PAT甲级1123 Is It a Complete AVL Tree【AVL树】

题目：https://pintia.cn/problem-sets/994805342720868352/problems/994805351302414336

题意：

给定n个树，依次插入一棵AVL树，按照层序遍历输出，最后判断这棵AVL树是不是完全二叉树。

思路：

这道题过段时间还要再来手搓一发。AVL模板要记住。

判断是不是完全二叉树的话只用看，如果有一个节点儿子是空，而他之后又出现了至少有一个儿子的节点的话，就不是完全二叉树。【蛮巧妙的】

 #include<cstdio>
 #include<cstdlib>
 #include<map>
 #include<set>
 #include<iostream>
 #include<cstring>
 #include<algorithm>
 #include<vector>
 #include<cmath>
 #include<stack>
 #include<queue>

 #define inf 0x7fffffff
 using namespace std;
 typedef long long LL;
 typedef pair<string, string> pr;

 int n;
 const int maxn = ;
 vector<int>level[maxn];
 typedef struct AvlNode{
     int val;
     AvlNode *left;
     AvlNode *right;
     int height;
 }*AvlTree, AvlNode;

 int Max(AvlTree a, AvlTree b)
 {
     int x = , y = ;
     if(a)x = a->height;
     if(b)y = b->height;
     if(x > y)return x;
     else return y;
 }

 AvlTree singleRotateWithRight(AvlTree T)
 {
     AvlTree L = T->left;
     T->left = L->right;
     L->right = T;
     T->height = Max(T->left, T->right) + ;
     L->height = Max(L->left, L->right) + ;
     return L;
 } 

 AvlTree singleRotateWithLeft(AvlTree T)
 {
     AvlTree R = T->right;
     T->right = R->left;
     R->left = T;
     T->height = Max(T->left, T->right) + ;
     R->height = Max(R->left, R->right) + ;
     return R;
 }

 AvlTree doubleRotateWithLeft(AvlTree T)
 {
     T->left = singleRotateWithLeft(T->left);
     return singleRotateWithRight(T);
 }

 AvlTree doubleRotateWithRight(AvlTree T)
 {
     T->right = singleRotateWithRight(T->right);
     return singleRotateWithLeft(T);
 }

 AvlTree Insert(AvlTree T, int val)
 {
     if(T == NULL){
         T = (AvlNode *)malloc(sizeof(struct AvlNode));
         if(T){
             T->val = val;
             T->left = NULL;
             T->right = NULL;
             T->height = ;
         }
     }
     else if(val < T->val){
         T->left = Insert(T->left, val);
         int l = , r = ;
         if(T->left){
             l = T->left->height;
         }
         if(T->right){
             r = T->right->height;
         }
         if(l - r == ){
             if(val < T->left->val){
                 T = singleRotateWithRight(T);
             }
             else{
                 T = doubleRotateWithLeft(T);
             }
         }
     }
     else if(val > T->val){
         T->right = Insert(T->right, val);
         int l = , r = ;
         if(T->left)l = T->left->height;
         if(T->right)r = T->right->height;
         if(r - l == ){
             if(val > T->right->val){
                 T = singleRotateWithLeft(T);
             }
             else{
                 T = doubleRotateWithRight(T);
             }
         }
     }
     T->height = Max(T->left, T->right) + ;
     return T;
 }

 bool after = false, iscomplete = true;
 bool first = false;
 void levelOrder(AvlTree T)
 {
     queue<AvlTree>que;
     que.push(T);
     while(!que.empty()){
         AvlTree now = que.front();que.pop();
         if(first)printf(" ");
         else first = true;
         printf("%d", now->val);
         level[now->height].push_back(now->val);
         if(now->left){
             if(after)iscomplete = false;
             que.push(now->left);
         }
         else{
             after = ;
         }
         if(now->right){
             if(after)iscomplete = false;
             que.push(now->right);
         }
         else{
             after = ;
         }
     }
 }

 int main()
 {
     scanf("%d", &n);
     AvlTree Tree = NULL;
     for(int i = ; i < n; i++){
         int x;
         scanf("%d", &x);
         Tree = Insert(Tree, x);
     }
     levelOrder(Tree);
     printf("\n");
     if(iscomplete)printf("YES\n");
     else printf("NO\n");
     return ;
 }