Implementing the Merge Sort Algorithm in Java

Merge sort is an efficient sorting algorithm based on the divide-and-conquer paradigm, with three core steps: divide, conquer, and merge. It recursively splits the array into single-element subarrays, sorts these subarrays, and finally merges two ordered subarrays into a fully ordered array. In Java implementation, the `mergeSort` method recursively divides the array into left and right halves, sorts each half, and then calls the `merge` method to combine them. The `merge` method uses three pointers to traverse the left and right subarrays, compares elements, and fills the result array, while directly copying remaining elements. Algorithm complexity: Time complexity is O(n log n) (each merge operation takes O(n) time, with log n recursive levels), space complexity is O(n) (requires extra space for storing merged results), and it is a stable sort (relative order of equal elements is preserved). Merge sort has a clear logic and is suitable for large-scale data sorting. It serves as a classic example of divide-and-conquer algorithms, efficiently sorting by recursively splitting and merging ordered subarrays.

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Implementing Heap Sort Algorithm in Java

Heap sort is an efficient sorting algorithm based on the heap data structure, with a time complexity of O(n log n) and a space complexity of O(1). It is an in-place sorting algorithm suitable for large-scale data. A heap is a special complete binary tree, divided into a max-heap (parent node value is greater than child node values) and a min-heap. Heap sort uses a max-heap. The core idea is: each time, take the maximum value at the top of the heap and place it at the end of the array, then adjust the remaining elements to form a new max-heap, and repeat until the array is sorted. The implementation consists of three steps: constructing a max-heap (starting from the last non-leaf node and using heapify to adjust each node); heap adjustment (recursively adjusting the subtree to maintain the max-heap property); and the sorting process (swapping the top of the heap with the end element, reducing the heap size, and repeating the adjustment). The core function heapify adjusts the subtree to a max-heap by comparing parent and child nodes recursively; buildMaxHeap constructs a complete max-heap starting from the second-to-last node; the main function integrates the above steps to complete the sorting. Heap sort achieves ordering through efficient heap adjustment, is suitable for scenarios with space constraints, and is an efficient choice for sorting large-scale data.

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Implementing the Selection Sort Algorithm in Java

Selection sort is a simple and intuitive sorting algorithm. Its core idea is to repeatedly select the smallest (or largest) element from the unsorted portion and place it at the end of the sorted portion until the entire array is sorted. The basic approach involves an outer loop to determine the end position of the sorted portion, and an inner loop to find the minimum value in the unsorted portion, followed by swapping this minimum value with the element at the current position of the outer loop. In Java implementation, the `selectionSort` method is implemented with two nested loops: the outer loop iterates through the array (with `i` ranging from 0 to `n-2`), and the inner loop (with `j` ranging from `i+1` to `n-1`) finds the index `minIndex` of the minimum value in the unsorted portion. Finally, the element at position `i` is swapped with the element at `minIndex`. Taking the array `{64, 25, 12, 22, 11}` as an example, the sorted array `[11, 12, 22, 25, 64]` is gradually constructed through each round of swaps. The time complexity is O(n²), making it suitable for small-scale data. This algorithm has a simple logic and easy-to-implement code, serving as a typical example for understanding the basic sorting concepts.

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Implementing Shell Sort Algorithm with Java

Shell Sort is an improved version of Insertion Sort that reduces the number of element movements during inversions by grouping elements. The core idea is to introduce a step size (Gap), which divides the array into Gap subsequences. After performing insertion sort on each subsequence, the Gap is gradually reduced to 1 (equivalent to standard Insertion Sort). Algorithm steps: Initialize Gap as half the array length. Perform insertion sort on each subsequence, then reduce the Gap and repeat until Gap becomes 0. In Java implementation, the outer loop controls the Gap to decrease from n/2. The inner loop iterates through elements, using a temporary variable to store the current element, then compares and shifts elements forward to their correct positions to complete insertion. Testing with the array {12, 34, 54, 2, 3} results in the sorted output [2, 3, 12, 34, 54]. By gradually ordering elements through grouping, Shell Sort improves efficiency, and optimizing the step size sequence (e.g., 3k+1) can further enhance performance.

