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 = 25;
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 = 0, y = 0;
    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) + 1;
    L->height = Max(L->left, L->right) + 1;
    return L;
} 

AvlTree singleRotateWithLeft(AvlTree T)
{
    AvlTree R = T->right;
    T->right = R->left;
    R->left = T;
    T->height = Max(T->left, T->right) + 1;
    R->height = Max(R->left, R->right) + 1;
    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 = 0;
        }
    }
    else if(val < T->val){
        T->left = Insert(T->left, val);
        int l = 0, r = 0;
        if(T->left){
            l = T->left->height;
        }
        if(T->right){
            r = T->right->height;
        }
        if(l - r == 2){
            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 = 0, r = 0;
        if(T->left)l = T->left->height;
        if(T->right)r = T->right->height;
        if(r - l == 2){
            if(val > T->right->val){
                T = singleRotateWithLeft(T);
            }
            else{
                T = doubleRotateWithRight(T);
            }
        }
    }
    T->height = Max(T->left, T->right) + 1;
    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 = 1;
        }
        if(now->right){
            if(after)iscomplete = false;
            que.push(now->right);
        }
        else{
            after = 1;
        }
    }
}

int main()
{
    scanf("%d", &n);
    AvlTree Tree = NULL;
    for(int i = 0; i < n; i++){
        int x;
        scanf("%d", &x);
        Tree = Insert(Tree, x);
    }
    levelOrder(Tree);
    printf("
");
    if(iscomplete)printf("YES
");
    else printf("NO
");
    return 0;
}