1123. Is It a Complete AVL Tree (30)

￡神魔★判官ぃ 2022-05-28 12:22 159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.

![mr_ohesevgnyny.jpg][] ![mr_ohesfdbkaep.jpg][]

![mr_oheseymzi13.jpg][] ![mr_ohesfjddti2.jpg][]

Now given a sequence of insertions, you are supposed to output the level-order traversal sequence of the resulting AVL tree, and to tell if it is a complete binary tree.

**Input Specification:**

Each input file contains one test case. For each case, the first line contains a positive integer N (<= 20). 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, insert the keys one by one into an initially empty AVL tree. Then first print in a line the level-order traversal sequence of the resulting AVL tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line. Then in the next line, print "YES" if the tree is complete, or "NO" if not.

**Sample Input 1:**

5
    88 70 61 63 65

**Sample Output 1:**

70 63 88 61 65
    YES

**Sample Input 2:**

8
    88 70 61 96 120 90 65 68

**Sample Output 2:**

88 65 96 61 70 90 120 68
    NO

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

题目大意：

代码：

#include<stdio.h>
    #include<stdlib.h>
    #include<queue>
    using namespace std;
    struct node
    {
        int data;
        struct node *lchild,*rchild;
    };
    int n,cnt=0;
    int getdeep(struct node *root)
    {
        if(root==NULL)
        {
            return 0;
        }
        int l=getdeep(root->lchild);
        int r=getdeep(root->rchild);
        return l>r?l+1:r+1;
    }
    struct node *LL(struct node *root)
    {
        struct node *tmp=root->lchild;
        root->lchild=tmp->rchild;
        tmp->rchild=root;
        return tmp;
    }
    struct node *RR(struct node *root)
    {
        struct node *tmp=root->rchild;
        root->rchild=tmp->lchild;
        tmp->lchild=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);
    }
    struct node * create(struct node *root,int value)
    {
        if(root==NULL)
        {
            root=(struct node *)malloc(sizeof(struct node));
            root->data=value;
            root->lchild=root->rchild=NULL;
        }
        else if(value>root->data)
        {
            root->rchild=create(root->rchild,value);
            if(getdeep(root->rchild)-getdeep(root->lchild)==2)
            {
                if(value>root->rchild->data)
                {
                    root=RR(root);
                }
                else
                {
                    root=RL(root);
                }
            }
        }
        else
        {
            root->lchild=create(root->lchild,value);
            if(getdeep(root->lchild)-getdeep(root->rchild)==2)
            {
                if(value<root->lchild->data)
                {
                    root=LL(root);
                }
                else
                {
                    root=LR(root);
                }
            }
        }
        return root;
    }
    void preorder(struct node *root)
    {
        if(root)
        {
           printf("%d ",root->data);
           preorder(root->lchild);
           preorder(root->rchild);
        }
    }
    void level(struct node *root)
    {
        queue<struct node *> q;
        q.push(root);
        int flag=0;
        while(!q.empty())
        {
            struct node *tmp=q.front();
            q.pop();
            if(tmp!=NULL)
            {
                if(flag==0)
            {
                printf("%d",tmp->data);
                flag=1;
            }
            else
            {
                printf(" %d",tmp->data);
            }
                q.push(tmp->lchild);
                q.push(tmp->rchild);
            }
        }
    }
    void level1(struct node *root)
    {
        queue<struct node *> q;
        q.push(root);
        while(!q.empty())
        {
            struct node *tmp=q.front();
            q.pop();
            if(tmp!=NULL)
                {
                    q.push(tmp->lchild);
                q.push(tmp->rchild);
                }
                if(tmp==NULL)
                    break;
                cnt++;
        }
    }
    int main()
    {
        int i,j,m,k,t;
        struct node *root=NULL;
        scanf("%d",&n);
        for(i=0;i<n;i++)
        {
            scanf("%d",&m);
            root=create(root,m);
        }
        //preorder(root);
        level(root);
        printf("\n");
        level1(root);
        if(cnt==n)
        {
            printf("YES\n");
        }
        else
        {
            printf("NO\n");
        }
        return 0;
    }

[mr_ohesevgnyny.jpg]: http://nos.patest.cn/mr_ohesevgnyny.jpg
[mr_ohesfdbkaep.jpg]: http://nos.patest.cn/mr_ohesfdbkaep.jpg
[mr_oheseymzi13.jpg]: http://nos.patest.cn/mr_oheseymzi13.jpg
[mr_ohesfjddti2.jpg]: http://nos.patest.cn/mr_ohesfjddti2.jpg