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Implementing the Insertion Sort Algorithm in Java

Insertion sort is a simple and intuitive sorting algorithm. Its core idea is to insert unsorted elements one by one into their correct positions in the sorted part, similar to organizing playing cards. It is suitable for small-scale data and has a simple implementation. Basic idea: Starting from the second element, mark the current element as the "element to be inserted". Compare it with the elements in the sorted part from back to front. If the sorted element is larger, shift it backward until the insertion position is found. Repeat this process until all elements are processed. In Java implementation, the element to be inserted needs to be saved, and the insertion is completed by looping through comparisons and shifting elements backward. The time complexity of the algorithm is: best O(n) (when already sorted), worst and average O(n²); space complexity O(1) (in-place sorting); stable sort, suitable for small-scale data or nearly sorted data. Its core lies in "gradual insertion", with simple implementation. Its stability and in-place nature make it perform well in small-scale sorting.

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Implementing QuickSort Algorithm in Java

QuickSort is based on the divide-and-conquer approach. Its core involves selecting a pivot element to partition the array into elements less than and greater than the pivot, followed by recursively sorting the subarrays. With an average time complexity of O(n log n), it is a commonly used and efficient sorting algorithm. **Basic Steps**: 1. Select a pivot (e.g., the rightmost element). 2. Partition the array based on the pivot. 3. Recursively sort the left and right subarrays. **Partition Logic**: Using the rightmost element as the pivot, define an index `i` to point to the end of the "less than pivot" region. Traverse the array, swapping elements smaller than the pivot into this region. Finally, move the pivot to its correct position. The Java code implements this logic. The time complexity is O(n log n) on average and O(n²) in the worst case, with an average space complexity of O(log n). A notable drawback is that QuickSort is an unstable sort, and its worst-case performance can be poor, so optimizing the pivot selection is crucial to improve performance.

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Implementing the Bubble Sort Algorithm in Java

Bubble Sort is a basic sorting algorithm whose core idea is to repeatedly compare adjacent elements and swap their positions, allowing larger elements to "bubble up" to the end of the array (in ascending order). Its sorting process is completed through multiple iterations: each iteration determines the position of the largest element in the current unsorted portion and moves it to the end until the array is sorted. In Java implementation, the outer loop controls the number of sorting rounds (at most n-1 rounds), while the inner loop compares adjacent elements and performs swaps. A key optimization is using a `swapped` flag; if no swaps occur in a round, the algorithm terminates early, reducing the best-case time complexity to O(n). The worst and average-case time complexities are O(n²), with a space complexity of O(1) (in-place sorting). Despite its simple and intuitive principle, which makes it suitable for teaching the core concepts of sorting, bubble sort is inefficient and only applicable for small-scale data or educational scenarios. For large-scale data sorting, more efficient algorithms like Quick Sort are typically used.

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Introduction to PyTorch Neural Networks: Fully Connected Layers and Backpropagation Principles

This paper introduces the basics of PyTorch neural networks, with a core focus on fully connected layers and backpropagation. A fully connected layer enables full connectivity between neurons of the previous layer and the current layer, producing an output calculated as the product of a weight matrix and the input, plus a bias vector. Forward propagation is the forward computation process of data from the input layer through fully connected layers and activation functions to the output layer, for example, in a two - layer network: input → fully connected → ReLU → fully connected → output. Backpropagation is the core of neural network learning, adjusting parameters through gradient descent. Based on the chain rule, it reversely calculates the gradient of the loss with respect to each parameter starting from the output layer. PyTorch's autograd automatically records the computation graph and completes gradient calculation. The process includes forward propagation, loss calculation, backpropagation (loss.backward()), and parameter update (using an optimizer like SGD). Key concepts: Fully connected layers implement feature combination, forward propagation performs forward computation, backpropagation minimizes loss through gradient descent, and automatic differentiation simplifies gradient calculation. Understanding these principles is conducive to model debugging and optimization.

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Quick Start with PyTorch: Tensor Dimension Transformation and Common Operations

This article introduces the core knowledge of PyTorch tensors, including basics, dimension transformations, common operations, and exercise suggestions. Tensors are the basic structure for storing data in PyTorch, similar to NumPy arrays, and support GPU acceleration and automatic differentiation. They can be created using `torch.tensor()` from lists/numbers, `torch.from_numpy()` from NumPy arrays, or built-in functions to generate tensors of all zeros, ones, or random values. Dimension transformation is a key operation: `reshape()` flexibly adjusts the shape (keeping the total number of elements unchanged), `squeeze()` removes singleton dimensions, `unsqueeze()` adds singleton dimensions, and `transpose()`/`permute()` swap dimensions. Common operations include basic arithmetic operations, matrix multiplication with `matmul()`, broadcasting (automatic dimension expansion for operations), and aggregation operations such as `sum()`, `mean()`, and `max()`. The article suggests consolidating tensor operations through exercises, such as dimension adjustment, broadcasting mechanisms, and dimension swapping, to master the "shape language" and lay a foundation for subsequent model construction.

