搭建AVL树

最新推荐文章于 2025-05-25 21:16:23 发布

转载最新推荐文章于 2025-05-25 21:16:23 发布 · 58 阅读

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CC 4.0 BY-SA版权

原文链接：http://www.cnblogs.com/KennyRom/p/6209488.html

本文详细介绍了AVL树的实现过程，包括节点插入、平衡调整（左旋、右旋、双旋）等核心操作，并通过具体代码展示了如何保持AVL树的高度平衡特性。

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#include<iostream>
using namespace std;

struct TreeNode
{
    int height;   //每一个结点都要保存自己的高度
    int data;
    TreeNode* leftC;
    TreeNode* rightC;
};

//得到此时结点高度
int getHeight(TreeNode* s)
{
    if (s != NULL)
    {
        return s->height;
    }
    return -1;
}

//右旋
void rightRotate(TreeNode*& root)
{
    TreeNode *l1 = root;
    TreeNode *l2 = root->leftC;
    l1->leftC = l2->rightC;
    l2->rightC = l1;
    l1->height = (getHeight(l1->leftC) > getHeight(l1->rightC) ? getHeight(l1->leftC) : getHeight(l1->rightC)) + 1;
    l2->height = (getHeight(l2->leftC) > getHeight(l2->rightC) ? getHeight(l2->leftC) : getHeight(l2->rightC)) + 1;
    root = l2;
}

//左旋
void leftRotate(TreeNode*& root)
{
    TreeNode *l1 = root;
    TreeNode *l2 = root->rightC;
    l1->rightC = l2->leftC;
    l2->leftC = l1;
    l1->height = (getHeight(l1->leftC) > getHeight(l1->rightC) ? getHeight(l1->leftC) : getHeight(l1->rightC)) + 1;
    l2->height = (getHeight(l2->leftC) > getHeight(l2->rightC) ? getHeight(l2->leftC) : getHeight(l2->rightC)) + 1;
    root = l2;
}

//左右，先左旋，再右旋
void DoubleRotateLR(TreeNode* &n1)
{
    leftRotate(n1->leftC);
    rightRotate(n1);
}

//右左，先右旋，后左旋
void DoubleRotateRL(TreeNode* &n1)
{
    rightRotate(n1->rightC);
    leftRotate(n1);
}


void Insert(TreeNode** node, int data)
{
    if (*node == NULL)
    {
        TreeNode* tmp = new TreeNode();
        tmp->data = data;
        tmp->height = 0;
        tmp->leftC = NULL;
        tmp->rightC = NULL;
        *node = tmp;
        return;
    }
    if ((*node)->data > data)//结点的值大于data
    {
        Insert(&((*node)->leftC), data);//不断插入

        if ((getHeight((*node)->leftC) - getHeight((*node)->rightC)) == 2)
        {//说明需要右旋
            if (data < (*node)->leftC->data)
            {
                rightRotate(*node);
            }
            else
            {
                DoubleRotateLR(*node);
            }
        }

    }
    else if ((*node)->data < data)//没有相同的值
    {
        Insert(&((*node)->rightC), data);
        //如果高度之差为2的话就失去了平衡,需要旋转
        if (2 == getHeight((*node)->rightC) - getHeight((*node)->leftC))
        {
            if (data > (*node)->rightC->data)
            {
                leftRotate(*node);
            }
            else
            {
                DoubleRotateRL(*node);
            }
        }
    }
    
    (*node)->height = (getHeight((*node)->leftC) > getHeight((*node)->rightC) ? getHeight((*node)->leftC) : getHeight((*node)->rightC)) + 1;
}

void preOrder(TreeNode* node)
{
    if (node == NULL)
    {
        return;
    }
    cout << node->data << " ";
    preOrder(node->leftC);
    preOrder(node->rightC);
}

void  inOrderTraversal(TreeNode* root)
{
    if(root)
    {
    	inOrderTraversal(root->leftC);
    	cout << root->data << " ";
    	inOrderTraversal(root->rightC);
    }
}

int main()
{
	int n;
	cin>>n;
	while(n-->0)
	{
	    int num;
	    cin>>num;

	    TreeNode *head=NULL;

        int point;

        for(int i=0;i<num;i++)
        {
            cin>>point;
            Insert(&head, point);
        }

        preOrder(head);
        cout<<endl;
        inOrderTraversal(head);
        cout<<endl;
    }

    return 0;
}

转载于:https://www.cnblogs.com/KennyRom/p/6209488.html