PAT_A1123#Is It a Complete AVL Tree

Posted 2021-12-18 blue-lin

Source:

PAT A1123 Is It a Complete AVL Tree (30 分)

Description:

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.

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

Keys:

• 二叉树的建立
• 二叉树的遍历
• 完全二叉树（Complete Binary Tree）
• 平衡二叉树（Self-balancing Binary Search Tree，AVL tree）

Attention:

• 愣是用一个变量搞定了输出和判断0,0

Code:

  1 /*
  2 Data: 2019-06-03 19:58:23
  3 Problem: PAT_A1123#Is It a Complete AVL Tree
  4 AC: 61:05
  5 
  6 题目大意：
  7 由插入序列构造一棵AVL树，输出层次遍历并判断是否为一棵完全二叉树
  8 */
  9 
 10 #include<cstdio>
 11 #include<algorithm>
 12 #include<queue>
 13 using namespace std;
 14 struct node
 15 
 16     int data,height;
 17     node *lchild, *rchild;
 18 ;
 19 
 20 int GetH(node *root)
 21 
 22     if(root == NULL)
 23         return 0;
 24     else
 25         return root->height;
 26 
 27 
 28 void UpH(node* &root)
 29 
 30     root->height=max(GetH(root->lchild),GetH(root->rchild))+1;
 31 
 32 
 33 int GetF(node *root)
 34 
 35     return GetH(root->lchild)-GetH(root->rchild);
 36 
 37 
 38 void LeftRot(node* &root)
 39 
 40     node *temp = root->rchild;
 41     root->rchild = temp->lchild;
 42     temp->lchild = root;
 43     UpH(root);
 44     UpH(temp);
 45     root = temp;
 46 
 47 
 48 void RightRot(node* &root)
 49 
 50     node *temp = root->lchild;
 51     root->lchild = temp->rchild;
 52     temp->rchild = root;
 53     UpH(root);
 54     UpH(temp);
 55     root = temp;
 56 
 57 
 58 void Insert(node* &root, int x)
 59 
 60     if(root == NULL)
 61     
 62         root = new node;
 63         root->data = x;
 64         root->height=1;
 65         root->lchild=root->rchild=NULL;
 66         return;
 67     
 68     if(x < root->data)
 69     
 70         Insert(root->lchild, x);
 71         UpH(root);
 72         if(GetF(root) == 2)
 73         
 74             if(GetF(root->lchild) == 1)
 75                 RightRot(root);
 76             else
 77                 LeftRot(root->lchild);
 78                 RightRot(root);
 79             
 80         
 81     
 82     else
 83     
 84         Insert(root->rchild, x);
 85         UpH(root);
 86         if(GetF(root) == -2)
 87         
 88             if(GetF(root->rchild) == -1)
 89                 LeftRot(root);
 90             else
 91                 RightRot(root->rchild);
 92                 LeftRot(root);
 93             
 94         
 95     
 96 
 97 
 98 void Travel(node *root)
 99 
100     int ans=0;
101     queue<node*> q;
102     q.push(root);
103     printf("%d", root->data);
104     while(!q.empty())
105     
106         root = q.front();
107         q.pop();
108         if(root)
109             if(ans!=0) printf(" %d", root->data);
110             else       ans=1;
111             q.push(root->lchild);
112             q.push(root->rchild);
113         
114         else
115             ans++;
116             while(!q.empty())
117                 root = q.front();
118                 if(root) break;
119                 else   q.pop();
120             
121             if(ans==2 && q.empty())
122                 printf("\nYES\n");
123                 return;
124             
125         
126     
127     printf("\nNO\n");
128 
129 
130 
131 int main()
132 
133 #ifdef    ONLINE_JUDGE
134 #else
135     freopen("Test.txt", "r", stdin);
136 #endif
137 
138     int n,x;
139     scanf("%d", &n);
140     node *root = NULL;
141     for(int i=0; i<n; i++)
142     
143         scanf("%d", &x);
144         Insert(root, x);
145     
146     Travel(root);
147 
148     return 0;
149