Learning PyTorch from Scratch: A Beginner's Guide from Tensors to Neural Networks
This article introduces the core content and basic applications of PyTorch. Renowned for its flexibility, intuitiveness, and Python-like syntax, PyTorch is suitable for deep learning beginners and supports GPU acceleration and automatic differentiation. The core content includes: 1. **Tensor**: The basic data structure, similar to a multi-dimensional array. It supports creation from data, all-zero/all-one, random numbers, conversion with NumPy, shape operations, arithmetic operations (element-wise/matrix), and device conversion (CPU/GPU). 2. **Automatic Differentiation**: Implemented through `autograd`. Tensors with `requires_grad=True` will track their computation history, and calling `backward()` automatically computes gradients. For example, for the function \( y = x^2 + 3x - 5 \), the gradient at \( x = 2 \) is 7.0. 3. **Neural Network Construction**: Based on the `torch.nn` module, it includes linear layers (`nn.Linear`), activation functions, loss functions (e.g., MSE), and optimizers (e.g., SGD). It supports custom model classes and composition with `nn.Sequential`. 4. **Practical Linear Regression**: Generates simulated data \( y = 2x + 3 + \text{noise} \), defines a linear model, MSE loss,
Read MoreFarewell to Dependency Chaos: Installation and Usage of Python Virtual Environment virtualenv
In Python development, version conflicts of dependencies across different projects (e.g., Project A requires Django 1.11 while Project B requires 2.2) often lead to "dependency chaos." Installing packages globally may overwrite library files, causing runtime errors. Virtual environments solve this by creating isolated Python environments for each project, each with its own interpreter and dependencies that do not interfere with others. Virtualenv is a commonly used lightweight open-source tool. Before installation, ensure Python and pip are already installed. Execute `pip install virtualenv` to install it. To create a virtual environment, navigate to the project directory and run `virtualenv venv` (where `venv` is the environment name and can be customized). This generates a `venv` folder containing the isolated environment. Activation of the virtual environment varies by operating system: - On Windows CMD: Use `venv\Scripts\activate.bat` - For PowerShell, set the execution policy first before running the activation script - On Mac/Linux: Execute `source venv/bin/activate` After activation, the command line prompt will show `(venv)`, indicating the virtual environment is active. Dependencies installed via `pip` in this state are isolated to the environment and can be verified with `pip list`. To export dependencies, use `pip freeze > requirements.txt`, allowing others to quickly install the same environment via `pip install -r requirements.txt`. To exit the environment, use `deactivate`. Deletion of the virtual environment folder directly removes the entire environment.
Read MoreFrontend and Backend Collaboration: Flask Template Rendering HTML Dynamic Data Example
This article introduces the basic method of implementing front - end and back - end data linkage rendering using the Flask framework. First, you need to install Flask and create a project structure (including app.py and templates folder). The back - end defines routes through @app.route, the view function prepares data (such as a user information dictionary), and passes the data to the front - end template using render_template. The front - end template uses Jinja2 syntax (variable output {{ }}, conditional judgment {% if %}, loop rendering {% for %}) to display the data. After running app.py and accessing localhost:5000, you can see the dynamically rendered user information. The core steps are: back - end data preparation and route rendering, and front - end template syntax parsing. After mastering this process, you can expand more data transfer and template reuse (such as multi - conditional judgment, list rendering), which is the basis for front - end and back - end collaboration in web development.
Read MoreData Storage Fundamentals: How Python Web Saves User Information with SQLite
This article introduces the basic method of implementing web data storage using SQLite and Flask. SQLite is lightweight and easy to use, built into Python, and requires no additional server, making it suitable for beginners. First, the Flask environment needs to be installed. The core steps include creating a user table (with auto-incrementing id, unique username, password, and email fields), implementing registration (parameterized data insertion) and user list display (querying and returning dictionary results) through Python operations. During operations, attention should be paid to password encryption (to prevent plaintext storage), SQL injection prevention, and proper connection closure. The article demonstrates the data persistence process with sample code, emphasizing that SQLite is suitable for small projects and serves as an entry-level tool for learning data storage, with potential for future expansion of functions such as login authentication and ORM.
