PAT甲级——A1064 Complete Binary Search Tree
A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:
- The left subtree of a node contains only nodes with keys less than the node's key.
- The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
- Both the left and right subtrees must also be binary search trees.
A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.
Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.
Input Specification:
Each input file contains one test case. For each case, the first line contains a positive integer N (≤). Then N distinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.
Output Specification:
For each test case, print in one line the level order traversal sequence of the corresponding complete binary search 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.
Sample Input:
10
1 2 3 4 5 6 7 8 9 0
Sample Output:
6 3 8 1 5 7 9 0 2 4
通过观察可以注意到,对完全二叉树当中的任何一个结点(设编号为x),其左孩子的编号一定是2x,而右孩子的编号一定是2x + 1。也就是说,完全二叉树可以通过建立一个大小为2k的数组来存放所有结点的信息,其中k为完全二叉树的最大高度,且1号位存放的必须是根结点(想一想为什么根结点不能存在下标为0处?)。这样就可以用数组的下标来表图95完全二又树编号示意示结点编号,且左孩子和右孩子的编号都可以直接计算得到。
事实上,如果不是完全二叉树,也可以视其为完全二叉树,即把空结点也进行实际的编号工作。但是这样做会使整棵树是一条链时的空间消耗巨大(对k个结点就需要大小为2k的数组),因此很少采用这种方法来存放一般性质的树。不过如果题目中已经规定是完全二叉树,那么数组大小只需要设为结点上限个数加1即可,这将会大大节省编码复杂度。
除此之外,该数组中元素存放的顺序恰好为该完全二叉树的层序遍历序列。而判断某个结点是否为叶结点的标志为:该结点(记下标为root)的左子结点的编号root * 2大于结点总个数n(想一想为什么不需要判断右子结点?);判断某个结点是否为空结点的标志为:该结点下标 root大于结点总个数n。
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int N, nums[], res[], index = ;
void levelOrder(int k)
{
if (k > N)//叶子节点
return;
levelOrder(k * );//遍历左子树
res[k] = nums[index++];//即遍历完左子树后,此时即为根节点
levelOrder(k * + );//遍历右子树
}
int main()
{
cin >> N;
for (int i = ; i < N; ++i)
cin >> nums[i];
sort(nums, nums + N, [](int a, int b) {return a < b; });
levelOrder();
for (int i = ; i <= N; ++i)
cout << res[i] << (i == N ? "" : " ");
return ;
}
PAT甲级——A1064 Complete Binary Search Tree的更多相关文章
- PAT 甲级 1064 Complete Binary Search Tree
https://pintia.cn/problem-sets/994805342720868352/problems/994805407749357568 A Binary Search Tree ( ...
- pat 甲级 1064. Complete Binary Search Tree (30)
1064. Complete Binary Search Tree (30) 时间限制 100 ms 内存限制 65536 kB 代码长度限制 16000 B 判题程序 Standard 作者 CHE ...
- PAT 甲级 1064 Complete Binary Search Tree (30 分)(不会做,重点复习,模拟中序遍历)
1064 Complete Binary Search Tree (30 分) A Binary Search Tree (BST) is recursively defined as a bin ...
- pat 甲级 1064 ( Complete Binary Search Tree ) (数据结构)
1064 Complete Binary Search Tree (30 分) A Binary Search Tree (BST) is recursively defined as a binar ...
- A1064. Complete Binary Search Tree
A Binary Search Tree (BST) is recursively defined as a binary tree which has the following propertie ...
- PAT Advanced 1064 Complete Binary Search Tree (30) [⼆叉查找树BST]
题目 A Binary Search Tree (BST) is recursively defined as a binary tree which has the following proper ...
- PAT_A1064#Complete Binary Search Tree
Source: PAT A1064 Complete Binary Search Tree (30 分) Description: A Binary Search Tree (BST) is recu ...
- PAT甲级:1064 Complete Binary Search Tree (30分)
PAT甲级:1064 Complete Binary Search Tree (30分) 题干 A Binary Search Tree (BST) is recursively defined as ...
- PAT题库-1064. Complete Binary Search Tree (30)
1064. Complete Binary Search Tree (30) 时间限制 100 ms 内存限制 32000 kB 代码长度限制 16000 B 判题程序 Standard 作者 CHE ...
随机推荐
- iserver中的服务数据迁移
今天需要将iserver测试服务器上的空间数据服务(数据源是Oracle Plus)迁移到客户的正式服务器,原想需要很大的工作量,其实是这样简单: 一.保证客户的iserver环境都已安装正确.对于o ...
- Classpath in jar关于java加载第三方jar的集中方法和详细解释。
转载地址:http://www.iteye.com/topic/332580 大家都知道一个java应用项目可以打包成一个jar,当然你必须指定一个拥有main函数的main class作为你这个ja ...
- SpringCloud学习笔记(六):Feign+Ribbon负载均衡
简介 官网解释: http://projects.spring.io/spring-cloud/spring-cloud.html#spring-cloud-feign Feign是一个声明式WebS ...
- pycharm同时使用python2.7和python3.5设置方法
pycharm同时使用python2.7和python3.5设置方法 - CSDN博客https://blog.csdn.net/qwerty200696/article/details/530159 ...
- ubuntu install redis/mongo 以及 监控安装
sudo apt-get updatesudo apt-get install redis-server mongodb sudo apt-get install htopsudo apt-get i ...
- DNS配置-BIND安装配置全过程
下载地址:ftp://ftp.isc.org/isc/ 下载bind,我下载的是bind-9.11.13.tar.gz 我下载的文件放在/root目录下进入目录解压缩 [root@localhost ...
- XCode的依赖库管理工具——CocoaPods
安装CocoaPods 首先,在启动台里打开终端(terminal),并在终端里输入“sudo gem install cocoapods”,按回车后输入电脑用户密码(注意:输入期间不会显示“***” ...
- 编写main方法
- bzoj2209 括号序列
题意:给你一个括号序列.操作1:询问需要更改多少个括号使之匹配. 操作2:反转序列,左括号变成右括号. 操作3:翻转序列,倒置. 标程: #include<cstdio> #include ...
- [转].NET4.0新特性集合贴
vs2010正式版4月12日发布了,前几天我也下了一个,但这几天都没有时间好好试用一下,今天针对C#语言的新特性使用了一下,感觉还不错,有几个新特性和大家分享一下,希望我没有太火星…… 一.新关键词— ...