AVL树底层实现

#pragma once
#include<iostream>
#include<assert.h>
using namespace std;
template<class K, class V>
struct AVLTreeNode
{
  AVLTreeNode(const pair<K, V>& kv)
    : _right(nullptr)
    , _left(nullptr)
    , _parent(nullptr)
    , _bf(0)
    , _kv(kv)
  {}
  AVLTreeNode<K, V>* _right;
  AVLTreeNode<K, V>* _left;
  AVLTreeNode<K, V>* _parent;
  pair<K, V> _kv;
  int _bf;
};
template<class K, class V>
class AVLTree
{
  typedef AVLTreeNode<K, V> AVLNode;
public:
  int Height(AVLNode* root)
  {
    if (root == nullptr)
      return 0;
    int leftHeight = Height(root->_left);
    int rightHeight = Height(root->_right);
    return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;
  }
  bool _IsAVLTree(AVLNode* root)
  {
    if (root == nullptr) return true;
    int Height1 = Height(root->_left);
    int Height2 = Height(root->_right);
    int diff = Height2 - Height1;
    if (diff != root->_bf)
    {
      cout << root->_kv.first << " 平衡因子异常" << endl;
      return false;
    }
    return _IsAVLTree(root->_left)
      && _IsAVLTree(root->_right)
      && abs(diff) < 2;
  }
  bool IsAVLTree()
  {
    return _IsAVLTree(_root);
  }
  void Order()
  {
    _Order(_root);
    cout << endl;
  }
  void _Order(AVLNode* root)
  {
    if (root == nullptr)
      return;
    _Order(root->_left);
    cout << root->_kv.first << " ";
    _Order(root->_right);
  }
  bool Insert(const pair<K, V>& kv)
  {
    // 首次插入，树为空的情况
    if (_root == nullptr)
    {
      _root = new AVLNode(kv);
      return true;
    }
    AVLNode* parent = nullptr; //记录父节点
    AVLNode* cur = _root;// 开始遍历
    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;// 不能找到！找到说明已经有 key 了，插入失败
      }
    }
    // 运行到此处，即将要插入的位置
    cur = new AVLNode(kv);
    // 调整 cur 和 parent 的一些指针
    if (parent->_kv.first > kv.first) // 使用 parent->_kv.first 与 kv.first的比较
    {
      parent->_left = cur;
    }
    else if (parent->_kv.first < kv.first)
    {
      parent->_right = cur;
    }
    cur->_parent = parent;
    // 判断更新后父亲结点的大小
    // cur原本为新增节点  但是根据逐步更新父节点 parent，它会一直是成为 parent 的子节点
    while (parent)
    {
      if (cur == parent->_right)// 插入节点在右边
      {
        parent->_bf++;
      }
      else if (cur == parent->_left)
      {
        parent->_bf--;
      }
      if (parent->_bf == 0)
      {
        // 等于0，说明不用往上更新了，恰好父亲的两边一样高了
        break;
      }
      else if (parent->_bf == 1 || parent->_bf == -1)
      {
        //说明高度增加了（是从0变为了1或者-1）
        cur = parent;
        parent = parent->_parent;
        // 向上更新一步
      }
      else if (parent->_bf == 2 || parent->_bf == -2) // 原来平衡因子等于 1 的节点的右子树插入了一个 或者原来平衡因子等于 -1 的节点左子树插入了一个
      {
        // 违反规则了，需要旋转
        if (parent->_bf == 2 && cur->_bf == 1)
        {
          // 1、新节点插入较高右子树的右侧———— 右右 左单旋
          RotateL(parent);
        }
        else if (parent->_bf == -2 && cur->_bf == -1)
        {
          // 2、新节点插入较高左子树的左侧———— 左左 右单旋
          RotateR(parent);
        }
        else if (parent->_bf == 2 && cur->_bf == -1)
        {
          // 3、新节点插入较高右子树的左侧———— 右左 右左双旋  先右旋再左旋
          RotateRL(parent);
        }
        else if (parent->_bf == -2 && cur->_bf == 1)
        {
          // 4、新节点插入较高左子树的右侧———— 左右 左右双旋  先左旋再右旋
          RotateLR(parent);
        }
        break;
      }
      else
      {
        assert(false);
      }
    }
    return true;
  }
  void RotateLR(AVLNode* parent)
  {
    AVLNode* subL = parent->_left;
    AVLNode* subLR = subL->_right;
    int bf = subLR->_bf;
    RotateL(subL);
    RotateR(parent);
    if (bf == 0)// 自己是新增节点
    {
      subL->_bf = 0;
      subLR->_bf = 0;
      parent->_bf = 0;
    }
    else if (bf == -1) // subL 左子树有新增节点
    {
      subLR->_bf = 0;
      subL->_bf = 0;
      parent->_bf = 1;
    }
    else if (bf == 1) // subL 右子树有新增节点
    {
      subLR->_bf = 0;
      subL->_bf = -1;
      parent->_bf = 0;
    }
  }
  void RotateRL(AVLNode* parent)
  {
    AVLNode* subR = parent->_right;
    AVLNode* subRL = subR->_left;
    int bf = subRL->_bf;
    RotateR(subR);
    RotateL(parent);
    if (bf == 0)  //subRL 自己就是新增节点
    {
      subRL->_bf = 0;
      subR->_bf = 0;
      parent->_bf = 0;
    }
    else if (bf == 1) // subRL 右子树有新增节点
    {
      subRL->_bf = 0;
      subR->_bf = 0;
      parent->_bf = -1;
    }
    else if (bf == -1)// subRL 左子树有新增节点
    {
      subRL->_bf = 0;
      subR->_bf = 1;
      parent->_bf = 0;
    }
  }
  void RotateR(AVLNode* parent)
  {
    AVLNode* subL = parent->_left;
    AVLNode* subLR = subL->_right;
    AVLNode* parentParent = parent->_parent;
    subL->_right = parent;
    parent->_parent = subL;
    parent->_left = subLR;
    if (subLR)
      subLR->_parent = parent;
    if (parent == _root)
    {
      _root = subL;
      subL-> _parent = nullptr;
    }
    else
    {
      if (parentParent->_left == parent)
      {
        parentParent->_left = subL;
      }
      else if (parentParent->_right == parent)
      {
        parentParent->_right = subL;
      }
      subL->_parent = parentParent;
    }
    subL->_bf = parent->_bf = 0;
  }
  void RotateL(AVLNode* parent)
  {
    AVLNode* subR = parent->_right;
    AVLNode* subRL = subR->_left;
    AVLNode* parentParent = parent->_parent;
    subR->_left = parent;
    parent->_parent = subR;
    if (subRL)
      subRL->_parent = parent;
    parent->_right = subRL;
    if (parent == _root)
    {
      _root = subR;
      subR->_parent = nullptr;
    }
    else
    {
      // 先找到 parent 是父亲的左子树还是右子树
      if (parentParent->_left == parent) // 左子树
      {
        parentParent->_left = subR;
      }
      else if (parentParent->_right == parent) // 右子树
      {
        parentParent->_right = subR;
      }
      subR->_parent = parentParent;
    }
    parent->_bf = subR->_bf = 0;
  }
private:
  AVLNode* _root = nullptr;
};