Read MoreBeginners' Guide: Variables and Loop Syntax in Django Template Engine Jinja2
This article introduces the core syntax of variables and loops in the Django template engine Jinja2. The template engine combines backend data with HTML templates to generate web pages. As Django's default engine, Jinja2 is the focus here, with emphasis on variables and loops. Variable syntax: Variables are enclosed in double curly braces {{}}. They support strings, numbers, booleans, and lists (displayed directly). Dictionaries can be accessed using dot notation (.) or square brackets ([]), such as {{ user.name }} or {{ user["address"]["city"] }}. Note that undefined variables will cause errors, and variables in templates are not modifiable. Loop syntax: Use {% for variable in list %} to iterate. It is accompanied by forloop.counter (for counting), first/last (for marking the first and last elements), and {% empty %} to handle empty lists. Examples include looping through lists or lists of dictionaries (e.g., each dictionary in a user list). Summary: Mastering variables and loops enables quick data rendering. Subsequent articles will cover advanced topics such as conditions and filters.
Read More3 Minutes to Understand: Defining and Using Routes in Python Web Development
This article introduces the concept of "routing" in web development and its application under the Flask framework. Routing is analogous to a restaurant waiter, responsible for receiving user requests (such as accessing a URL) and matching the corresponding processing logic (such as returning a web page), serving as the core that connects user requests with backend logic. The article focuses on the key usages of routing in Flask: 1. **Basic Routing**: Defined using `@app.route('/path')`, corresponding to a view function returning a response, such as the homepage at the root path `/`. 2. **Dynamic Parameters**: Receive user input via `<parameter_name>` or `<type:parameter_name>` (e.g., `int:post_id`), with automatic type conversion. 3. **HTTP Methods**: Specify allowed request methods using `methods=['GET','POST']`, combined with the `request` object to determine the request type. 4. **Reverse Lookup**: Dynamically generate routing URLs using `url_for('function_name', parameters)` to avoid hardcoding. The core is to achieve request distribution, parameter processing, and page interaction through routing. Mastering these basics can support page jumps and data interaction in web applications.
Read MoreIntroduction to User Authentication: Implementing Simple Login and Permission Control with Flask Session
This article introduces implementing user authentication and permission control for web applications using the Flask framework and Session mechanism, suitable for beginners. It first clarifies the concepts of user authentication (verifying identity) and permission control (judging access rights), emphasizing that Session is used to store user status, and Flask's `session` object supports direct manipulation. For environment preparation, install Flask, create an application, and configure `secret_key` to encrypt sessions. To implement the login function: collect username and password through a form, verify them (simulating a user database), set `session['username']`, and redirect to the personal center upon successful login. For permission control, use the `@login_required` decorator to check the Session and protect pages requiring login (e.g., the personal center). Logout clears the user status by `session.pop('username')`. Core content includes: Session basics, login verification, permission decorators, and logout functionality. The article summarizes the learned knowledge points and expands on directions such as database connection, password encryption, and multi-role permissions. Flask Session provides a simple and secure solution that can be gradually used to build complex applications.
Read MorePython Web Static Resource Management: Correctly Including CSS and JS Files in Flask
This article introduces methods to incorporate static resources like CSS and JS in Flask. Static resources, including CSS (styling), JS (interactivity), and images, should be placed in the `static` folder at the project root directory (automatically mapped to the `/static/` path by Flask). Template files are stored in the `templates` folder. The project structure should include `static` and `templates`. Static resources can be organized into subfolders by type (e.g., `css/`, `js/`). Within templates, use `url_for('static', filename='path')` to reference resources, for example: ```html <link rel="stylesheet" href="{{ url_for('static', filename='css/style.css') }}"> <script src="{{ url_for('static', filename='js/script.js') }}"></script> ``` Common issues: Path errors (such as incorrect filenames or missing subfolders) may result in 404 errors. Ensure the `static` folder exists and filenames are correct. Key points: Place static resources in `static`, use `url_for` for incorporation, and maintain a standardized structure to avoid issues.
