AVL树的C++实现

包括3个文件:AvlNode.h AvlTree.h和main.cpp
1.节点类的定义AvlNode.h

#ifndef AVLNODE_H
#define AVLNODE_H
#include <iostream>
using namespace std;

template <class T> class AvlTree; //声明AvlTree类

template <class T>
class AvlNode{
public:
friend class AvlTree<T>;//友元类

//构造函数
AvlNode():left(NULL),right(NULL),balance(0){};
AvlNode(const T& e,AvlNode<T> *lt = NULL,AvlNode<T> *rt = NULL):data(e),left(lt),right(rt),balance(0){};

int getBalance() const{return balance;}
AvlNode<T>* getLeft() const{return left;}
AvlNode<T>* getRight() const{return right;}
T getData() const{return data;}
private:
T data; //节点的值
AvlNode *left; //左孩子
AvlNode *right; //有孩子
int balance; //平衡因子,右子树的高度减去左子树的高度
};
#endif //AVLNODE_H

2.AvlTree.h

#ifndef AVLTREE_H
#define AVLTREE_H

#include <iostream>
#include <queue>
#include <iomanip>
#include "AvlNode.h"

using namespace std;

template <class T>
class AvlTree{
public:
AvlTree():root(NULL){}
AvlNode<T>* getRoot() const{return root;}

bool Insert(T x){ bool taller = false; return Insert(root,x,taller ); }
bool Delete(T x){ bool shorter = false; return Delete(root,x,shorter); }

void PrintTree() const{PrintTree(root,0);}
void PrintTreeLevel() const{PrintTreeLevel(root);}
void PrintTreePre() const{PrintTreePre(root);}
void PrintTreePost() const{PrintTreePost(root);}
void PrintTreeIn() const{PrintTreeIn(root);}
private:
AvlNode<T> *root;

bool Insert(AvlNode<T> *& sRoot,T x,bool &taller);
bool Delete(AvlNode<T> *& sRoot,T x,bool &shorter);

void RotateLeft(AvlNode<T> * &sRoot);
void RotateRight(AvlNode<T> * &sRoot);

void RightBalanceAfterInsert(AvlNode<T> * &sRoot,bool &taller);
void LeftBalanceAfterInsert(AvlNode<T> * &sRoot,bool &taller);
void RightBalanceAfterDelete(AvlNode<T> * &sRoot,bool &shorter);
void LeftBalanceAfterDelete(AvlNode<T> * &sRoot,bool &shorter);

void PrintTree(AvlNode<T> *t,int layer) const;
void PrintTreeLevel(AvlNode<T> *t) const;
void PrintTreePre(AvlNode<T> *t) const;
void PrintTreePost(AvlNode<T> *t) const;
void PrintTreeIn(AvlNode<T> *t) const;
};

template <typename T>
//左旋函数
void AvlTree<T>::RotateLeft(AvlNode<T> * &sRoot){
if( (sRoot == NULL) || (sRoot->right == NULL) ) return;

AvlNode<T> *temp = new AvlNode<T>(sRoot->data);
if(temp == NULL ) return;

temp->left = sRoot->left;
sRoot->left = temp;
temp->right = sRoot->right->left;
AvlNode<T> *toDelete = sRoot->right;
sRoot->data = toDelete->data;
sRoot->right = toDelete->right;

delete toDelete;
}

template <typename T>
//右旋函数
void AvlTree<T>::RotateRight(AvlNode<T> * &sRoot){
if( (sRoot == NULL) || (sRoot->left == NULL) ) return;

AvlNode<T> *temp = new AvlNode<T>(sRoot->data);
if(temp == NULL ) return;

temp->right = sRoot->right;
sRoot->right = temp;
temp->left = sRoot->left->right;
AvlNode<T> *toDelete = sRoot->left;
sRoot->data = toDelete->data;
sRoot->left = toDelete->left;

delete toDelete;
}

template <typename T>
void AvlTree<T>::RightBalanceAfterInsert(AvlNode<T> *&sRoot,bool &taller){
//如果插入节点后,sRoot的右高度增加引起不平衡，则调用此函数，使树重新平衡
if( (sRoot == NULL) || (sRoot->right == NULL) ) return;
AvlNode<T> *rightsub = sRoot->right,*leftsub;
switch(rightsub->balance){
case 1:
sRoot->balance = rightsub->balance = 0;
RotateLeft(sRoot);
taller = false; break;
case 0:
cout<<"树已经平衡化."<<endl; break;
case -1:
leftsub = rightsub->left;
switch(leftsub->balance){
case 1:
sRoot->balance = -1; rightsub->balance = 0; break;
case 0:
sRoot->balance = rightsub->balance = 0; break;
case -1:
sRoot->balance = 0; rightsub->balance = 1; break;
}
leftsub->balance = 0;
RotateRight(rightsub);
RotateLeft(sRoot);
taller = false; break;
}
}

