Instructions

1. Submit your responses in a single knitted file, following the Homework Structure which requires model outputs, plots, and code for all questions to be submitted in a single HTML file by Sept 29 at 11:59 p.m. Eastern**. [Time converter]**
2. The solutions will be made available on Oct 1 at 1:00 a.m. Eastern. You will need to assess three of your peers to complete the Data Analysis by Oct 6 at 11:59 p.m. Eastern**. Students who do not submit the graded assessments before the deadline will receive a zero on their own Data Analysis.**
3. Before you begin, please review the following document: DONT_CHEAT.docx. Cheating is not helping you learn and be successful. It does the opposite. While you may collaborate with other students, please submit your own responses to the data analysis questions. Please refrain from consulting prior homework solutions or other materials that provide answers to the data analysis questions. Any case identified as potential plagiarism will result in a zero grade for the assignment and it will be reported to the OMSA program.

Introduction

This project is inspired by a genre of video game, where players choose the actions that their characters take in a turn-based battle. Some examples include the battle systems in Super Mario RPG, Pokémon, Final Fantasy and table-top games like Dungeons and Dragons.

Question 1

Three devices are monitored until failure. The observed lifetimes are 1.1, 2.2, and 0.4 years. If the lifetimes are modeled as exponential distribution with rate $\lambda$,

Instructions:

1. Print your First and Last name and NetID on your answer sheets
2. Submit all your answers including Python scripts and report in a single Jupyter Lab file (.ipynb) or along with a single PDF to Brightspace by due date. No other file formats will be graded. No late submission will be accepted.
3. Total 5 problems. Total points: 100

二叉树（Binary Tree）是一种非线性数据结构，代表“祖先”与“后代”之间的派生关系，体现了“一分为二”的分治逻辑。与链表类似，二叉树的基本单元是节点，每个节点包含值、左子节点引用和右子节点引用。

class TreeNode:
    """二叉树节点类"""
    def __init__(self, val: int):
        self.val: int = val                # 节点值
        self.left: TreeNode | None = None  # 左子节点引用
        self.right: TreeNode | None = None # 右子节点引用

Due dates:

• Implementation: Thu, Sep. 26 at 8:59pm
• Self-evaluation: Fri, Sep. 27 at 11:59pm

Starter files: code.zip

你好，我是悦创。

Java 的 Builder 模式（建造者模式）是一种设计模式，通常用于构建复杂对象。它通过一步步地构建一个对象来避免构造函数参数过多的问题，同时提高代码的可读性和灵活性。我们可以通过 Builder 模式在构建对象时指定我们需要的字段，而不必每次都传递所有的参数。

1. 什么时候使用 Builder 模式？

1. 构造函数参数过多：如果类有多个可选参数，直接使用构造函数可能会显得混乱。
2. 对象不可变：通过 Builder 模式，创建对象的过程在构造完成之后就不会再被修改。
3. 提高可读性：可以按需设置不同的参数，而不用处理多个构造函数的重载。

This assignment is a set of practice problems to help you get familiar with Python and its environment.

Please copy the following files to your computer, and for each question write your answers in the corresponding file: q1.py, q2.py,
q3.py, and q4.py. To get all the files at once, download a1_starting_files.zip and extract them to your computer.

1. Question 1

1.1 多边形内角和

正六边形的内角和可以通过计算其内角数来得到。

对于任何多边形，内角和的公式是：

$$\text{内角和} = (n - 2) \times 180^\circ$$

1. 介绍

你好，我是悦创。

Python 中的线性查找（Linear Search）是一种简单的查找算法，用于在列表或数组中查找特定元素。

线性查找的基本思想是从列表的第一个元素开始，逐一比较每个元素，直到找到目标元素或遍历完整个列表为止。

2. 线性查找的基本步骤

1. 从第一个元素开始，将其与目标值进行比较。
2. 如果找到目标值，则返回该元素所在的索引。
3. 如果没有找到目标值，继续比较列表中的下一个元素。
4. 如果遍历完整个列表仍然没有找到目标值，表示目标值不存在于列表中。（一般返回 -1）。

Question 1

Let $y_i \mid \theta \sim^{iid} \text{Uniform} (-\theta, \theta)$, for $i = 1, \dots, n$. Assume the prior distribution for $\theta$ to be $\text{Pareto}(a, b)$, where

1. 排序简介

排序通常指把毫无规律的数据，按照一种特定的规律，整理成有序排列的状态。一般情况下，排序算法按照关键字的大小，以从小到大或从大到小的顺序将数据排列。

排序算法是最基础也最重要的算法之一，在处理大量数据时，使用一个优秀的排序算法可以节省大量时间和空间。因为不同的排序算法拥有不同的特点，所以我们根据情况选择合适的排序算法。

直观地讲，插入排序算法把给定数组中的元素依次插入到一个新的数组中，最终得到一个完整的有序数组。

插入排序（insertion sort）是一种简单的排序算法，它的工作原理与手动整理一副牌的过程非常相似。

1. 前置知识

• 随机库：random

  • random.randint(a, b)

    import random
    
    r = random.randint(1,2) # 左闭右闭
    print(r)

• 内置函数：

  • len() ✅
  • range() ✅

• 语法：

  • for ✅
  • function
  • 比较运算符 ✅
  • 多个变量同时赋予不同值 ｜ 引入多一个变量