Read MoreDjango ORM Practical Guide: CRUD Operations with SQLite Database
This article introduces the operation methods of Django framework combined with SQLite database, focusing on the use of ORM tools. Django ORM allows database operations through Python code, avoiding the need to write complex SQL statements. SQLite is lightweight and easy to use, making it suitable for development and learning. Preparatory work includes: creating a new Django project (`startproject`/`startapp`), configuring SQLite by default in `settings.py`, defining models (such as a `User` class), and executing `makemigrations` and `migrate` to generate database tables. The core is the CRUD operations of Django ORM: **Creation** can be done via `create()` or instantiation followed by `save()`; **Reading** uses `all()`, `filter()`, `get()` (supporting conditions and sorting); **Updating** uses `update()` for batch operations or querying first then modifying; **Deletion** uses `delete()` for batch operations or querying first then deleting. It is important to note the lazy execution of QuerySet, using `unique=True` to prevent duplicates, and exception handling for `get()`. Summary: By defining models, migrating table structures, and calling ORM methods, database operations can be completed. The code is concise and easy to maintain, making it suitable for quickly getting started with web development.
Read MoreFlask Form Handling: Complete Process from User Input to Data Display
This article introduces the complete process of implementing form handling using Flask and Flask-WTF, suitable for web development scenarios requiring user information collection. First, install the Flask and Flask-WTF extensions, then create form classes by inheriting the `FlaskForm` class, defining fields (e.g., username, password) and validation rules (required, length, email format, etc.). In Flask applications, view functions must handle GET (rendering the form) and POST (validating submitted data) requests. Use `form.validate_on_submit()` to check the request type and validate data. If validation fails, error messages are stored in `form.<field>.errors`, and templates display errors through loops. Templates must include `form.hidden_tag()` to enable CSRF protection and avoid form submission failures. Key details include: setting `SECRET_KEY` to ensure CSRF security, using redirects to prevent duplicate submissions, and encrypting stored data (e.g., passwords with bcrypt). The complete workflow is: user fills out form → frontend validation → backend validation → data processing → result display. Advanced features can extend to custom validators, multi-form handling, or file uploads. This article helps quickly master core skills of Flask form implementation from definition to data processing.
Read MoreRESTful API Getting Started: Developing a Simple GET Data Interface with Flask
This article introduces the concept of RESTful APIs and implementing a GET interface with Flask. RESTful APIs are HTTP-based front-end and back-end interaction architectures centered on resources, manipulating resources through GET/POST/PUT/DELETE operations, stateless, and returning JSON data. Flask is chosen for its lightweight and flexibility, making it suitable for beginner development. Flask can be installed via `pip install flask` (virtual environment is optional). Implementation involves two steps: first, define the root path `/` to return "Hello, Flask!", with the core code being the `@app.route('/')` decorator and the `return` statement with a string; second, implement the `/users` interface to return user list JSON data, requiring the import of `jsonify` and returning the converted list. After starting the application, access `http://localhost:5000/users` through a browser, curl, or Postman for testing. Core steps include: importing Flask, initializing the application, defining route functions, returning data, and starting the service. Future extensions can include more routes or database integration.
Read MoreJinja2 Template Engine: Dynamically Rendering Data in Web Pages with Flask (with Examples)
This article introduces the role of template engines in web development and the application of Jinja2 in Flask. Template engines solve the cumbersome problem of splicing backend data with frontend HTML, allowing developers to focus on separating data logic from page structure. Jinja2 is Flask's default template engine, with a concise syntax that supports variable substitution, conditional judgment, loops, filters, and other features. The basic process of using Jinja2 involves: first installing Flask, creating an application and defining routes, preparing backend data (such as user information and article lists), and rendering the template through render_template. Template files should be placed in the 'templates' folder, where data is embedded using {{ variables }}, conditional logic and loops are implemented with {% if %} and {% for %}, and filters are applied using the | operator to process data. Template inheritance, through base.html and child templates, promotes code reusability by reusing page structures. The core syntax of Jinja2 includes variable substitution, conditional judgment, loop traversal, and filters, while template inheritance further optimizes project structure. Mastering Jinja2 enables efficient implementation of dynamic page rendering and is a key tool for connecting data and interfaces in web development.
