1123. Is It a Complete AVL Tree (30)

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#PAT #AVL Tree #complete binary tree

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本文介绍了一种自平衡二叉搜索树——AVL树的实现方法，包括插入操作及旋转调整等核心算法，并通过层级遍历验证了树结构是否符合完全二叉树特性。

#include<iostream>
#include<vector>
#include<queue>
#include<set>
#include<algorithm>
using namespace std;
struct node{
	int v,height;
	int order;
	node *lchild,*rchild;
};
node* newNode(int v){
	node* Node = new node;
	Node->v = v;
	Node->height = 1;
	Node->lchild = Node->rchild = NULL;
	return Node;
}
int getHeight(node* root){
	if(root == NULL) return 0;
	return root->height;
}
int getBalanceFactor(node* root){
	return getHeight(root->lchild)-getHeight(root->rchild);
}
void updateHeight(node* root){
	root->height=max(getHeight(root->lchild),getHeight(root->rchild))+1;
}
void L(node* &root){
	node* temp = root->rchild;
	root->rchild = temp->lchild;
	temp->lchild = root;
	updateHeight(root);
	updateHeight(temp);
	root = temp;
}
void R(node* &root){
	node* temp = root->lchild;
	root->lchild = temp->rchild;
	temp->rchild = root;
	updateHeight(root);
	updateHeight(temp);
	root = temp;
}
void insert(node* &root,int v){
	if(root == NULL){
		root = newNode(v);
		return;
	}
	if(v < root->v){
		insert(root->lchild,v);
		updateHeight(root);
		if(getBalanceFactor(root) == 2){
			if(getBalanceFactor(root->lchild) == 1){//LL
				R(root);
			}
			else if(getBalanceFactor(root->lchild) == -1){//LR
				L(root->lchild);
				R(root);
			}
		}
	}
	else{
		insert(root->rchild,v);
		updateHeight(root);
		if(getBalanceFactor(root) == -2){
			if(getBalanceFactor(root->rchild) == -1){//RR
				L(root);
			}
			else if(getBalanceFactor(root->rchild) == 1){//RL
				R(root->rchild);
				L(root);
			}
		}    	
	}
}
node* Creat(int data[],int n){
	node* root = NULL;
	for(int i=0;i<n;i++){
		insert(root,data[i]);
	}
	return root;
}
vector<node*> level;
void levelorder(node* root){
	node* p=root;
	root->order = 1;//利用完全二叉树父子节点序号的关系来判断是否为完全二叉树 
	queue<node*> qu;
	qu.push(p);
	while(!qu.empty()){
		p=qu.front();
		qu.pop();
		level.push_back(p);
		if(p->lchild!=NULL){
			qu.push(p->lchild);
			p->lchild->order = 2*p->order;
		}
		if(p->rchild!=NULL){
			qu.push(p->rchild);
			p->rchild->order = 2*p->order+1;
		}
	}
}
int main(){
	int n;
	cin>>n;
	int data[n];
	for(int i=0;i<n;i++){
		scanf("%d",&data[i]);
	}
	node* root = Creat(data,n);
	levelorder(root);
	for(int i=0;i<n;i++){
		if(i != 0) printf(" ");
		printf("%d",level[i]->v);
	}
	printf("\n");
	//cout<<level[n-1]->order<<endl;
	if(level[n-1]->order!=n){
		printf("NO");
	}
	else{
		printf("YES");
	}
	return 0;
}