLACK;grandparent->_col = RED;cur = grandparent;parent = cur->_parent;}else{if (grandparent->_left == parent && parent->_left == cur){RotateR(grandparent);}else{RotateLR(grandparent);}parent->_col = BLACK;grandparent->_col = RED;cur = grandparent;parent = cur->_parent;}}else{Node* uncle = grandparent->_left;if (uncle && uncle->_col == RED){parent->_col = BLACK;uncle->_col = BLACK;grandparent->_col = RED;cur = grandparent;parent = cur->_parent;}else{if (grandparent->_right == parent && parent->_right == cur){RotateL(grandparent);}else{RotateRL(grandparent);}parent->_col = BLACK;grandparent->_col = RED;cur = grandparent;parent = cur->_parent;}}}_root->_col = BLACK;return true;}void InOder(){_InOder(_root);}bool IsBalance(){return _IsBalance(_root, 0);}~RBTree(){Destory(_root);_root = nullptr;}private:bool _IsBalance(Node* root,int MaxBlack) //验证是否是红黑树{if (root == nullptr){cout << MaxBlack + 1 << endl;return true;}Node* parent = root->_parent;if (_root->_col == RED){return false;}if (root->_col == RED && parent && parent->_col == RED){return false;}if (root->_col == BLACK){++MaxBlack;}return _IsBalance(root->_left, MaxBlack) && _IsBalance(root->_right, MaxBlack);}void RotateR(Node* root){Node* SubL = root->_left;Node* SubLR = SubL->_right;if (root == _root){_root = SubL;}else{Node* parent = root->_parent;if (parent->_left == root){parent->_left = SubL;}else{parent->_right = SubL;}}root->_left = SubLR;SubL->_right = root;SubL->_parent = root->_parent;root->_parent = SubL;}void RotateL(Node* root){Node* SubR = root->_right;Node* SunRL = SubR->_left;if (root == _root){_root = SubR;}else{Node* parent = root->_parent;if (parent->_left == root){parent->_left = SubR;}else{parent->_right = SubR;}}root->_right = SunRL;SubR->_left = root;SubR->_parent = root->_parent;root->_parent = SubR;}void RotateLR(Node* root){Node* SubL = root->_left;Node* SubLR = SubL->_right;RotateL(SubL);RotateR(root);}void RotateRL(Node* root){Node* SubR = root->_right;Node* SubRL = SubR->_left;RotateR(SubR);RotateL(root);}void _InOder(Node* root){if (root == nullptr){return;}_InOder(root->_left);cout << root->_kv.first << " " << root->_col << endl;_InOder(root->_right);}void Destory(Node* root){if (root == nullptr){return;}Destory(root->_left);Destory(root->_right);delete root;}Node* _root = nullptr;};


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