04-树5 Root of AVL Tree (25 分)【每日一题】

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.

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 N (≤20) which is the total number of keys to be inserted. Then N 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

Code

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

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

AVLTree Insert(AVLTree T,ElementType X);
int Max(int a,int b);
int GetHeight(AVLTree T);
AVLTree SingleLeftRotation ( AVLTree A );
AVLTree DoubleLeftRightRotation ( AVLTree A );
AVLTree SingleRightRotation(AVLTree T);
AVLTree DoubleRightLeftRotation(AVLTree T);

int main()
{
    int N,X;
    AVLTree Tree=NULL;
    scanf("%d",&N);
    for(int i=0;i<N;i++)
    {
        scanf("%d",&X);
        Tree = Insert(Tree,X);

    }
    printf("%d\n",Tree->Data);
    return 0;
}

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

int GetHeight(AVLTree T)
{
    if(!T) return -1;
    else return T->Height;
}

AVLTree Insert(AVLTree T,ElementType X)
{
    /*对于输入样例二：88 70 61 96 120 90 65 1.读入元素X，若为空树新建根节点，否则，与当前结点比较， 若X小于当前结点，递归插入左子树， 若大于，递归插入右子树； 2.插入成功后，更新该新结点树高； 3.从插入时遍历的路线，从新结点一个个往回遍历，判断，是否存在麻烦结点； （麻烦结点即为平衡被破坏的结点，即左右子树高度相差2及以上） 4.若存在，則在最先找出的麻烦结点进行调整： （左单旋，左-右双旋，右单旋，右-左双旋） 若不存在：跟新树高即可； */
    if(!T)
    {
        T=(AVLTree)malloc(sizeof(struct TNode));
        T->Data = X;
        T->Left = T->Right = NULL;
        T->Height = 0;
    }else if(X<T->Data){
    
        T->Left = Insert(T->Left,X);
        if(GetHeight(T->Left)-GetHeight(T->Right)==2){
// printf("T=%d\n",T->Data);
            if(X< T->Left->Data)
                T = SingleLeftRotation(T);
            else
                T = DoubleLeftRightRotation(T);
        }

    }else if(X>T->Data){
        T->Right = Insert(T->Right,X);
        if(GetHeight(T->Right)-GetHeight(T->Left)==2){
// printf("T=%d\n",T->Data);
            if(X>T->Right->Data)
                T = SingleRightRotation(T);
            else
                T = DoubleRightLeftRotation(T);
        }
    }
    //更新树高
    T->Height = Max(GetHeight(T->Left),GetHeight(T->Right))+1;
    return T;
}

AVLTree SingleLeftRotation ( AVLTree A )
{ /* 注意：A必须有一个左子结点B */
  /* 将A与B做左单旋，更新A与B的高度，返回新的根结点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 DoubleLeftRightRotation ( AVLTree A )
{ /* 注意：A必须有一个左子结点B，且B必须有一个右子结点C */
  /* 将A、B与C做两次单旋，返回新的根结点C */

    /* 将B与C做右单旋，C被返回 */
    A->Left = SingleRightRotation(A->Left);
    /* 将A与C做左单旋，C被返回 */
    return SingleLeftRotation(A);
}

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