AVL树的插入(包含更新平衡因子)

bool Insert(const pair<K, V>& kv){//1.搜索树的规则插入//2.看是是否违反平衡规则，如果违反就需要处理：旋转if (_root == nullptr){_root = new Node(kv);_root->_bf = 0;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);if (parent->_kv.first < kv.first){parent->_right = cur;}else{parent->_left = cur;}cur->_parent = parent;//...//更新平衡因子while (parent)//最远要更新根{if (cur == parent->_right){parent->_bf++;}else{parent->_bf--;}//是否继续更新？if (parent->_bf == 0)//1 or -1 ->插入节点填上了矮的那边{//高度不变，更新结束break;}else if(parent->_bf == 1 || parent->_bf == -1)//0 -> 1 or -1插入节点导致一边变高了 {//子树的高度变了，继续更新祖先cur = cur->_parent;parent = parent->_parent;}else if (parent->_bf == 2 || parent->_bf == -2)//-1 or 1 -> 2or-2 插入节点导致一边变高了{//子树不平衡 -- 需要旋转处理//...if (parent->_bf ==  2 && cur->_bf == 1)//左单旋{RotateL(parent);}else if (parent->_bf == 2 && cur->_bf == 1)//右单选{RotateR(parent);}else if (parent->_bf == -2 && cur->_bf == -1)//左右双旋{RotateLR(parent);}else if (parent->_bf == 2 && cur->_bf == -1)//右左双旋{RotateRL(parent);}break;}else{//插入之前AVL树就存在不平衡子树，平衡因子的绝对值>=2的节点assert(false);}}return true;}

子树的旋转

子树的左旋转

 void RotateL(Node* parent)//左单旋{Node* subR = parent->_right;Node* subRL = subR->_left;parent->_right = subRL;if(subRL)subRL->_parent = parent;//易错Node* ppNode = parent->_parent;subR->_left = parent;parent->_parent = subR;//易错if (parent == _root){_root = subR;_root->_parent = nullptr;}else{if (parent == ppNode->_left){ppNode->_left = subR;}else{ppNode->_right = subR;}subR->_parent = ppNode;}//更新平衡因子parent->_bf = 0;subR->_bf = 0;}

子树的右旋转

 void RotateR(Node* parent){Node* subL = parent->_left;Node* subLR = subL->_right;parent->_left = subLR;if (subLR)subLR->_parent = parent;//易错Node* ppNode = parent->_parent;subL->_right = parent;parent->_parent = subL;//易错if (parent == _root){_root = subL;_root->_parent = nullptr;}else{if (parent == ppNode->_left){ppNode->_left = subL;}else{ppNode->_right = subL;}subL->_parent = ppNode;}//更新平衡因子parent->_bf = 0;subL->_bf = 0;}

左右双旋

void RotateLR(Node* parent){Node* subL = parent->_left;Node* subLR = subL->_right;int bf = subLR->_bf;RotateL(parent->_left);RotateR(parent);//更新平衡因子if (bf == 0){parent->_bf = 0;subL->_bf = 0;subLR->_bf = 0;}else if (bf == 1){parent->_bf = 0;subL->_bf = -1;subLR->_bf = 0;}else if(bf == -1){parent->_bf = 1;subL->_bf = 0;subLR->_bf = 0;}else{//subLR->_bf旋转前就有问题assert(false);}}

右左双旋

void RotateRL(Node* parent){Node* subR = parent->_right;Node* subRL = subR->_left;int bf = subRL->_bf;RotateR(parent->_right);RotateL(parent);if (bf == 0){subRL->_bf = 0;parent->_bf = 0;subR->_bf = 0;}else if (bf == 1){subRL->_bf = 0;parent->_bf = -1;subR->_bf = 0;}else if (bf == -1){subRL->_bf = 0;parent->_bf = 0;subRL->_bf = 1;}else{//subLR->_bf旋转前就有问题assert(false);}}

求树的高度

 int _Height(Node* root){if (root == nullptr)return 0;int lh = _Height(root->_left);int rh = _Height(root->_right);return lh > rh ? lh + 1 : rh + 1;}int Height(){return _Height(_root);}

