04-树5 Root of AVL Tree

　　此题要求找出AVL树的根节点，只需将课上讲的AVL树的基本操作运用起来即可。重点就是AVL树各种旋转以及插入新元素时的操作过程。

#include <stdio.h>
#include <stdlib.h>

typedef struct AVLNode *AVLTree;
struct AVLNode{
    AVLTree Left;
    AVLTree Right;
    int Data;
    int Height;
};

int Max(int a, int b)
{
    return a > b ? a : b;
}

int GetHeight(AVLTree T)
{
    if(!T)
        return 0;
    else
        return T->Height;
}


AVLTree SingleLeftRotation(AVLTree A)
{   //A必须有一个左子节点B
    //将A与B做单左旋，更新A与B的高度，返回新的根节点B
    AVLTree B = A->Left;
    A->Left = B->Right;
    B->Right = A;
    A->Height = Max(GetHeight(A->Left), GetHeight(A->Right)) + 1;
    B->Height = Max(GetHeight(B->Left), A->Height) + 1;
    return B;
}

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

AVLTree DoubleLeftRightRotation(AVLTree A)
{    //A必须有一个左子节点B，且B必须有一个右子节点C
    //将A、B与C做两次单旋，返回新的根节点C
    A->Left = SingleRightRotation(A->Left);  //B与C做右单旋，C被返回
    return SingleLeftRotation(A);  //A与C做左单旋，C被返回
}

AVLTree DoubleRightLeftRotation(AVLTree A)
{
    A->Right = SingleLeftRotation(A->Right);  
    return SingleRightRotation(A);  
}

AVLTree Insert(AVLTree T, int X)
{
    if(!T){  //插入空树，新建包含一个结点的树
        T = (AVLTree)malloc(sizeof(struct AVLNode));
        T->Data = X;
        T->Height = 0;
        T->Left = T->Right = NULL;
    }

    else if(X < T->Data){  //插入T的左子树
        T->Left = Insert(T->Left, X);
        //如果需要左旋
        if(GetHeight(T->Left) - GetHeight(T->Right) == 2)
            if(X < T->Left->Data)  //X在“左左上”
                T = SingleLeftRotation(T);  //左单旋
            else  //X在“左右”上，LR旋
                T = DoubleLeftRightRotation(T);
    }

    else if(X > T->Data){
        T->Right = Insert(T->Right, X);
        if(GetHeight(T->Left) - GetHeight(T->Right) == -2)
            if(X > T->Right->Data)
                T = SingleRightRotation(T);
            else
                T = DoubleRightLeftRotation(T);
    }

    T->Height = Max(GetHeight(T->Left), GetHeight(T->Right)) + 1;
    
    return T;
}

int main(int argc, char const *argv[])
{
    int N, i, data;
    AVLTree T;
    scanf("%d", &N);
    for(i = 0; i < N; i++){
        scanf("%d", &data);
        T = Insert(T, data);
    }
    printf("%d\n", T->Data);
    return 0;
}