#include <iostream>
#include<stack>
using namespace std;struct AvlNode;
typedef struct AvlNode *Position;
typedef struct AvlNode *Avltree;struct AvlNode    //AVL树节点
{int Element;Avltree Left;Avltree Right;int Hight;int Isdelete;  //指示该元素是否被删除
};///AVL平衡树的函数的相关声明//
Avltree MakeEmpty(Avltree T);   //清空一棵树
static int Height(Position P);  //返回节点的高度
Avltree Insert(int x, Avltree T);   //在树T中插入元素x
Avltree Insert_not_recursion (int x, Avltree T);  //在树T中插入元素x,非递归版本
Position FindMax(Avltree T);   //查找Avl树的最大值，和二叉树一样
Avltree Delete(int x,Avltree T);   //删除元素，非懒惰删除///AVL平衡树的函数的相关定义//
Avltree MakeEmpty(Avltree T)
{if (T != NULL){MakeEmpty(T->Left);MakeEmpty(T->Right);delete T;// free(T);}return NULL;
}static int Height(Position P)   //返回节点的高度
{if(P == NULL)return -1;elsereturn P->Hight;
}static int Element(Position P)   //返回节点的元素
{if(P == NULL)return -1000;elsereturn P->Element;
}int Max(int i,int j)    //返回最大值
{if(i > j)return i;elsereturn j;
}static Position SingleRotateWithLeft (Position k2)   //单旋转，左子树高度比较高
{Position k1;k1 = k2->Left;k2->Left = k1->Right;k1->Right = k2;k2->Hight = Max(Height(k2->Left), Height(k2->Right)) + 1;k1->Hight = Max(Height(k1->Left), Height(k1->Right)) + 1;return k1;  //新的根
}static Position SingleRotateWithRight (Position k1)   //单旋转，右子树的高度比较高
{Position k2;k2 = k1->Right;k1->Right = k2->Left;k2->Left = k1;k1->Hight = Max(Height(k1->Left), Height(k1->Right)) + 1;k2->Hight = Max(Height(k2->Left), Height(k2->Right)) + 1;return k2;  //新的根
}static Position DoubleRotateWithLeft (Position k3)   //双旋转，当k3有左儿子而且k3的左儿子有右儿子
{k3->Left = SingleRotateWithRight(k3->Left);return SingleRotateWithLeft(k3);
}static Position DoubleRotateWithRight (Position k1)   //双旋转，当k1有右儿子而且k1的又儿子有左儿子
{k1->Right = SingleRotateWithLeft(k1->Right);return SingleRotateWithRight(k1);
}//对Avl树执行插入操作，递归版本
Avltree Insert(int x, Avltree T)
{if(T == NULL)  //如果T为空树，就创建一棵树，并返回{T = static_cast<Avltree>(malloc(sizeof(struct AvlNode)));if (T == NULL){cout << "out of space!!!" << endl;}else                    {T->Element = x;T->Left = NULL;T->Right = NULL;T->Hight = 0;T->Isdelete = 0;}}else   //如果不是空树{if(x < T->Element){T->Left = Insert(x,T->Left);if(Height(T->Left) - Height(T->Right) == 2 ){if(x < T->Left ->Element )T = SingleRotateWithLeft(T);elseT = DoubleRotateWithLeft(T);}}else{if(x > T->Element ){T->Right = Insert(x,T->Right );if(Height(T->Right) - Height(T->Left) == 2 ){if(x > T->Right->Element )T = SingleRotateWithRight(T);elseT = DoubleRotateWithRight(T);}}}}T->Hight = Max(Height(T->Left), Height(T->Right)) + 1;return T;
}//对Avl树进行插入操作，非递归版本
Avltree Insert_not_recursion (int x, Avltree T)
{stack<Avltree> route; //定义一个堆栈使用//找到元素x应该大概插入的位置，但是还没进行插入Avltree root = T;while(1){if(T == NULL)  //如果T为空树，就创建一棵树，并返回{T = static_cast<Avltree>(malloc(sizeof(struct AvlNode)));if (T == NULL) cout << "out of space!!!" << endl;  else                    {T->Element = x;T->Left = NULL;T->Right = NULL;T->Hight = 0;T->Isdelete = 0;route.push (T);break;}}else if (x < T->Element){route.push (T);T = T->Left;continue;}else if (x > T->Element){route.push (T);T = T->Right;continue;}else{T->Isdelete = 0;return root;}}//接下来进行插入和旋转操作Avltree father,son;while(1){son = route.top ();   route.pop();   //弹出一个元素if(route.empty())return son;   father = route.top ();  route.pop();   //弹出一个元素if(father->Element < son->Element )   //儿子在右边{father->Right = son;if( Height(father->Right) - Height(father->Left) == 2){if(x >  Element(father->Right))father = SingleRotateWithRight(father);elsefather = DoubleRotateWithRight(father);}route.push(father);}else if (father->Element > son->Element)    //儿子在左边{father->Left = son;if(Height(father->Left) - Height(father->Right) == 2){if(x < Element(father->Left))father = SingleRotateWithLeft(father);elsefather = DoubleRotateWithLeft(father);}route.push(father);}father->Hight = max(Height(father->Left),Height(father->Right )) + 1;}}Position FindMax(Avltree T)
{if(T != NULL){while(T->Right != NULL){T = T->Right;}}return T;
}Position FindMin(Avltree T)
{if(T == NULL){return NULL;}else{if(T->Left == NULL){return T;}else{return FindMin(T->Left );}}
}Avltree Delete(int x,Avltree T)    //删除Avl树中的元素x
{Position Temp;if(T == NULL)return NULL;else if (x < T->Element)   //左子树平衡条件被破坏{T->Left = Delete(x,T->Left );if(Height(T->Right) - Height(T->Left) == 2){if(x > Element(T->Right) )T = SingleRotateWithRight(T);elseT = DoubleRotateWithRight(T);  }}else if (x > T->Element)   //右子树平衡条件被破坏{T->Right = Delete(x,T->Right );if(Height(T->Left) - Height(T->Right) == 2){if(x < Element(T->Left) )T = SingleRotateWithLeft(T);elseT = DoubleRotateWithLeft(T);  }}else    //执行删除操作{if(T->Left && T->Right)   //有两个儿子{Temp = FindMin(T->Right);T->Element = Temp->Element;T->Right = Delete(T->Element ,T->Right);}else  //只有一个儿子或者没有儿子{Temp = T;if(T->Left == NULL)T = T->Right;else if(T->Right == NULL)T = T->Left;free(Temp);}}return T;
}int main ()
{Avltree T = NULL;T = Insert_not_recursion(3, T);  //T一直指向树根T = Insert_not_recursion(2, T);T = Insert_not_recursion(1, T);T = Insert_not_recursion(4, T);T = Insert_not_recursion(5, T);T = Delete(1,T);// T = Insert_not_recursion(6, T);/*  T = Insert(3, T);  //T一直指向树根T = Insert(2, T);T = Insert(1, T);T = Insert(4, T);T = Insert(5, T);T = Insert(6, T);*/cout << T->Right->Right->Element << endl;return 0;}