1066. Root of AVL Tree (25)

缺乏、安全感 2022-05-29 23:57 157阅读 0赞

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.

![79_mtxjq1kj3gx.jpg][] ![79_mtxjqnwja2o.jpg][]

![79_mtxjr4gyzdg.jpg][] ![79_mtxjrh51o9y.jpg][]

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 ythe root of the resulting AVL tree in one line.

**Sample Input 1:**

5
    88 70 61 96 120

**Sample Output 1:**

**Sample Input 2:**

7
    88 70 61 96 120 90 65

**Sample Output 2:**

--------------------

题目大意：

代码：

#include<stdio.h>
    #include<stdlib.h>
    struct node
    {
        int data;
        struct node *lchild,*rchild;
    };
    struct node * RR(struct node *root)
    {
        struct node *tmp=root->rchild;
        root->rchild=tmp->lchild;
        tmp->lchild=root;
        return tmp;
    }
    struct node * LL(struct node *root)
    {
        struct node *tmp=root->lchild;
        root->lchild=tmp->rchild;
        tmp->rchild=root;
        return tmp;
    }
    struct node * RL(struct node *root)
    {
        root->rchild=LL(root->rchild);
        return RR(root);
    }
    struct node * LR(struct node *root)
    {
        root->lchild=RR(root->lchild);
        return LL(root);
    }
    int getbalancenum(struct node *root)
    {
        if(root==NULL)
            return 0;
            int left=getbalancenum(root->lchild);
            int right=getbalancenum(root->rchild);
        return left>right?left+1:right+1;
    }
    struct node * insert_AVL_tree(struct node *root,int k)
    {
        if(root==NULL)
        {
            root=(struct node *)malloc(sizeof(struct node));
            root->data=k;
            root->lchild=NULL;
            root->rchild=NULL;
        }
        else if(k<root->data)
        {
            root->lchild=insert_AVL_tree(root->lchild,k);
            if(getbalancenum(root->lchild)-getbalancenum(root->rchild)==2)
            {
                if(k<root->lchild->data)
                {
                    root=LL(root);
                }
                else
                {
                    root=LR(root);
                }
            }
        }
        else
        {
          root->rchild=insert_AVL_tree(root->rchild,k);
           if(getbalancenum(root->rchild)-getbalancenum(root->lchild)==2)
            {
                if(k<root->rchild->data)
                {
                    root=RL(root);
                }
                else
                {
                    root=RR(root);
                }
            }
        }
        return root;
    };
    int main()
    {
        int i,j,n,m,k,t;
        struct node *root=NULL;
        scanf("%d",&n);
        for(i=0;i<n;i++)
        {
            scanf("%d",&k);
            root=insert_AVL_tree(root,k);
        }
        printf("%d\n",root->data);
        return 0;
    }

[79_mtxjq1kj3gx.jpg]: http://nos.patest.cn/79_mtxjq1kj3gx.jpg
[79_mtxjqnwja2o.jpg]: http://nos.patest.cn/79_mtxjqnwja2o.jpg
[79_mtxjr4gyzdg.jpg]: http://nos.patest.cn/79_mtxjr4gyzdg.jpg
[79_mtxjrh51o9y.jpg]: http://nos.patest.cn/79_mtxjrh51o9y.jpg