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PyTorch Basics Tutorial: Practical Data Loading with Dataset and DataLoader

Data loading is a crucial step in machine learning training, and PyTorch's `Dataset` and `DataLoader` are core tools for efficient data management. As an abstract base class for data storage, `Dataset` requires inheriting to implement `__getitem__` (to read a single sample) and `__len__` (to get the total number of samples). Alternatively, `TensorDataset` can be directly used to wrap tensor data. `DataLoader`, on the other hand, handles batch processing and supports parameters such as `batch_size` (batch size), `shuffle` (shuffling order), and `num_workers` (multithreaded loading) to optimize training efficiency. In practice, taking MNIST as an example, image data can be loaded via `torchvision`, and combined with `Dataset` and `DataLoader` to achieve efficient iteration. It should be noted that under Windows, `num_workers` is defaulted to 0 to avoid memory issues. During training, `shuffle=True` should be used to shuffle the data, while `shuffle=False` is set for the validation/test sets to ensure reproducibility. Key steps: 1. Define a `Dataset` to store data; 2. Create a `DataLoader` with specified parameters; 3. Iterate over the `DataLoader` to input data into the model for training. These two components are the cornerstones of data processing. Once mastered, they can be flexibly applied to various data loading requirements.

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Playing with PyTorch from Scratch: Data Visualization and Model Evaluation Techniques

This article introduces core skills of data visualization and model evaluation in PyTorch to facilitate efficient model debugging. For data visualization, Matplotlib can observe data distributions (e.g., histograms of MNIST samples and labels), and TensorBoard can monitor training processes (e.g., scalar changes, model structures). In model evaluation, classification tasks should focus on accuracy and confusion matrices (e.g., MNIST classification example), while regression tasks use MSE and MAE. In practice, using visualization to identify issues (e.g., confusion between "8" and "9") enables iterative model optimization. Advanced applications include GAN visualization and real-time metric calculation. Mastering these skills allows quick problem localization and data understanding, laying a foundation for developing complex models.

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PyTorch Beginner's Guide: Understanding Model Construction with Simple Examples

This PyTorch beginner's tutorial covers core knowledge points: PyTorch is Python-based with obvious advantages in dynamic computation graphs and simple installation (`pip install torch`). The core data structure is the Tensor, which supports GPU acceleration, and can be created, manipulated (addition, subtraction, multiplication, division, matrix multiplication), and converted to/from NumPy. Automatic differentiation (autograd) is implemented via `requires_grad=True` for gradient calculation, e.g., the derivative of \( y = x^2 + 3x \) at \( x = 2 \) is 7. A linear regression model inherits `nn.Module` for definition, with forward propagation implementing \( y = wx + b \). For data preparation, simulated data (\( y = 2x + 3 + \text{noise} \)) is generated, and batched loaded using `TensorDataset` and `DataLoader`. Training uses MSE loss and SGD optimizer, with gradient zeroing, backpropagation, and parameter updates in the loop. After 1000 epochs, results are validated and visualized, with learned parameters close to the true values. The core process covers tensor operations, automatic differentiation, model construction, data loading, and training optimization, enabling scalability to complex models.

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Beginner-Friendly: Basics of PyTorch Loss Functions and Training Loops

This article introduces the roles and implementation of loss functions and training loops in machine learning. Loss functions measure the gap between model predictions and true labels, while training loops adjust parameters to minimize loss for model learning. Common loss functions include: Mean Squared Error (MSE) for regression tasks (e.g., housing price prediction), accessible via `nn.MSELoss()` in PyTorch, and Cross-Entropy Loss for classification tasks (e.g., cat-dog recognition), accessible via `nn.CrossEntropyLoss()`. The core four steps of a training loop are: forward propagation (model prediction) → loss calculation → backpropagation (gradient computation) → parameter update (optimizer adjustment). It is critical to zero out gradients before backpropagation. Using linear regression as an example, the article generates simulated data, defines a linear model, trains it with MSE loss and the Adam optimizer, and iteratively optimizes parameters. Key considerations include: gradient zeroing, switching between training/inference modes, optimizer selection (e.g., Adam), and batch training with DataLoader. Mastering these concepts enables models to learn patterns from data, laying the foundation for complex models.

