An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.
 |  |
|---|---|
 |  |
Now given a sequence of insertions, you are supposed to output the level-order traversal sequence of the resulting AVL tree, and to tell if it is a complete binary tree.
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer N (≤ 20). Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.
Output Specification:
For each test case, insert the keys one by one into an initially empty AVL tree. Then first print in a line the level-order traversal sequence of the resulting AVL tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line. Then in the next line, print YES if the tree is complete, or NO if not.
Sample Input 1:
5
88 70 61 63 65
Sample Output 1:
70 63 88 61 65
YES
Sample Input 2:
8
88 70 61 96 120 90 65 68
Sample Output 2:
88 65 96 61 70 90 120 68
NO
在左子树的右结点 上添加一个new 结点
（1）
（2）
在右子树的左子树上 添加同理，分为两种情况
#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
#define rep(i,a,b) for(int i=a;i<b;++i)
const int INF=0x3f3f3f3f;
const int N=50;
struct Node {
int x;
int b;
Node *l,*r;
};
int arr[N];
void R_Rotate(Node* &now)
{
Node* lc=now->l;
now->l=lc->r;
lc->r=now;
now=lc;
}
void L_Rotate(Node* &now)
{
Node* rc=now->r;
now->r=rc->l;
rc->l=now;
now=rc;
}
void bala_l(Node* &now)
{
Node* l=now->l,*rc=NULL;
switch(l->b) {
case 1:
now->b=l->b=0;
R_Rotate(now);
break;
case -1:
rc=l->r;
switch(rc->b) {
case 1:
l->b=0;
rc->b=0;
now->b=-1;
break;
//这里也不能省略，可能出现下面这种情况
/*
x
/ \
x x
/
x
\
x
*/
case 0:
now->b=l->b=0;
break;
case -1:
l->b=1;
rc->b=0;
now->b=0;
break;
}
L_Rotate(now->l);
R_Rotate(now);
break;
}
}
void bala_r(Node* &now)
{
Node* r=now->r,*lc=r->l;
switch(r->b) {
case -1:
now->b=r->b=0;
L_Rotate(now);
break;
case 1:
lc=r->l;
switch(lc->b) {
case 1:
r->b=-1;
lc->b=0;
now->b=0;
break;
case 0:
now->b=r->b=0;
break;
case -1:
r->b=0;
lc->b=0;
now->b=1;
break;
}
R_Rotate(now->r);
L_Rotate(now);
break;
}
}
void insert_(Node* &now,int x,int& taller)
{
if(now==NULL) {
now=new Node;
now->x=x;
now->l=now->r=NULL;
now->b=0;
taller=1;
return;
}
if(x<=now->x) {
insert_(now->l,x,taller);
if(taller) {
switch(now->b) {
case -1:
now->b=0;
taller=0;
break;
case 0:
now->b=1;
break;
case 1:
// printf("***x:%d\n",now->x);
bala_l(now);
taller=0;
break;
}
}
} else {
insert_(now->r,x,taller);
if(taller) {
switch(now->b) {
case -1:
bala_r(now);
taller=0;
break;
case 0:
now->b=-1;
break;
case 1:
now->b=0;
taller=0;
break;
}
}
}
}
queue<Node*> q;
int n;
/*
最方便的是用到了引用，这样的话，一颗子树的旋转就会很容易，指针的赋值就会比较方便
每次插入都得调整一下，路径上点的平衡因子。
旋转的话，只有两种 L型和R型，细分又分为LR，LL。区别就是看看L那个子树的平衡因子
*/
int res[N];
void bfs(Node* rt)
{
q.push(rt);
int cnt=0;
int wrong=0,f=0;
while(!q.empty()) {
Node* now=q.front();
q.pop();
res[cnt++]=now->x;
if(now->l)q.push(now->l);
if(now->r)q.push(now->r);
// printf("%d l:%x r:%x\n",now->x,now->l,now->r);
if(f&&(now->l!=NULL||now->r!=NULL))wrong=1;
if(now->l==NULL||now->r==NULL)f=1;
if(now->l==NULL&&now->r!=NULL)wrong=1;
}
// printf("***cnt:%d\n",cnt);
rep(i,0,cnt)printf("%d%c",res[i],i==cnt-1?'\n':' ');
if(wrong)printf("NO\n");
else printf("YES\n");
}
/*
3
1 2 3
3
3 2 1
5
88 70 61 63 65
6
88 70 61 96 120 90
*/
int main()
{
scanf("%d",&n);
rep(i,0,n)scanf("%d",&arr[i]);
Node *rt=NULL;//
int taller;
rep(i,0,n){
//printf("\n\n\n");
insert_(rt,arr[i],taller);
//bfs(rt);
}
bfs(rt);
return 0;
}
