1123 Is It a Complete AVL Tree（30 分）(cj)

1123 Is It a Complete AVL Tree（30 分）

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

新知识：AVL树用数组来实现比较困难，因为涉及整个树的数据转移，会占用不必要内存时间，难度也会很大。

树的平衡在每一次插入后进行平衡。全部插入完后进行平衡虽然也能得到AVL树，但是元素的位置是不好预测的，结果也可能会与测试数据不同。 

数组处理完全二叉树真的好用。

code

#pragma warning(disable:4996)
#include <iostream>
#include <algorithm>
using namespace std;
class avltree {
public:
	int val;
	avltree* left = NULL, *right=NULL;
	int getheight(avltree* t) {
		if (t==NULL) return 0;
		return max(getheight(t->left), getheight(t->right)) + 1;
	}
	int getbf(avltree* t) {
		int f = getheight(t->left) - getheight(t->right);
		return f;
	}
	void doll(avltree*& t) {
		avltree* pa = t->left, *p = t;
		p->left = pa->right;
		pa->right = p;
		t = pa;
	}
	void dorr(avltree*& t) {
		avltree * pa = t->right, *p = t;
		p->right = pa->left;
		pa->left = p;
		t = pa;
	}
	void dolr(avltree*& t) {
		avltree *p = t, *pa = t->left, *pb = t->left->right;
		pa->right = pb->left;
		pb->left = pa;
		p->left = pb->right;
		pb->right = p;
		t = pb;
	}
	void dorl(avltree*& t) {
		avltree* p = t, *pa = t->right, *pb = t->right->left;
		pa->left = pb->right;
		pb->right = pa;
		p->right = pb->left;
		pb->left = p;
		t = pb;
	}
	void balance(avltree*& t) {
		if (t == NULL) return;
		balance(t->left);
		balance(t->right);
		if (getbf(t) > 1) {
			if (getbf(t->left) > 0) doll(t);
			else dolr(t);
		}
		else if (getbf(t) < -1) {
			if (getbf(t->right) < 0) dorr(t);
			else dorl(t);
		}
	}
};
void avlinsert(avltree*& t, int x) {
	if (t == NULL) {
		t = new avltree;
		t->val = x;
		return;
	}
	if (x > t->val) {
		avlinsert(t->right, x);
	}
	else avlinsert(t->left, x);
}
int treearr[100];
void print(avltree* t,int pos) {
	if (t == NULL) return;
	treearr[pos] = t->val;
	print(t->left, pos * 2);
	print(t->right, pos * 2 + 1);
}
int main() {
	int n,x;
	cin >> n;
	avltree* head = NULL;
	for (int i = 0; i < n; ++i) {
		cin >> x;
		avlinsert(head, x);
		head->balance(head);
	}
	print(head, 1);
	bool f = 1, ff = 1;
	for (int i = 1; i < 100; ++i) {
		if (i <= n && treearr[i] == 0) f = 0;
		if (treearr[i] != 0) {
			if (ff) ff = 0;
			else cout << ' ';
			cout << treearr[i];
		}
	}
	cout << endl;
	if (f) cout << "YES" << endl;
	else cout << "NO" << endl;
	system("pause");
	return 0;
}