PAT A 1123 1123. Is It a Complete AVL Tree (30)

最新推荐文章于 2022-10-03 08:41:43 发布

原创最新推荐文章于 2022-10-03 08:41:43 发布 · 194 阅读

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本文介绍了一个使用AVL树结构实现的算法，该算法不仅能够进行高效的插入操作，同时还能判断构建的树是否为完全二叉树。通过高度平衡旋转保持树的平衡，并利用队列遍历来检查树的完全性。

AVL树 + 判断是否为完全二叉树

#include <bits/stdc++.h>
using namespace std;
struct Node
{
	int key, height;
	Node *left, *right;
};
vector<int> ans;
int height(Node *node)
{
	if (node == NULL) return 0;
	return node->height;
}
int getBalance(Node *node)
{
	if (node == NULL) return 0;
	return height(node->left) - height(node->right);
}
Node *newNode(int key)
{
	Node *node = (Node*)malloc(sizeof(Node));
	node->key = key;
	node->left = NULL;
	node->right = NULL;
	node->height = 1;
	return node;
}
void maintain(Node *node)
{
	node->height = max(height(node->left), height(node->right)) + 1;
}
Node *leftRotate(Node *x)
{
	Node *y = x->right;
	Node *T2 = y->left;
	y->left = x;
	x->right = T2;
	maintain(x);
	maintain(y);
	return y;
}
Node *rightRotate(Node *y)
{
	Node *x = y->left;
	Node *T2 = x->right;
	x->right = y;
	y->left = T2;
	maintain(y);
	maintain(x);
	return x;
}
Node *insert(Node *node, int key)
{
	if (node == NULL) return newNode(key);
	if (key < node->key) node->left = insert(node->left, key);
	else if (key > node->key) node->right = insert(node->right, key);
	else return node;
	maintain(node);
	int balance = getBalance(node);
	if (balance > 1 && key < node->left->key) return rightRotate(node); // LL
	if (balance < -1 && key > node->right->key) return leftRotate(node); // RR
	if (balance > 1 && key > node->left->key) { //LR
		node->left = leftRotate(node->left);
		return rightRotate(node);
	}
	if (balance < -1 && key < node->right->key) { //RL
		node->right = rightRotate(node->right);
		return leftRotate(node);
	}
	return node;
}
void printGivenLevel(Node *node, int level)
{
	if (node == NULL) return;
	if (level == 1) ans.push_back(node->key);
	else if (level > 1) {
		printGivenLevel(node->left, level - 1);
		printGivenLevel(node->right, level - 1);
	}
}
void printLevelOrder(Node *node)
{
	int h = height(node);
	for (int i = 1; i <= h; i++) printGivenLevel(node, i);
}
bool isComplete(Node *root)
{
	if (root == NULL) return true;
	queue<Node*> q;
	bool flag = false;
	q.push(root);
	while (!q.empty()) {
		Node *now = q.front();
		q.pop();
		if (now->left != NULL) {
			if (flag) return false;
			q.push(now->left);
		} else flag = true;
		if (now->right != NULL) {
			if (flag) return false;
			q.push(now->right);
		} else flag = true;
	}
	return true;
}
int main()
{
	Node *root = NULL;
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		int x;
		scanf("%d", &x);
		root = insert(root, x);
	}
	printLevelOrder(root);
	cout << ans[0];
	for (int i = 1; i < ans.size(); i++) cout << ' ' << ans[i];
	cout << endl;
	if (isComplete(root)) cout << "YES" << endl; else cout << "NO" << endl;
	return 0;
}