1066 Root of AVL Tree (25 分)

最新推荐文章于 2025-12-23 20:45:06 发布

原创最新推荐文章于 2025-12-23 20:45:06 发布 · 198 阅读

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本文探讨了如何在AVL和红黑树中实现插入操作并保持树的平衡，通过LL、LR、RR、RL旋转函数展示节点调整过程，同时介绍了get_balance_factor和get_height辅助函数。着重于理解平衡条件及其实现策略。

#include <iostream>
#include <algorithm>
using namespace std;
typedef struct TreeNode
{
    int val, height;
    TreeNode *left, *right;
} TreeNode;

TreeNode *root = nullptr;
int getheight(TreeNode *node)
{
    if (node == nullptr)
        return 0;
    else
        return node->height;
}
void updateheight(TreeNode *node)
{
    node->height = max(getheight(node->left), getheight(node->right)) + 1;
}
void LL(TreeNode *node)
{
    TreeNode *tmp=node->left;
    node->left=tmp->left;
    tmp->left=tmp->right;
    tmp->right=node->right;
    node->right=tmp;
    swap(node->val,tmp->val);
    updateheight(node->left);
    updateheight(tmp);
    updateheight(node);
}
void LR(TreeNode *node)
{
    TreeNode *tmpB=node->left,*tmpC=tmpB->right;
    node->left=tmpC;
    tmpB->right=tmpC->left;
    tmpC->left=tmpB;
    updateheight(tmpB);
    updateheight(tmpC);
    LL(node);
}
void RR(TreeNode *node)
{
    TreeNode *tmp=node->right;
    node->right=tmp->right;
    tmp->right=tmp->left;
    tmp->left=node->left;
    node->left=tmp;
    swap(node->val,tmp->val);
    updateheight(node->right);
    updateheight(tmp);
    updateheight(node);
}
void RL(TreeNode *node)
{
    TreeNode *tmpB=node->right,*tmpC=tmpB->left;
    node->right=tmpC;
    tmpB->left=tmpC->right;
    tmpC->right=tmpB;
    updateheight(tmpB);
    updateheight(tmpC);
    RR(node);
}



int getbalancefactor(TreeNode *node)
{
    if(node==nullptr) return 0;
    return getheight(node->right) - getheight(node->left);
}
void insert(TreeNode *&node, int val)
{
    if (node == nullptr)
    {
        node = new TreeNode;
        node->val = val;
        node->height = 1;
        return;
    }
    if (val <= node->val)
    {
        insert(node->left, val);
        updateheight(node);
        if(getbalancefactor(node)==-2&&getbalancefactor(node->left)==-1)
            LL(node);
        else if(getbalancefactor(node)==-2&&getbalancefactor(node->left)==1)
            LR(node);
    }
    else
    {
        insert(node->right, val);
        updateheight(node);
        if(getbalancefactor(node)==2&&getbalancefactor(node->right)==1)
            RR(node);
        else if(getbalancefactor(node)==2&&getbalancefactor(node->right)==-1)
            RL(node);
    }
    return;
}
int main()
{
    int N, tmp;
    scanf("%d", &N);
    for (int i = 0; i < N; i++)
    {
        scanf("%d", &tmp);
        insert(root, tmp);
    }
    printf("%d", root->val);
    return 0;
}