template <typename T>
void AvlTree<T>::LeftBalanceAfterInsert(AvlNode<T> *&sRoot,bool &taller){
//如果插入节点后,sRoot的左高度增加,引起不平衡，则调用此函数，使树重新平衡
AvlNode<T> *leftsub = sRoot->left,*rightsub;
switch(leftsub->balance){
case -1:
sRoot->balance = leftsub->balance = 0;
RotateRight(sRoot);
taller = false; break;
case 0:
cout<<"树已经平衡化."<<endl; break;
case 1:
rightsub = leftsub->right;
switch(rightsub->balance){
case -1:
sRoot->balance = 1; leftsub->balance = 0; break;
case 0:
sRoot->balance = leftsub->balance = 0; break;
case 1:
sRoot->balance = 0; leftsub->balance = -1; break;
}
rightsub->balance = 0;
RotateLeft(leftsub);
RotateRight(sRoot);
taller = false; break;
}
}

template <typename T>
void AvlTree<T>::RightBalanceAfterDelete(AvlNode<T> * &sRoot,bool &shorter){
//如果删除节点后，sRoot的左高度减少，引起不平衡，则调用此函数，使树重新平衡
AvlNode<T> *rightsub = sRoot->right,*leftsub;
switch(rightsub->balance){
case 1: sRoot->balance = sRoot->balance = 0; RotateLeft(sRoot); break;
case 0: sRoot->balance = 0; rightsub->balance = -1; RotateLeft(sRoot); break;
case -1:
leftsub = rightsub->left;
switch(leftsub->balance){
case -1: sRoot->balance = 0; rightsub->balance = 1; break;
case 0: sRoot->balance = rightsub->balance = 0; break;
case 1: sRoot->balance = -1; rightsub->balance = 0; break;
}
leftsub->balance = 0;
RotateRight(rightsub);
RotateLeft(sRoot);
shorter = false; break;
}
}

template <typename T>
void AvlTree<T>::LeftBalanceAfterDelete(AvlNode<T> * &sRoot,bool &shorter){
//如果删除节点后，sRoot的右高度减少，引起不平衡，则调用此函数，使树重新平衡
AvlNode<T> *leftsub = sRoot->left,*rightsub;
switch(leftsub->balance){
case 1: sRoot->balance = sRoot->balance = 0; RotateRight(sRoot); break;
case 0: sRoot->balance = 0; leftsub->balance = -1; RotateRight(sRoot); break;
case -1:
rightsub = leftsub->right;
switch(rightsub->balance){
case -1: sRoot->balance = 0; leftsub->balance = 1; break;
case 0: sRoot->balance = leftsub->balance = 0; break;
case 1: sRoot->balance = -1; leftsub->balance = 0; break;
}
rightsub->balance = 0;
RotateLeft(leftsub);
RotateRight(sRoot);
shorter = false; break;
}
}

template <typename T>
bool AvlTree<T>::Insert(AvlNode<T> *& sRoot,T x,bool &taller){
//递归函数,从sRoot这棵树寻找合适的位置,插入值为x的节点
bool success;
if ( sRoot == NULL ) {//函数的出口,从叶节点插入
sRoot = new AvlNode<T>(x);
success = sRoot != NULL ? true : false;
if ( success ) taller = true;
}
else if ( x < sRoot->data ) {//如果x的值小于sRoot的值

//Insert的递归调用,从sRoot的左子树寻找合适的位置插入
success = Insert ( sRoot->left, x, taller );
if ( taller ){//如果插入后使得sRoot的左高度增加
switch ( sRoot->balance ) {
case -1 : LeftBalanceAfterInsert( sRoot, taller ); break;
case 0 : sRoot->balance = -1; break;
case 1 : sRoot->balance = 0; taller = false; break;
}
}
}
else if ( x > sRoot->data ) {//如果x的值大于sRoot的值

