AVL树：又称高度平衡的二叉搜索树，它能保持二叉树的高度平衡，尽量降低二叉树的高度，减少树的平均搜索长度。
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AVL树的性质
左子树和右子树的高度之差的绝对值不超过1
树中的每个左子树和右子树都是AVL树
#pragma once
#include
using namespace std;
template
struct AVLTreeNode
{
AVLTreeNode* _left;
AVLTreeNode* _right;
AVLTreeNode* _parent;
K _key;
V _value;
int _bf;
AVLTreeNode(const K& key, const V& value)
:_left(NULL)
, _right(NULL)
, _parent(NULL)
, _key(key)
, _value(value)
, _bf(0)
{}
};
template
class AVLTree
{
typedef AVLTreeNode Node;
public:
AVLTree()
:_root(NULL)
{}
~AVLTree()
{}
bool Insert(const K& key, const V& value)
{
if (_root == NULL)
{
_root = new Node(key, value);
return true;
}
Node* cur = _root;
Node* parent = NULL;
while (cur)
{
if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_key>key)
{
parent = cur;
cur = cur->_left;
}
else
{
cout << "该节点已经存在" << endl;
return false;
}
}
cur = new Node(key, value);
if (parent->_key < key)
{
parent->_right = cur;
cur->_parent = parent;
}
else
{
parent->_left = cur;
cur->_parent = parent;
}
//更新平衡因子
while (parent)
{
if (cur == parent->_right)
++parent->_bf;
else if (cur == parent->_left)
--parent->_bf;
if (parent->_bf == 0)
break;
else if (parent->_bf == -1 || parent->_bf == 1)
{
cur = parent;
parent = cur->_parent;
}
else //平衡因子为2或-2时的情况
{
if (parent->_bf == 2)
{
if (cur->_bf == 1)
{ //左旋转
RotateL(parent);
}
else if (cur->_bf==-1)
{
RotateRL(parent);
}
}
else
{
if (cur->_bf == -1)
{//右旋转
RotateR(parent);
}
else if (cur->_bf == 1)
{
RotateLR(parent);
}
}
break;
}
}
return true;
}
Node* Find(const K& key)
{
if (_root == NULL)
return NULL;
Node* cur = _root;
while (cur)
{
if (cur->_key < key)
{
cur = cur->_right;
}
else if (cur->_key>key)
{
cur = cur->_left;
}
else
{
cout << "找到该数" << endl;
return cur;
}
}
return NULL;
}
bool Remove(const K& key)
{
if (_root == NULL)
return false;
Node* cur = _root;
Node* parent = NULL;
while (cur)
{
if (cur->_key < key)
{
parent = cur;
cur = cur->_right;
}
else if (cur->_key>key)
{
parent = cur;
cur = cur->_left;
}
else
{
if (cur->_left == NULL && cur->_right == NULL)
{//1.左右都为空
if (parent == NULL)
_root = NULL;//若只有一个节点
else
{
if (parent->_left == cur)
parent->_bf++;
else
parent->_bf--;
}
delete cur;
cur = NULL;
}
else if (cur->_left&&cur->_right)
{//2.左右都不为空
Node* RightMin = cur->_right;
while (RightMin->_left)
{
parent = RightMin;
RightMin = RightMin->_left;
}
cur->_key = RightMin->_key;//采用替换法删除
cur->_value = RightMin->_value;
if (parent->_left == RightMin)
{
parent->_bf++;
parent->_left = RightMin->_right;
}
else
{
parent->_bf--;
parent->_right = RightMin->_right;
}
delete RightMin;
RightMin = NULL;
}
else
{//3.左为空或右为空
if (cur->_left)
{//1).右为空
if (parent == NULL)
{//只有两个节点，且为左孩子
_root = cur->_left;
_root->_bf = 0;
}
else
{
if (parent->_left == cur)
{
parent->_left = cur->_left;
parent->_bf++;
}
else
{
parent->_right = cur->_left;
parent->_bf--;
}
}
}
else
{//2).cur的左为空
if (parent == NULL)
{//只有两个节点，且为左孩子
_root = cur->_right;
_root->_bf = 0;
}
else
{
if (parent->_left == cur)
{
parent->_left = cur->_right;
parent->_bf++;
}
else
{
parent->_right = cur->_right;
parent->_bf--;
}
}
}
delete cur;
cur = NULL;
}
