AVL树自平衡的几种旋转

标注: AVL树的基本题,仔细想想动手画画RS, LS,LRS,RLS!!code

04-树5 Root of AVL Tree   (25分)

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

《AVL树自平衡的几种旋转》
《AVL树自平衡的几种旋转》

《AVL树自平衡的几种旋转》《AVL树自平衡的几种旋转》

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer NN (\le 2020) which is the total number of keys to be inserted. Then NN distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the root of the resulting AVL tree in one line.

Sample Input 1:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

#include 
#include 
#include 
#define MAX(a,b) (a>b)?a:b
typedef int Element;
typedef struct AVLtreeNode* AVLTree;
struct AVLtreeNode
{
    Element data;
    AVLTree left;
    AVLTree right;
    int height;
};
AVLTree AVl_Insertion(Element x,AVLTree T);
Element GetHeight(AVLTree A);
AVLTree SingleLeftRotation(AVLTree A);
AVLTree SingleRightRotation(AVLTree A);
AVLTree DoubleLeftRightRotation(AVLTree A);
AVLTree DoubleRightLeftRotation(AVLTree A);
int main()
{
   // freopen("11.txt","r",stdin);
    int N;
    AVLTree T = NULL;
    scanf("%d",&N);
    while (N--)
    {
        int x;
        scanf("%d",&x);
        T = AVl_Insertion(x,T);
    }
    printf("%d\n",T->data);
    return 0;
}

Element GetHeight(AVLTree A)
{
    int HL,HR,Maxh;

    if (A)
    {
        HL = GetHeight(A->left);
        HR = GetHeight(A->right);
        Maxh = MAX(HL,HR);
        return (Maxh+1);
    }
    else return 0;
}
AVLTree AVl_Insertion(Element x,AVLTree T)
{
    if(!T)
    {
        T = (AVLTree)malloc(sizeof(struct AVLtreeNode));
        T->data=x;
        T->height = 0;
        T->left=T->right=NULL;

    }
    else if (x < T->data)
    {
        T->left = AVl_Insertion(x,T->left);
        if(GetHeight(T->left)-GetHeight(T->right)==2)
        {
            if (x < T->left->data)
            {
                T = SingleLeftRotation(T);
            }
            else
            {
                T = DoubleLeftRightRotation(T);
            }
        }
    }
    else if (x > T->data)
    {
        T->right = AVl_Insertion(x,T->right);
        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;
}
AVLTree SingleLeftRotation(AVLTree A)
{
    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),GetHeight(B->right)) + 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->left),GetHeight(B->right)) + 1;
    return B;
}
AVLTree DoubleLeftRightRotation(AVLTree A)
{
    A->left = SingleRightRotation(A->left);
    return SingleLeftRotation(A);
}
AVLTree DoubleRightLeftRotation(AVLTree A)
{
    A->right = SingleLeftRotation(A->right);
    return SingleRightRotation(A);
}

    原文作者:AVL树
    原文地址: https://blog.csdn.net/chris_csdner/article/details/70186245
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