1. add-comments.md英文

You are tasked with adding comments to a piece of code to make it more understandable for AI systems or human developers. The code will be provided to you, and you should analyze it and add appropriate comments.

To add comments to this code, follow these steps:

1. Analyze the code to understand its structure and functionality.
2. Identify key components, functions, loops, conditionals, and any complex logic.
3. Add comments that explain:

• The purpose of functions or code blocks
• How complex algorithms or logic work
• Any assumptions or limitations in the code
• The meaning of important variables or data structures
• Any potential edge cases or error handling

When adding comments, follow these guidelines:

• Use clear and concise language
• Avoid stating the obvious (e.g., don’t just restate what the code does)
• Focus on the “why” and “how” rather than just the “what”
• Use single-line comments for brief explanations
• Use multi-line comments for longer explanations or function/class descriptions

Your output should be the original code with your added comments. Make sure to preserve the original code’s formatting and structure.

Remember, the goal is to make the code more understandable without changing its functionality. Your comments should provide insight into the code’s purpose, logic, and any important considerations for future developers or AI systems working with this code.

2. add-comments.md中文

您需要为一段代码添加注释，使其对AI系统或开发人员更易理解。您将获得代码，请分析并添加适当的注释。

添加注释时请遵循以下步骤：

1. 分析代码以理解其结构和功能
2. 识别关键组件、函数、循环、条件语句和复杂逻辑
3. 添加注释解释以下内容：

• 函数或代码块的作用
• 复杂算法或逻辑的运行方式
• 代码中的假设或限制
• 重要变量或数据结构的含义
• 潜在的边界情况或错误处理

添加注释时需遵守以下准则：

• 使用简洁清晰的语言
• 避免陈述显而易见的内容（例如不要简单复述代码行为）
• 关注"为什么"和"如何"而非仅"是什么"
• 简短解释使用单行注释
• 较长解释或函数/类描述使用多行注释

输出应为添加注释后的原始代码，保留原有格式和结构。

注意：目标是通过注释提升代码可读性但不改变其功能。注释应阐明代码目的、逻辑以及未来开发者或AI系统需要注意的重要事项。