Read MoreEssential Python Web Tools: Installation and Dependency Management of Virtual Environment venv
Why are virtual environments needed? They resolve dependency conflicts between different projects (e.g., compatibility issues between Django 2.2 and 4.0), prevent pollution of the system Python environment, and facilitate shared dependencies in team collaboration. Python 3.3+ includes the built-in `venv` module, which is a lightweight tool for creating virtual environments without requiring additional installations. Steps to use: 1. **Create**: Navigate to the project directory and run `python -m venv venv` to generate an independent `venv` folder. 2. **Activate**: Commands vary by system: Use the appropriate path for activation in Windows (cmd/PowerShell) or Mac/Linux. A successful activation will show `(venv)` in the terminal. 3. **Verify**: Run `python --version` and `pip --version` to confirm the environment is active. 4. **Dependency Management**: Install packages with `pip install` while activated. After installation, export dependencies with `pip freeze > requirements.txt`. For a new environment or another project, install dependencies quickly using `pip install -r requirements.txt`. 5. **Deactivate and Delete**: Exit with `deactivate`, and delete the `venv` folder directly to remove the environment. `venv` effectively isolates project dependencies, ensuring safety and efficiency, making it an essential tool for Python development.
Read MoreHTTP Requests and Responses: Fundamental Core Concepts in Python Web Development
In Python web development, HTTP is the core for communication between the client (e.g., a browser) and the server, based on the "request-response" mechanism. The client generates an HTTP request, which includes methods (GET/POST, etc.), URLs, header information (e.g., User-Agent, Cookie), and a request body (POST data). After processing, the server returns an HTTP response, which contains a status code (e.g., 200 for success, 404 for not found), response headers (e.g., Content-Type), and a response body (web pages/data). The process is: client sends a request → server parses and processes it → returns a response → client renders the response (e.g., HTML to render a web page). Python frameworks (e.g., Flask) simplify this process. In the example, Flask uses `request` to access the request and `return` to directly send back the response content. Understanding this mechanism is fundamental to web development and lays the foundation for advanced studies such as HTTPS and Cookies.
Read MoreDjango from Scratch: Build a Simple Blog System with ORM and Template Engine in 3 Steps
This article introduces how to quickly build a blog system displaying article lists using Django, with a core understanding of ORM operations for data and template rendering for pages. Step 1: Environment preparation and project initialization. After installing Django, create the project `myblog` and the app `blog`. The project structure includes configuration directories, app directories, and command-line tools. Step 2: Define data models using ORM. Write a `Post` class (with fields: title, content, publication time) in `blog/models.py`, which is automatically mapped to a database table. Activate the model (configure `settings.py`) and execute migrations to generate the table. Step 3: Views and template rendering. Write a view function in `views.py` to retrieve article data and configure routing to distribute requests. Render the article list in the template `index.html` using Django template syntax, supporting loops and variable output. Running `python manage.py runserver` allows access to the blog. The core is to master Django's ORM model definition, view processing, and template rendering processes, with potential for subsequent feature expansion.
Read MoreStep-by-Step Guide: Flask Routes and View Functions, Build Your First Web Page in 10 Minutes
Flask is a lightweight Python Web framework, simple and flexible, suitable for beginners, and supports extensibility as needed. Installation requires Python 3.6+, and can be done via `pip install flask`. To verify, use `flask --version`. The core of a basic application: Import the Flask class and instantiate an `app` object; define the root route with `@app.route('/')`, binding to the view function `home()`, which returns content (e.g., "Hello, Flask!"); `app.run()` starts the development server (default port 5000). For advanced support, dynamic routing is available, such as `/user/<username>`, where the view function receives parameters to implement personalized responses, supporting types like `int` and `float`. Core concepts: Routes bind URLs to functions, view functions handle requests and return content, and `app.run()` starts the service. Key techniques: `if __name__ == '__main__'` ensures the service starts when the script is run directly, and dynamic routing enhances page flexibility.