//Insert的递归调用,从sRoot的右子树寻找合适的位置插入
success = Insert ( sRoot->right, x, taller );

if ( taller ){//如果插入后使得sRoot的右高度增加
switch ( sRoot->balance ) {
case -1 : sRoot->balance = 0; taller = false; break;
case 0 : sRoot->balance = 1; break;
case 1 : RightBalanceAfterInsert( sRoot, taller ); break;
}
}
}
return success;
}

template <typename T>
bool AvlTree<T>::Delete(AvlNode<T> *& sRoot,T x,bool &shorter){
//递归函数,从sRoot这棵子树寻找值为x的节点，并删除之.
bool success = false;
if(sRoot == NULL) return false; //空树，操作失败
if(x == sRoot->data) {//如果sRoot就是要删除的节点
if(sRoot->left != NULL && sRoot->right != NULL) {//如果sRoot有个子女

//寻找 sRoot的中序遍历的前驱节点,用r表示
AvlNode<T> *r = sRoot->left;
while(r->right != NULL) {
r = r->right;
}

//交换sRoot和r的值
T temp = sRoot->data;
sRoot->data = r->data;
r->data = temp;

//递归函数调用,从sRoot的左子树寻找值为x的节点，并删除之.
success = Delete(sRoot->left, x, shorter);
if(shorter) {//如果删除后引起sRoot的左高度减少
switch(sRoot->balance) {
case -1: sRoot->balance = 0; break;
case 0: sRoot->balance = 1; shorter = 0; break;
case 1: RightBalanceAfterDelete(sRoot, shorter);break;
}
}
}
else {//sRoot最多只有一个子女,这是递归的出口
AvlNode<T> *p = sRoot;
sRoot = sRoot->left != NULL ? sRoot->left : sRoot->right;//令sRoot指向它的子女
delete p;//释放原来sRoot所占的内存空间
success = true;
shorter = true;
}
}

else if(x < sRoot->data) {
//递归函数调用,从sRoot的左子树寻找值为x的节点，并删除之.
success = Delete(sRoot->left, x, shorter);
if(shorter) {//如果删除后引起sRoot的左高度减少
switch(sRoot->balance) {
case -1: sRoot->balance = 0; break;
case 0: sRoot->balance = 1; shorter = 0; break;
case 1: RightBalanceAfterDelete(sRoot, shorter); break;
}
}
}

else if(x > sRoot->data) {
//递归函数调用,从sRoot的右子树寻找值为x的节点，并删除之.
success = Delete(sRoot->right, x, shorter);
if(shorter) {//如果删除后引起sRoot的右高度减少
switch(sRoot->balance) {
case -1: LeftBalanceAfterDelete(sRoot, shorter); break;
case 0: sRoot->balance = -1; shorter = 0; break;
case 1: sRoot->balance = 0; break;
}
}
}
return success;
}


template <typename T>
void AvlTree<T>::PrintTree(AvlNode<T> *t,int layer) const{
if(t == NULL ) return;
if(t->right) PrintTree(t->right,layer+1);
for(int i =0;i<layer;i++) cout<<" ";
cout<<t->data<<endl;
if(t->left) PrintTree(t->left,layer+1);
}
template <typename T>
void AvlTree<T>::PrintTreeLevel(AvlNode<T> *t) const{
if(t == NULL) return;
queue<AvlNode<T>*> NodeQueue;
AvlNode<T> *node;
NodeQueue.push(t);
while(!NodeQueue.empty()){
node = NodeQueue.front();
NodeQueue.pop();
cout<<node->data<<",";
if(node->left != NULL) NodeQueue.push(node->left);
if(node->right != NULL) NodeQueue.push(node->right);
}
}

template <typename T>
void AvlTree<T>::PrintTreePre(AvlNode<T> *t) const{
if(t){
cout<<t->data<<",";
PrintTreePre(t->left);
PrintTreePre(t->right);
}
}

template <typename T>
void AvlTree<T>::PrintTreePost(AvlNode<T> *t) const{
if(t){
PrintTreePost(t->left);
PrintTreePost(t->right);
cout<<t->data<<",";
}
}

template <typename T>
void AvlTree<T>::PrintTreeIn(AvlNode<T> *t) const{
if(t){
PrintTreeIn(t->left);
cout<<t->data<<",";
PrintTreeIn(t->right);
}
}
#endif //AVLsRoot_H

3.main.cpp

#include <iostream>
#include <stdlib.h>
#include "AvlTree.h"
//#include "BTree.h"
//#include "BSTree.h"
using namespace std;
int main(){
AvlTree<int> l;
for(int i = 1 ; i <= 15 ; i++){
l.Insert(i);
}
l.PrintTree();
while(true){
int toDelete;
cout<<"请输入要删除节点的值:"<<endl;
cin>>toDelete;
l.Delete(toDelete);
cout<<"删除后的树为:"<<endl;
l.PrintTree();
}
return 0;
system("PAUSE");
}