判断是否为平衡二叉树

bool _IsBalanceTree(Node* root){// 空树也是AVL树if (nullptr == root)return true;// 计算pRoot节点的平衡因子：即pRoot左右子树的高度差int leftHeight = _Height(root->_left);int rightHeight = _Height(root->_right);int diff = rightHeight - leftHeight;// 如果计算出的平衡因子与pRoot的平衡因子不相等，或者// pRoot平衡因子的绝对值超过1，则一定不是AVL树if (abs(diff) >= 2){cout << root->_kv.first << "节点平衡因子异常" << endl;return false;}if (diff != root->_bf){cout << root->_kv.first << "节点平衡因子不符合实际" << endl;return false;}// pRoot的左和右如果都是AVL树，则该树一定是AVL树return _IsBalanceTree(root->_left)&& _IsBalanceTree(root->_right);}bool IsBalanceTree(){return _IsBalanceTree(_root);}

层序遍历

vector<vector<int>> levelOrder() {vector<vector<int>> vv;if (_root == nullptr)return vv;queue<Node*>q;int levelSize = 1;q.push(_root);while (!q.empty()){// levelSize控制一层一层出vector<int> levelV;while (levelSize--){Node* front = q.front();q.pop();levelV.push_back(front->_kv.first);if (front->_left)q.push(front->_left);if (front->_right)q.push(front->_right);}vv.push_back(levelV);for (auto e : levelV){cout << e << " ";}cout << endl;// 上一层出完，下一层就都进队列levelSize = q.size();}return vv;}