Read MoreFrom Insertion Sort to Quick Sort: A Beginner's Comparison of Sorting Algorithms
Sorting algorithms are methods to convert unordered data into ordered sequences. They are fundamental core algorithms in computer science, enabling optimization of subsequent operations such as searching and statistics. This article introduces four typical sorting algorithms: Insertion sort is similar to sorting playing cards, gradually building an ordered sequence. It has a time complexity of O(n²), space complexity of O(1), is stable, and is suitable for small-scale or nearly ordered data. Bubble sort involves comparing and swapping adjacent elements, allowing larger elements to "bubble up". It also has O(n²) time complexity, is stable but inefficient, and is only suitable for extremely small-scale data or educational purposes. Merge sort is based on the divide-and-conquer principle, decomposing arrays and merging ordered subarrays. It has O(n log n) time complexity, O(n) space complexity, is stable, and is suitable for large-scale data or scenarios requiring high stability. Quick sort combines divide-and-conquer with pivot partitioning. It has an average time complexity of O(n log n), O(log n) space complexity, is unstable, and is the most commonly used efficient algorithm in engineering, suitable for large-scale data. The article compares and summarizes the time complexity, space complexity, stability, and applicable scenarios of these algorithms. It suggests that beginners first understand the core ideas, learn from simple to complex cases gradually, and deepen their understanding through hands-on simulation.
Read More"Two-Dimensional" View of Sorting Algorithms: An Introduction to Time and Space Complexity
The two-dimensional complexity (time and space) of sorting algorithms is a core criterion for algorithm selection. In terms of time complexity, for small datasets (n ≤ 1000), simple quadratic-time algorithms like bubble sort, selection sort, and insertion sort (O(n²)) are suitable, while for large datasets (n > 10000), efficient linearithmic algorithms such as quicksort, mergesort, and heapsort (O(n log n)) are preferred. Regarding space complexity, heapsort and bubble sort are in-place with O(1) space, quicksort requires O(log n) auxiliary space, and mergesort needs O(n) space. A balance between time and space is essential: mergesort trades O(n) space for stable O(n log n) time, while quicksort uses O(log n) space to optimize efficiency. Beginners should first master simple algorithms before advancing to high-performance ones, selecting based on data size and space constraints to achieve "on-demand sorting."
Read MoreWhy is Bubble Sort Considered a "Beginner-Friendly" Sorting Algorithm?
Bubble Sort is known as a "beginner-friendly" sorting algorithm due to its intuitive logic, simple code, and clear examples, which help beginners quickly grasp the core idea of sorting. **Definition**: It repeatedly compares adjacent elements and gradually "bubbles" larger elements to the end of the array, ultimately achieving order. The core is a "compare-swap" loop: the outer loop controls the number of rounds (at most n-1 rounds), and the inner loop traverses adjacent elements, comparing and swapping them. If no swaps occur in a round, the process terminates early. **Reasons for being beginner-friendly**: 1. **Intuitive Logic**: Similar to "adjusting a queue," it intuitively understands pairwise swaps and gradual ordering. 2. **Simple Code**: Implemented with nested loops, with a clear structure (outer loop for rounds, inner loop for comparison/swaps, optimized with early termination). 3. **Clear Examples**: The sorting process of [5, 3, 8, 4, 2] (where the largest number "bubbles up" to the end in each round) is easy to follow with step-by-step understanding. 