break;
}
}
while (parent)
{//平衡因子为0或1、-1对这个树的高度不会产生影响
if (parent->_parent->_left == parent)
parent->_parent->_bf++;
else
parent->_parent->_bf--;
if (parent->_parent->_bf == 0)
return true;
else if (parent->_parent->_bf==1 || parent->_parent->_bf==-1)
{
cur = parent;
parent = cur->_parent;
}
else
{
if (parent->_bf == -2)
{
if (cur->_bf == -1)
{
RotateR(parent);
}
else
{
RotateLR(parent);
}
}
else
{
if (cur->_bf == 1)
{
RotateL(parent);
}
else
{
RotateRL(parent);
}
}
cout << "删除成功" << endl;
return true;
}
}
return false;
}
void RotateR(Node* parent)
{
Node* subL = parent->_left;
Node* subLR = subL->_right;
parent->_left = subLR;
if (subLR)
{
subLR->_parent = parent;
}
Node* ppNode = parent->_parent;
subL->_right = parent;
parent->_parent = subL;
if (ppNode == NULL)//若要调整的节点为根节点
{
_root = subL;
subL->_parent = NULL;
}
else
{
if (parent == ppNode->_left)
{
ppNode->_left=subL;
}
else
{
ppNode->_right = subL;
}
subL->_parent = ppNode;
}
subL->_bf = parent->_bf= 0;
}
void RotateL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;
parent->_right = subRL;
if (subRL)
{
subRL->_parent = parent;
}
Node* ppNode = parent->_parent;
subR->_left = parent;
parent->_parent = subR;//*若有父节点一定要指向它的父节点
if (ppNode== NULL)//若要调整的节点为根节点
{
_root = subR;
subR->_parent = NULL;
}
else
{
if (parent == ppNode->_left)
{
ppNode->_left = subR;
}
else
{
ppNode->_right = subR;
}
subR->_parent = ppNode;
}
subR->_bf =parent->_bf=0;
}
void RotateRL(Node* parent)
{
Node* subR = parent->_right;
Node* subRL = subR->_left;
int bf = subRL->_bf;
RotateR(parent->_right);
RotateL(parent);
if (bf == 1)
{
parent->_bf = -1;
subR->_bf = 0;
}
else if (bf == -1)
{
parent->_bf = 0;
subR->_bf = 1;
}
else //bf=0;
{
subR->_bf = parent->_bf = 0;
}
//subRL->_bf = 0;
}
void RotateLR(Node* parent)
{
Node* subL = parent->_left;
Node* subLR = subL->_right;
int bf = subLR->_bf;
RotateL(parent->_left);
RotateR(parent);
if (bf == -1)
{
parent->_bf = 1;
subL->_bf = 0;
}
else if (bf == 1)
{
parent->_bf = 0;
subL->_bf = -1;
}
else //bf=0;
{
subL->_bf = parent->_bf = 0;
}
//subLR->_bf = 0;
}
void InOrder()
{
_InOrder(_root);
cout << endl;
}
bool IsBalance()
{
return _IsBalance(_root);
}
int Height()
{
return _Height(_root);
}
protected:
int _Height(Node* root)
{
if (root == NULL)
{
return 0;
}
int left = _Height(root->_left);
int right = _Height(root->_right);
return left > right ? left + 1 : right + 1;
}
bool _IsBalance(Node* root)
{
if (root == NULL)
{
return true;
}
int left = _Height(root->_left);
int right = _Height(root->_right);
if ((right-left) != root->_bf)
{
cout << root->_key <<"平衡因子异常" << endl;
return false;
}
return abs(right - left) < 2 && _IsBalance(root->_left) && _IsBalance(root->_right);
}
void _InOrder(Node* root)
{
if (root == NULL)
{
return;
}
_InOrder(root->_left);
cout << root->_key << " ";
_InOrder(root->_right);
}
protected:
Node* _root;
};
void Test()
{
AVLTree avl;
int arr[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
//int arr[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };
int size = sizeof(arr) / sizeof(arr[0]);
for (int i = 0; i
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