AVL树的插入删除操作

// Demo2.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"

#include <iostream>
using namespace std;
#define max(a,b) ((a)>(b)?(a):(b))

typedef struct AVLtree
{
struct AVLtree * left,*right,*parent;
int hight;
int data;
}AVLTree,*PAVLTree;

PAVLTree rightleft(PAVLTree p);
PAVLTree leftright(PAVLTree p);
PAVLTree rightright(PAVLTree p);
PAVLTree leftleft(PAVLTree p);
PAVLTree insert(int x,PAVLTree p);
PAVLTree find(int data,PAVLTree p);
PAVLTree avl_delete(int data,PAVLTree p);
PAVLTree findMin(PAVLTree p);
PAVLTree findMax(PAVLTree p);
int Height(PAVLTree p);

PAVLTree findMin(PAVLTree p)
{
while(p && p->left)
{
p = p->left;
}
return p;
}
PAVLTree findMax(PAVLTree p)
{

while(p && p->right)
{
p = p->right;
}
return p;
}

//删除节点可能会导致根节点的改变，所以必须返回根节点,以利于后面的操作
PAVLTree avl_delete(int data,PAVLTree p)
{
if(!p) return NULL;
while(1)
{
if(data > p->data)
{
p=p->right;
if( (Height(p->right)-Height(p->left)) ==2 )
{
if(data<p->right->data)
{
p=rightleft(p);
}else
{
p=rightright(p);
}
}
}else if( data < p->data )
{
p=p->left;
if( (Height(p->left)-Height(p->right)) ==2 )
{
if(data > (p->left->data) )
{
p=leftright(p);
}else
{
p=leftleft(p);
}
}
}else if(p->left && p->right)
{
PAVLTree t = findMin(p->right);
p->data = t->data;

data=t->data;
p=p->right;
}else
{
PAVLTree t = p->parent;

if(t->left && t->left->data == data)
{
t->left=NULL;
}else if(t->right && t->right->data==data)
{
t->right = p->right;
}
p->left=p->right=NULL;
free(p);
p=NULL;
p=t;
break;
}
if(p)
p->hight = max(Height(p->left),Height(p->right))+1;
}

while(p)
{
p->hight = max(Height(p->left),Height(p->right))+1;

if( (Height(p->left)-Height(p->right)) ==2 )
{
if(p->left->left->hight < p->left->right->hight)
{
p =leftright(p);
}else
{
p=leftleft(p);
}
}

if( (Height(p->right)-Height(p->left)) ==2 )
{
if(p->right->left->hight>p->right->right->hight)
{
p=rightleft(p);
}else
{
p=rightright(p);
}
}
if(p->parent)
p=p->parent;
else break;
}
return p;
}

PAVLTree find(int data,PAVLTree p)
{
while(p)
{
if(data >p->data)
p = p->right;
else if(data < p->data)
p = p->left;
else
return p;
}

return NULL;
}

int Height(PAVLTree p)
{
if(p==NULL)
return -1;
else
return p->hight;
}
PAVLTree leftright(PAVLTree p)
{
PAVLTree tmp=rightright(p->left);
p->left=tmp;
tmp->parent=p;
return leftleft(p);

}
PAVLTree leftleft(PAVLTree p)
{
PAVLTree t = p->left;

p->left =t->right;
if(p->left)
p->left->parent=p;
p->parent=t;
t->right=p;
t->parent=NULL;

p->hight = max(Height(p->left),Height(p->right))+1;
t->hight = max(Height(t->left),Height(t->right))+1;

return t;
}//=====================================================================================================

PAVLTree rightleft(PAVLTree p)
{
PAVLTree tmp= leftleft(p->right);
p->right = tmp;
tmp->parent=p;
return rightright(p);
}

PAVLTree rightright(PAVLTree p)
{
PAVLTree t= p->right;
p->right=t->left;
if(p->right)
p->right->parent=p;
p->parent=t;

t->left=p;
t->parent=NULL;

p->hight = max(Height(p->left),Height(p->right))+1;
t->hight = max(Height(t->left),Height(t->right))+1;

return t;
}

PAVLTree insert(int x,PAVLTree p)
{
if(p==NULL)
{
p = (PAVLTree)malloc(sizeof(AVLTree));
if(p==NULL)
{
return NULL;
}else
{
p->data=x;
p->left=p->right=p->parent=NULL;
p->hight=0;
}
}else if(x < p->data )
{
p->left=insert(x,p->left); // 80
p->left->parent = p;
if( (Height(p->left)-Height(p->right)) ==2 )
{
if(x > (p->left->data) )
{
p=leftright(p);
}else
{
p=leftleft(p);
}
}
}else if(x > p->data)
{
//返回的值是为了计算深度
p->right = insert(x,p->right);
p->right->parent =p;
if( (Height(p->right)-Height(p->left)) ==2 )
{
if(x<p->right->data)
{
p=rightleft(p);
}else
{
p=rightright(p);
}
}
}
p->hight = max(Height(p->left),Height(p->right))+1;

return p;
}

void print_tree(PAVLTree t)
{
if(t)
{
cout<<t->data<<" ";
print_tree(t->left);
print_tree(t->right);
}
}

int _tmain(int argc, _TCHAR* argv[])
{
AVLTree *pt=NULL;
/*
pt=insert(100,pt);
pt=insert(80,pt);
pt=insert(110,pt);
pt=insert(70,pt);
pt=insert(85,pt);
pt=insert(60,pt);
*/

//测试左右旋转
/*
pt=insert(120,pt);
pt=insert(110,pt);
pt=insert(150,pt);
pt=insert(70,pt);
pt=insert(111,pt);
pt=insert(115,pt);
*/

pt=insert(150,pt);
pt=insert(130,pt);
pt=insert(180,pt);
pt=insert(170,pt);
pt=insert(200,pt);
pt=insert(160,pt);
pt=insert(161,pt);
pt=insert(162,pt);
pt=insert(165,pt);

print_tree(pt);
cout<<endl;
cout<<find(180,pt)->data<<endl;
cout<<"Max = "<<findMax(pt)->data<<endl;
cout<<"Min = "<<findMin(pt)->data<<endl;
pt=avl_delete(161,pt);
cout<<" After del 161"<<endl;
print_tree(pt);
pt=avl_delete(200,pt);
pt=avl_delete(162,pt);
cout<<endl;
cout<<" After del 200"<<endl;
print_tree(pt);

getchar();
return 0;
}

细节后续完善...