4. **Understanding the Essence**: Helps grasp core sorting elements such as "order," "swaps," and "termination conditions." Despite its O(n²) time complexity and low efficiency, as a sorting启蒙 tool, it allows beginners to "first learn to walk" and lays the foundation for subsequent algorithms like Quick Sort. (Note: "启蒙" was translated as "enlightenment" here to maintain the technical educational context; "启蒙 tool" effectively conveys the purpose of foundational learning.) **Corrected translation (more precise term for 启蒙)**: Despite its O(n²) time complexity and low efficiency, as a **foundational sorting tool**, it enables beginners to "first learn to walk" and lays the groundwork for subsequent algorithms like Quick Sort. **Final translation**: Bubble Sort is known as a "beginner-friendly" sorting algorithm due to its intuitive logic, simple code, and clear examples, which help beginners quickly grasp the core idea of sorting. **Definition**: It repeatedly compares adjacent elements and gradually "bubbles" larger elements to the end of the array, ultimately achieving order. The core is a "compare-swap" loop: the outer loop controls the number of rounds (at most n-1 rounds), and the inner loop traverses adjacent elements, comparing and swapping them. If no swaps occur in a round, the process terminates early. **Reasons for being beginner-friendly**: 1. **Intuitive Logic**: Similar to "adjusting a queue," it intuitively understands pairwise swaps and gradual ordering. 2. **Simple Code**: Implemented with nested loops, with a clear structure (outer loop for rounds, inner loop for comparison/swaps, optimized with early termination). 3. **Clear Examples**: The sorting process of [5, 3, 8, 4, 2] (where the largest number "bubbles up" to the end in each round) is easy to follow with step-by-step understanding. 4. **Understanding the Essence**: Helps grasp core sorting elements such as "order," "swaps," and "termination conditions." Despite its O(n²) time complexity and low efficiency, as a **foundational sorting tool**, it enables beginners to "first learn to walk" and lays the groundwork for subsequent algorithms like Quick Sort.
Read More"Memory Consumption of Sorting Algorithms: An Introduction to Space Complexity"
The space complexity (memory consumption) of sorting algorithms is a critical consideration, especially in scenarios with limited memory. Space complexity describes the relationship between the additional storage space used by the algorithm during execution and the data size \( n \), denoted as \( O(1) \), \( O(n) \), or \( O(\log n) \). Key space characteristics of major sorting algorithms: - **In-place sorting** (Bubble Sort, Selection Sort, Insertion Sort, Heap Sort): Require no additional arrays, with space complexity \( O(1) \); - **Merge Sort**: Requires temporary arrays during the merge step of divide-and-conquer, with space complexity \( O(n) \); - **Quick Sort**: Uses recursive partitioning, with average space complexity \( O(\log n) \). Selection strategy: Prioritize \( O(1) \) algorithms when memory is limited; choose Merge Sort for stable sorting with sufficient memory; pursue average performance (e.g., standard library sorting) with Quick Sort. Understanding space characteristics enables balancing time and space to write efficient code.
Read MoreInspiration from Poker Sorting: A Life Analogy and Implementation of Insertion Sort
This article introduces the insertion sort algorithm. Its core idea is to gradually build an ordered sequence: the first element is defaulted as sorted, and starting from the second element, each element (the element to be inserted) is inserted into the correct position in the previously sorted sequence (where larger elements need to be moved to make space). Taking the array `[5, 3, 8, 4, 2]` as an example, the process of comparing and moving elements from back to front is demonstrated. The key steps are: traversing the array, temporarily storing the element to be inserted, moving the sorted elements, and inserting at the correct position. Algorithm characteristics: Advantages include simplicity and intuitiveness, in-place sorting (space complexity O(1)), stability, and suitability for small-scale or nearly ordered data; disadvantages include the worst-case time complexity of O(n²) and a relatively large number of move operations. In summary, insertion sort is a foundation for understanding sorting algorithms. It is explained through a life analogy (e.g., sorting playing cards) to aid comprehension and is applicable to simple scenarios or sorting small-scale data.
Read MoreBubble, Selection, Insertion Sort: Who is the Entry-Level 'Sorting King'?
