Root of AVL Tree

Posted 2022-09-15 manual-linux

• 题目描述：
  

• 题目思路：

这道题主要为了考察对AVL树的插入与旋转等操作。

• C语言实现

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

struct AVLNode

    int Data;  //节点数据
    struct AVLNode* Left;  //指向左子树
    struct AVLNode* Right;  //指向右子树
    int Height;  //树高
;

int Max(int a,int b)

    return a > b ? a : b;


//返回树的高度
int GetH(struct AVLNode* T)

    if (T)
    
        return T->Height;
    
    else
    
        return -1;
    


//右单旋 RR
struct AVLNode* RR(struct AVLNode* A)

    struct AVLNode* B;  //旋转后的根节点
    B = A->Right;
    A->Right = B->Left;
    B->Left = A;
    //更新树的高度
    A->Height = Max(GetH(A->Left),GetH(A->Right)) + 1;
    B->Height = Max(GetH(B->Left),A->Height) + 1;
    return B;


struct AVLNode* LL(struct AVLNode* A)

    struct AVLNode* B;
    B = A->Left;
    A->Left = B->Right;
    B->Right = A;
    A->Height = Max(GetH(A->Left),GetH(A->Right)) + 1;
    B->Height = Max(GetH(B->Left), A->Height) + 1;
    return B;


//LR双旋直接实现
struct AVLNode* LR(struct AVLNode* A)

    struct AVLNode* B, *C;
    B = A->Left;
    C = B->Right;
    B->Right = C->Left;
    A->Left = C->Right;
    C->Left = B;
    C->Right = A;

    B->Height = Max(GetH(B->Left), GetH(B->Right)) + 1;
    A->Height = Max(GetH(A->Left),GetH(A->Right)) + 1;
    C->Height = Max(B->Height,A->Height) + 1;
    return C;


//RL双旋直接实现
struct AVLNode* RL(struct AVLNode* A)

    struct AVLNode* B, *C;
    B = A->Right;
    C = B->Left;
    B->Left = C->Right;
    A->Right = C->Left;
    C->Left = A;
    C->Right = B;

    B->Height = Max(GetH(B->Left), GetH(B->Right)) + 1;
    A->Height = Max(GetH(A->Left), GetH(A->Right)) + 1;
    C->Height = Max(A->Height, B->Height) + 1;
    return C;


//作用:将x插入AVL树T中，并且返回调整后的AVL树
struct AVLNode* Insert(struct AVLNode* T, int x)

    if (!T)
    
        //若插入空树 则新建包含一个节点的树
        T = (struct AVLNode*)malloc(sizeof(struct AVLNode));
        T->Data = x;
        T->Left = NULL;
        T->Right = NULL;
        T->Height = 0;
    
    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 (GetH(T->Left) - GetH(T->Right)  == 2)
        
            if (x < T->Left->Data)
            
                //左单旋
                T = LL(T);
            
            else
            
                //左右双旋
                T = LR(T);
            
        
    
    else if (x > T->Data)
    
        //插入T的右子树
                //插入T的左子树
        T->Right = Insert(T->Right, x);

        //如果需要左旋
        if (GetH(T->Left) - GetH(T->Right) == -2)
        
            if (x > T->Right->Data)
            
                //右单旋
                T = RR(T);
            
            else
            
                //右左双旋
                T = RL(T);
            
        

    //else if 插入右子树结束

    //更新树高
    T->Height = Max(GetH(T->Left),GetH(T->Right)) + 1;
    return T;


int main()

    int N;
    int K;
    struct AVLNode* T = NULL;
    scanf("%d",&N);
    for (int i = 0; i< N;i++)
    
        scanf("%d",&K);
        T = Insert(T, K);
    
    printf("%d",T->Data);
    //system("pause");
    return 0;