代码总览

#pragma once
#include<assert.h>
#include<vector>
#include<time.h>
#include<queue>template<class K,class V>
struct AVLTreeNode
{pair<K, V>* _kv;AVLTreeNode<K, V>* _left;AVLTreeNode<K, V>* _right;AVLTreeNode< K,V>*_parent;//左右子树高度差int _bf; //balence factor 平衡因子AVLTreeNode(const pair<K, V>& kv)//构造函数:_kv(kv), _left(nullptr), _right(nullptr), _parent(nullptr),_bf(0){}//AVL树并没有规定必须要实现平衡因子//只是一个实现的选择，方便控制平衡
};template<class K,class V>
class AVLTree
{typedef AVLTreeNode<K, V>Node;
public:bool Insert(const pair<K, V>& kv){//1.搜索树的规则插入//2.看是是否违反平衡规则，如果违反就需要处理：旋转if (_root == nullptr){_root = new Node(kv);_root->_bf = 0;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);if (parent->_kv.first < kv.first){parent->_right = cur;}else{parent->_left = cur;}cur->_parent = parent;//...//更新平衡因子while (parent)//最远要更新根{if (cur == parent->_right){parent->_bf++;}else{parent->_bf--;}//是否继续更新？if (parent->_bf == 0)//1 or -1 ->插入节点填上了矮的那边{//高度不变，更新结束break;}else if(parent->_bf == 1 || parent->_bf == -1)//0 -> 1 or -1插入节点导致一边变高了 {//子树的高度变了，继续更新祖先cur = cur->_parent;parent = parent->_parent;}else if (parent->_bf == 2 || parent->_bf == -2)//-1 or 1 -> 2or-2 插入节点导致一边变高了{//子树不平衡 -- 需要旋转处理//...if (parent->_bf ==  2 && cur->_bf == 1)//左单旋{RotateL(parent);}else if (parent->_bf == 2 && cur->_bf == 1)//右单选{RotateR(parent);}else if (parent->_bf == -2 && cur->_bf == -1)//左右双旋{RotateLR(parent);}else if (parent->_bf == 2 && cur->_bf == -1)//右左双旋{RotateRL(parent);}break;}else{//插入之前AVL树就存在不平衡子树，平衡因子的绝对值>=2的节点assert(false);}}return true;}private:void RotateL(Node* parent)//左单旋{Node* subR = parent->_right;Node* subRL = subR->_left;parent->_right = subRL;if(subRL)subRL->_parent = parent;//易错Node* ppNode = parent->_parent;subR->_left = parent;parent->_parent = subR;//易错if (parent == _root){_root = subR;_root->_parent = nullptr;}else{if (parent == ppNode->_left){ppNode->_left = subR;}else{ppNode->_right = subR;}subR->_parent = ppNode;}//更新平衡因子parent->_bf = 0;subR->_bf = 0;}void RotateR(Node* parent){Node* subL = parent->_left;Node* subLR = subL->_right;parent->_left = subLR;if (subLR)subLR->_parent = parent;//易错Node* ppNode = parent->_parent;subL->_right = parent;parent->_parent = subL;//易错if (parent == _root){_root = subL;_root->_parent = nullptr;}else{if (parent == ppNode->_left){ppNode->_left = subL;}else{ppNode->_right = subL;}subL->_parent = ppNode;}//更新平衡因子parent->_bf = 0;subL->_bf = 0;}void RotateLR(Node* parent){Node* subL = parent->_left;Node* subLR = subL->_right;int bf = subLR->_bf;RotateL(parent->_left);RotateR(parent);//更新平衡因子if (bf == 0){parent->_bf = 0;subL->_bf = 0;subLR->_bf = 0;}else if (bf == 1){parent->_bf = 0;subL->_bf = -1;subLR->_bf = 0;}else if(bf == -1){parent->_bf = 1;subL->_bf = 0;subLR->_bf = 0;}else{//subLR->_bf旋转前就有问题assert(false);}}void RotateRL(Node* parent){Node* subR = parent->_right;Node* subRL = subR->_left;int bf = subRL->_bf;RotateR(parent->_right);RotateL(parent);if (bf == 0){subRL->_bf = 0;parent->_bf = 0;subR->_bf = 0;}else if (bf == 1){subRL->_bf = 0;parent->_bf = -1;subR->_bf = 0;}else if (bf == -1){subRL->_bf = 0;parent->_bf = 0;subRL->_bf = 1;}else{//subLR->_bf旋转前就有问题assert(false);}}void _InOrder(Node* root){if (root == nullptr)return;_InOrder(root->_left);cout << root->_kv.first << " ";_InOrder(root->_right);}int _Height(Node* root){if (root == nullptr)return 0;int lh = _Height(root->_left);int rh = _Height(root->_right);return lh > rh ? lh + 1 : rh + 1;}bool _IsBalanceTree(Node* root){// 空树也是AVL树if (nullptr == root)return true;// 计算pRoot节点的平衡因子：即pRoot左右子树的高度差int leftHeight = _Height(root->_left);int rightHeight = _Height(root->_right);int diff = rightHeight - leftHeight;// 如果计算出的平衡因子与pRoot的平衡因子不相等，或者// pRoot平衡因子的绝对值超过1，则一定不是AVL树if (abs(diff) >= 2){cout << root->_kv.first << "节点平衡因子异常" << endl;return false;}if (diff != root->_bf){cout << root->_kv.first << "节点平衡因子不符合实际" << endl;return false;}// pRoot的左和右如果都是AVL树，则该树一定是AVL树return _IsBalanceTree(root->_left)&& _IsBalanceTree(root->_right);}public:void InOrder(){_InOrder(_root);cout << endl;}vector<vector<int>> levelOrder() {vector<vector<int>> vv;if (_root == nullptr)return vv;queue<Node*>q;int levelSize = 1;q.push(_root);while (!q.empty()){// levelSize控制一层一层出vector<int> levelV;while (levelSize--){Node* front = q.front();q.pop();levelV.push_back(front->_kv.first);if (front->_left)q.push(front->_left);if (front->_right)q.push(front->_right);}vv.push_back(levelV);for (auto e : levelV){cout << e << " ";}cout << endl;// 上一层出完，下一层就都进队列levelSize = q.size();}return vv;}bool IsBalanceTree(){return _IsBalanceTree(_root);}int Height(){return _Height(_root);}private:Node* _root = nullptr;
};void TestAVLTree1()
{//int a[] = { 1, 2, 3, 4, 5, 6, 7, 8 };int a[] = { 30,29,28,27,26,25,24,11,8,7,6,5,4,3,2,1 };AVLTree<int, int> t;for (auto e : a){t.Insert(make_pair(e, e));}t.levelOrder();
}void TestAVLTree2()
{const size_t N = 1024 * 1024 * 10;vector<int> v;v.reserve(N);srand(time(0));for (size_t i = 0; i < N; ++i){//v.push_back(rand());v.push_back(i);}AVLTree<int, int> t;for (auto e : v){t.Insert(make_pair(e, e));}//t.levelOrder();//cout << endl;cout << "是否平衡?" << t.IsBalanceTree() << endl;cout << "高度:" << t.Height() << endl;//t.InOrder();
}

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C++ AVL树(补充)

AVL树的插入(包含更新平衡因子)

子树的旋转

子树的左旋转

子树的右旋转

左右双旋

右左双旋

求树的高度

判断是否为平衡二叉树

层序遍历

代码总览

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