PAT 1123 Is It a Complete AVL Tree

题目链接：点击打开链接

思路：先按照AVL树的建树规则创建一棵二叉搜索树，得到层序遍历后，判断是否为完全二叉树，完全二叉树的判断方法为：逐层遍历每个节点，当遇到一个空节点，若仍然有未遍历的非空节点，说明不是完全二叉树。

#include 
#include 
#include 
#include 
#include 
using namespace std;
int root,data[25],le[25],rig[25];
int getHeight(int loc){
	if(!loc){
		return 1;
	}
	int h1 = getHeight(le[loc]);
	int h2 = getHeight(rig[loc]);
	return (h1>h2?h1:h2) + 1;
}
void leftSingleRotate(int &r){
	int t = le[r];
	le[r] = rig[t];
	rig[t] = r;
	r = t;
	return; 
} 
void rightSingleRotate(int &r){
	int t = rig[r];
	rig[r] = le[t];
	le[t] = r;
	r = t;
	return;
}
void leftRightRotate(int &r){
	rightSingleRotate(le[r]);
	leftSingleRotate(r);
	return;
}
void rightLeftRotate(int &r){
	leftSingleRotate(rig[r]);
	rightSingleRotate(r);
	return;
}
void add(int &r,int loc){
	int h1,h2;
	if(!r){
		r = loc;
		le[r] = rig[r] = 0;
		return;
	}
	else if(data[loc] < data[r]){
		add(le[r],loc);
		h1 = getHeight(le[r]);
		h2 = getHeight(rig[r]);
		if(abs(h1 - h2) >= 2){
			if(data[loc] < data[le[r]]){//left-single-rotate
				leftSingleRotate(r);
			}
			else{//left-right-double-rotate
				leftRightRotate(r);
			}
		}
	}
	else{
		add(rig[r],loc);
		h1 = getHeight(le[r]);
		h2 = getHeight(rig[r]);
		if(abs(h1 - h2) >= 2){
			if(data[loc] > data[rig[r]]){//right-single-rotate
				rightSingleRotate(r);
			}
			else{//right-left-double-rotate
				rightLeftRotate(r);
			}
		}
	}
	return;
}
void bfs(int r){//层序遍历 
	queue q;
	vector v;
	q.push(r);
	while(!q.empty()){
		int t = q.front();
		q.pop();
		v.push_back(data[t]);
		if(le[t]) q.push(le[t]);
		if(rig[t]) q.push(rig[t]);
	}
	for(int i = 0;i < v.size();i++){
		printf("%d%c",v[i],i == v.size() - 1 ? '\n':' ');
	}
	return;
}
int judge(int r){//判断二叉树是否为完全二叉树 
	queue q;
	q.push(r);
	while(!q.empty()){
		int t = q.front();
		q.pop();
		if(!t) break;//遇到空节点 
		q.push(le[t]);
		q.push(rig[t]);
	}
	while(!q.empty()){
		if(q.front() != 0){
			return 0;
		}
		q.pop();
	}
	return 1;
}
int main(){
	int n;
	root = 0;
	scanf("%d",&n);
	for(int i = 1;i <= n;i++){
		scanf("%d",&data[i]);
		add(root,i);
	}
	bfs(root);
	int flag = judge(root);
	puts(flag?"YES":"NO");
	return 0;
}