数据结构——AVL平衡二叉树(递归法）

原创已于 2022-08-30 21:05:41 修改 · 508 阅读

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#数据结构 #c++ #算法

于 2022-08-30 19:10:43 首次发布

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本文详细介绍了AVL树中的四种旋转操作：LL型、RR型、LR型和RL型，并提供了完整的C语言实现代码。通过这些旋转操作，AVL树能够保持其平衡特性，从而确保高效的查找、插入和删除操作。

1、LL型
在这里插入图片描述

void LL_Rotation(TreeNode* node,TreeNode** nodePtr){
    TreeNode* temp = node->left;
    node->left = temp->right;
    temp->right = node;
    node->height = max(getHeight(node->left),getHeight(node->right))+1;
    temp->height = max(getHeight(temp->left),getHeight(temp->right))+1;
    *nodePtr = temp;
}

2、RR型
在这里插入图片描述

void RR_Rotation(TreeNode* node,TreeNode** nodePtr){
    TreeNode* temp = node->right;
    node->right = temp->left;
    temp->left = node;
    node->height = max(getHeight(node->left),getHeight(node->right))+1;
    temp->height = max(getHeight(temp->left),getHeight(temp->right))+1;
    *nodePtr = temp;
}

3、LR型
在这里插入图片描述

void LR_Rotation(TreeNode* node,TreeNode** nodePtr){
    TreeNode* temp = node->left->right;
	RR_Rotation(node->left,&(node->left));
    LL_Rotation(node,&node);
    *nodePtr = temp;
}

4、RL型
在这里插入图片描述

void RL_Rotation(TreeNode* node,TreeNode** nodePtr){
    TreeNode* temp = node->right->left;
	LL_Rotation(node->right,&(node->right));
    RR_Rotation(node,&node);
    *nodePtr = temp;
}

完整代码：

#include <stdio.h>
#include <stdlib.h>
typedef struct TreeNode{
    int data,height;
    struct TreeNode *left,*right;
}TreeNode;
int getHeight(TreeNode* node){
    if(node == NULL){
        return 0;
    }else{
        return node->height;
    }
}
int max(int a,int b){
    return a > b ? a : b;
}
void RR_Rotation(TreeNode* node,TreeNode** nodePtr){
    TreeNode* temp = node->right;
    node->right = temp->left;
    temp->left = node;
    node->height = max(getHeight(node->left),getHeight(node->right))+1;
    temp->height = max(getHeight(temp->left),getHeight(temp->right))+1;
    *nodePtr = temp;
}
void LL_Rotation(TreeNode* node,TreeNode** nodePtr){
    TreeNode* temp = node->left;
    node->left = temp->right;
    temp->right = node;
    node->height = max(getHeight(node->left),getHeight(node->right))+1;
    temp->height = max(getHeight(temp->left),getHeight(temp->right))+1;
    *nodePtr = temp;
}
void LR_Rotation(TreeNode* node,TreeNode** nodePtr){
    TreeNode* temp = node->left->right;
	RR_Rotation(node->left,&(node->left));
    LL_Rotation(node,&node);
    *nodePtr = temp;
}
void RL_Rotation(TreeNode* node,TreeNode** nodePtr){
    TreeNode* temp = node->right->left;
	LL_Rotation(node->right,&(node->right));
    RR_Rotation(node,&node);
    *nodePtr = temp;
}
void avlInsert(TreeNode** T,int data){
    if(*T == NULL){
        *T =  (TreeNode*)malloc(sizeof(TreeNode));
        (*T)->data = data;
        (*T)->height = 0;
        (*T)->right = (*T)->left = NULL;
    }else if(data < (*T)->data){
        avlInsert(&(*T)->left,data);
        //拿到当前节点左右子树的高度
        int LH = getHeight((*T)->left);
        int RH = getHeight((*T)->right);
        //判断高度差
        if(LH-RH == 2){
            if(data < (*T)->left->data){//LL型调整
                LL_Rotation(*T,T);
            }else{//LR调整
                //RR_Rotation((*T)->left,&(*T)->left);
                //LL_Rotation(*T,T);
                LR_Rotation(*T,T);
            }
        }
    }else if(data > (*T)->data){
        avlInsert(&(*T)->right,data);
        //拿到当前节点左右子树的高度
        int LH = getHeight((*T)->left);
        int RH = getHeight((*T)->right);
        if(RH - LH == 2){
            if(data > (*T)->right->data){//RR型调整
                RR_Rotation(*T,T);
            }else{//RL调整
                //LL_Rotation((*T)->right,&(*T)->right);
                //RR_Rotation(*T,T);
                RL_Rotation(*T,T);
            }
        }
    }
    (*T)->height = max(getHeight((*T)->left),getHeight((*T)->right))+1;
}
void preOrder(TreeNode* T){
    if(T){
        printf("%d ",T->data);
        preOrder(T->left);
        preOrder(T->right);
    }
}
int main() {
    TreeNode* T = NULL;
    int num[5] = {5,4,3,2,1};
    for(int i = 0; i < sizeof (num)/sizeof (num[0]);i++){
        avlInsert(&T,num[i]);
    }
    preOrder(T);
    return 0;
}