04-树5 Root of AVL Tree（25 分）

题该参照主要点击打开链接
代码内，singleLeft针对的是题目中如图一的情况，singleRight针对的是题目中Figure2的情况
DoubleLeft针对的是题目中Figure4的情况，可以转化为先针对61结点进行singleRight，然后变成了SingleLeft的情况
DoubleRight针对的是题目中的Figure3的情况，同样可以转化为先针对88结点进行singleLeft，然后就变成了SingleRight的情况。#include <iostream>
#include <string>

typedef struct AVLTreeNode {
int Data;
AVLTreeNode *Left;
AVLTreeNode *Right;
int Height;
}nAVLTree, *pAVLTree;

pAVLTree AVLInsertion(int nodeValue, pAVLTree pAvl);
int GetALVHeight(pAVLTree);
pAVLTree SingleLeftRotation(pAVLTree);
pAVLTree DoubleLeftRotation(pAVLTree);
pAVLTree SingleRightRotation(pAVLTree);
pAVLTree DoubleRightRotation(pAVLTree);
int Max(int hight1, int hight2);
using namespace std;

int main()
{
int num;
int i;
int value;
pAVLTree pAvl;
pAvl = NULL;
cin >> num;
for (i = 0; i < num; i++)
{
cin >> value;
pAvl = AVLInsertion(value, pAvl);
}
cout << pAvl->Data;
}

pAVLTree AVLInsertion(int nodeValue, pAVLTree pAvl)
{
if (pAvl == NULL)
{
pAvl = (pAVLTree)malloc(sizeof(nAVLTree));
pAvl->Left = pAvl->Right = NULL;
pAvl->Data = nodeValue;
pAvl->Height = 0;
}
else if (nodeValue < pAvl->Data)
{
pAvl->Left = AVLInsertion(nodeValue, pAvl->Left);
if (GetALVHeight(pAvl->Left) - GetALVHeight(pAvl->Right) == 2)
{
if (nodeValue < pAvl->Left->Data)
{
pAvl = SingleLeftRotation(pAvl);
}
else
{
pAvl = DoubleLeftRotation(pAvl);
}
}
}
else if (nodeValue > pAvl->Data)
{
pAvl->Right = AVLInsertion(nodeValue, pAvl->Right);
if (GetALVHeight(pAvl->Right) - GetALVHeight(pAvl->Left) == 2)
{
if (nodeValue > pAvl->Right->Data)
{
pAvl = SingleRightRotation(pAvl);
}
else
{
pAvl = DoubleRightRotation(pAvl);
}
}
}
pAvl->Height = Max(GetALVHeight(pAvl->Left), GetALVHeight(pAvl->Right)) + 1;
return pAvl;
}

pAVLTree SingleLeftRotation(pAVLTree A)
{
pAVLTree B = A->Left;
A->Left = B->Right;
B->Right = A;
A->Height = Max(GetALVHeight(A->Left), GetALVHeight(A->Right)) + 1;
B->Height = Max(GetALVHeight(B->Left), A->Height) + 1;
return B;
}

pAVLTree DoubleLeftRotation(pAVLTree A)
{
A->Left = SingleRightRotation(A->Left);
return SingleLeftRotation(A);
}

pAVLTree SingleRightRotation(pAVLTree A)
{
pAVLTree B = A->Right;
A->Right = B->Left;
B->Left = A;
A->Height = Max(GetALVHeight(A->Left), GetALVHeight(A->Right)) + 1;
B->Height = Max(GetALVHeight(B->Right), A->Height) + 1;
return B;
}

pAVLTree DoubleRightRotation(pAVLTree A)
{
A->Right = SingleLeftRotation(A->Right);
return SingleRightRotation(A);
}

int GetALVHeight(pAVLTree pAvl)
{
if (pAvl == NULL)
{
return 0;
}
else
{
return pAvl->Height;
}
}

int Max(int hight1, int hight2)
{
return hight1 > hight2 ? hight1 : hight2;
}