PAT1123 AVL树的调整与判断完全二叉树

解析：这题我学了一天AVL树的调整，建好了树，又用了一个多小时尝试各种方法判断是否为完全二叉树，最后败在了输出层次遍历上。。

解题步骤：

• 建立AVL树，其中涉及AVL树的四种调整
• 输出层次遍历，用队列输出，不能用stack！
• 判断一棵树是否为完全二叉树，可以给每个节点编号，比如某个节点编号为id，它左儿子为2*id,右儿子为2*id+1，如果最大的编号为n，即为完全二叉树。（这也是完全二叉树的一个性质）

代码示例：

#include<iostream>
#include<cstdio>
#include<queue>
using namespace std;
typedef struct AVLNode *position;
typedef position AVLTree;
int maxid = -1;
struct AVLNode{
	int data;
	AVLTree left;
	AVLTree right;
	int h;
};
int GetHight(AVLTree A){
	if(A == NULL)	return -1;
	return A->h;
}
//左单旋
AVLTree SLR(AVLTree A){
	AVLTree B = A->left;
	A->left = B->right;
	B->right = A;
	A->h = max(GetHight(A->left),GetHight(A->right))+1;
	B->h = max(GetHight(B->left),GetHight(B->right))+1;
	return B;
} 
//右单旋
AVLTree SRR(AVLTree A){
	AVLTree B = A->right;
	A-> right = B->left;
	B->left = A;
	A->h = max(GetHight(A->left),GetHight(A->right))+1;
	B->h = max(GetHight(B->left),GetHight(B->right))+1;
	return B;
}
//左右双旋
AVLTree DLRR(AVLTree A){
	AVLTree B = A->left;
	A->left = SRR(B);
	return SLR(A);
}
//右左双旋 
AVLTree DRLR(AVLTree A){
	AVLTree B = A->right;
	A->right = SLR(B);
	return SRR(A);
}
AVLTree Insert(AVLTree T,int x){
	if(T == NULL){
		T = new AVLNode();
		T->data = x;
		T->left = NULL;
		T->right = NULL;
		T->h = 0;
	}else if(x < T->data){
		T->left = Insert(T->left,x);
		if(GetHight(T->left) - GetHight(T->right) == 2)
			if(x < T->left->data)	T = SLR(T);
			else T = DLRR(T);
	}else if(x > T->data){
		T->right = Insert(T->right,x);
		if(GetHight(T->left)-GetHight(T->right) == -2)
			if(x > T->right->data)	T = SRR(T);
			else	T = DRLR(T);
	}
	T->h = max(GetHight(T->left),GetHight(T->right))+1;
	return T;
}
void printTree(AVLTree T){
	if(!T)	return;
	queue<AVLTree> q;
	q.push(T);
	int cnt = 0;
	while(q.size()){
		AVLTree a = q.front();
		q.pop();
		if(cnt == 0)	printf("%d",a->data);
		else	printf(" %d",a->data);
		cnt++;
		if(a->left)	q.push(a->left);
		if(a->right)	q.push(a->right);
	} 
	printf("
");
}
void solve(AVLTree T,int id){
	maxid = max(id,maxid);
	if(T->left)	solve(T->left,id<<1);
	if(T->right)	solve(T->right,id<<1|1);
	return;
}
bool judge(AVLTree T,int n){
	solve(T,1);
	if(maxid != n)	return false;
	return true;
}
int main()
{
	int n,x;
	scanf("%d",&n);
	AVLTree T = NULL;
	for(int i = 0;i < n;i++){
		scanf("%d",&x);
		T = Insert(T,x);
	}
	if(n == 0)	puts("NO");
	else{
		printTree(T);
		if(judge(T,n))	puts("YES");
		else puts("NO");
	}
	
	return 0;
}