This article introduces the significance of sorting and three basic sorting algorithms. Sorting is a fundamental operation that rearranges data according to rules to achieve a more ordered state, and it is a prerequisite for understanding complex algorithms. The core ideas and characteristics of the three algorithms are as follows: Bubble Sort repeatedly "bubbles" the largest number to the end through multiple passes, with an intuitive logic but frequent swaps, having a time complexity of O(n²). Selection Sort selects the smallest number in each round and inserts it, with fewer swaps but instability, also with O(n²) complexity. Insertion Sort is similar to arranging playing cards, suitable for small-scale or nearly ordered data, and its complexity is close to O(n). Although these three algorithms are simple, they form the foundation of more complex sorts (such as Heap Sort and Merge Sort). For beginners, it is more important to grasp the core ideas of "selecting the smallest, inserting appropriately, and bubbling the largest," and to understand the thinking of "gradually building an ordered sequence," rather than getting caught up in efficiency. This is the key to understanding the essence of sorting.
Read MoreHow Sorting Algorithms Implement Ascending/Descending Order? A Guide for Data "Obedience"
This article introduces methods for sorting algorithms to implement data in ascending/descending order, with the core being to make data "obey" through algorithmic rules. The significance of sorting: arranging messy data in ascending order (from small to large) or descending order (from large to small), such as organizing playing cards. Three basic algorithm implementation rules: 1. **Bubble Sort**: When ascending, large numbers "bubble" and move backward (swap if front > back); when descending, small numbers "sink" and move backward (swap if front < back), like bubbles rising/falling. 2. **Selection Sort**: When ascending, select the smallest number in each round and place it on the left; when descending, select the largest number and place it on the left, similar to selecting class monitors to take their positions in order. 3. **Insertion Sort**: When ascending, insert the new number into the correct position in the already sorted part (from left to right, increasing); similarly for descending (from left to right, decreasing), like inserting playing cards into a sorted sequence. Core logic: Adjust the comparison rule (> or <) to determine the data movement direction. Ascending/descending order essentially involves "making data move according to the rules". It is recommended to first master basic algorithms and manually simulate data movement to understand the logic.
Read MoreThe "Fairness" of Sorting: What is Stability? A Case Study of Insertion Sort
The "stability" of sorting refers to whether the relative order of equal elements remains unchanged after sorting; if it does, the sort is stable. Insertion sort achieves stability through its unique insertion logic. The core of insertion sort is to insert unordered elements one by one into the ordered portion. When inserting equal elements, no swap occurs; instead, the element is directly inserted after the equal elements. For example, in the array [3, 1, 3, 2], when processing the second 3, since it is equal to the 3 at the end of the ordered portion, it is directly inserted after it. The final sorted result is [1, 2, 3, 3], and the relative order of the original two 3s remains unchanged. The key to stability lies in preserving the original order of equal elements. This is crucial in practical scenarios such as grade ranking and order processing, where fair sorting according to the original order is required. Due to its logic of "no swap for equal elements, insert later", insertion sort naturally guarantees stability, ensuring that duplicate elements always remain in their original order and reflecting the "fairness" of the sort.
Read More选择排序：最简单排序之一，最少交换实现方法
选择排序是计算机科学基础排序算法，因逻辑简单且交换次数最少，成为初学者入门首选。其核心思路是将数组分为已排序和未排序两部分，每次在未排序部分中找到最小元素，与未排序部分的首元素交换，逐步扩展已排序部分，最终完成排序。例如对数组[64,25,12,22,11]，通过多轮寻找最小元素并交换（如第一轮交换11至首，第二轮交换12至第二位等），可实现升序排列。 选择排序交换次数最少（最多n-1次），时间复杂度为O(n²)（无论最佳、最坏或平均情况），空间复杂度仅O(1)。其优点是算法简单、交换成本低、空间需求小；缺点是时间效率低、不稳定排序（相等元素相对顺序可能改变），适用于小规模数据排序或对交换次数敏感的场景（如嵌入式系统）。掌握选择排序有助于理解排序核心思想，为学习更复杂算法奠定基础。
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