PAT_A1123#Is It a Complete AVL Tree

  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 }