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Introduction to PyTorch Optimizers: Practical Implementation of Optimization Algorithms like SGD and Adam

### Optimizers: The "Navigation System" for Deep Learning Optimizers are core tools in deep learning for updating model parameters and minimizing loss functions, similar to a navigation system when climbing a mountain, guiding the model from "high-loss" peaks to "low-loss" valleys. Their core task is to adjust parameters to improve the model's performance on training data. Different optimizers are designed for distinct scenarios: The basic SGD (Stochastic Gradient Descent) is simple but converges slowly and requires manual hyperparameter tuning; SGD+Momentum incorporates "inertia" to accelerate convergence; Adam combines momentum and adaptive learning rates, performing exceptionally well with default parameters and being the first choice for most tasks; AdamW adds weight decay (L2 regularization) to Adam, effectively preventing overfitting. PyTorch's `torch.optim` module provides various optimizers: SGD is suitable for simple models, SGD+Momentum accelerates models with fluctuations (e.g., RNNs), Adam adapts to most tasks (e.g., CNNs, Transformers), and AdamW is ideal for small datasets or complex models. In practical tasks, comparing linear regression (e.g., `y=2x+3`), Adam converges faster with smoother loss and parameters closer to the true values, while SGD is prone to oscillations. Beginners are advised to prioritize Adam, and if parameter control is required... (Note: The original text cuts off here, so the translation concludes at the available content.)

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Learning PyTorch from Scratch: A Basic Explanation of Activation Functions and Convolutional Layers

### Overview of Activation Functions and Convolutional Layers **Activation Functions**: Neural networks require non-linear transformations to fit complex relationships, and activation functions introduce this non-linearity. Common functions include: - **ReLU**: `y = max(0, x)`, simple computation, solves the vanishing gradient problem, and is the most widely used (PyTorch: `nn.ReLU()`). - **Sigmoid**: `y = 1/(1+exp(-x))`, outputs in (0,1) for binary classification but suffers from vanishing gradients (PyTorch: `nn.Sigmoid()`). - **Tanh**: `y=(exp(x)-exp(-x))/(exp(x)+exp(-x))`, outputs in (-1,1) with a mean of 0, easier to train but still prone to vanishing gradients (PyTorch: `nn.Tanh()`). **Convolutional Layers**: A core component of CNNs, convolutional layers extract local features via convolution kernels. Key concepts include: input (e.g., RGB images with shape `(batch, in_channels, H, W)`), convolution kernel (small matrix), stride (number of pixels the kernel slides), and padding (edge zero-padding to control output size). Implemented in PyTorch via `nn.Conv2d`, critical parameters include `in_channels` (input

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Beginner's Guide to PyTorch: A Practical Tutorial on Data Loading and Preprocessing

Data loading and preprocessing are crucial foundations for training deep learning models, and PyTorch efficiently implements this through tools like `Dataset`, `DataLoader`, and `transforms`. As a data container, `Dataset` defines how samples are retrieved—for example, built-in datasets such as MNIST in `torchvision.datasets` can be used directly, while custom datasets require implementing `__getitem__` and `__len__`. `DataLoader` handles batch loading, with core parameters including `batch_size`, `shuffle` (set to `True` during training), and `num_workers` (for multi-threaded acceleration). Data preprocessing is achieved via `transforms`, such as `ToTensor` for converting to tensors, `Normalize` for normalization, and data augmentation techniques like `RandomCrop` (used only for the training set). `Compose` allows combining multiple transformations. For practical implementation using MNIST as an example, the full workflow involves defining preprocessing steps, loading the dataset, and creating a `DataLoader`. Key considerations include normalization parameters, applying data augmentation only to the training set, and setting `num_workers=0` under Windows to avoid multi-thread errors. Mastering these skills enables efficient data handling and lays the groundwork for model training.

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Mastering PyTorch Basics: A Detailed Explanation of Tensor Operations and Automatic Differentiation

This article introduces the basics of Tensors in PyTorch. Tensors are the fundamental units for storing and manipulating data, similar to NumPy arrays but with GPU acceleration support, making them a core structure of neural networks. Creation methods include converting from lists/NumPy arrays (`torch.tensor()`/`as_tensor()`) and using constructors like `zeros()`/`ones()`/`rand()`. Key attributes include shape (`.shape`/`.size()`), data type (`.dtype`), and device (`.device`), which can be converted via `.to()`. Major operations cover arithmetic (addition, subtraction, multiplication, division, matrix multiplication), indexing/slicing, reshaping (`reshape()`/`squeeze()`/`unsqueeze()`), and concatenation/splitting (`cat()`/`stack()`/`split()`). Autograd is central: `requires_grad=True` enables gradient tracking, `backward()` computes gradients, and `grad` retrieves them. Important considerations include handling gradients of non-leaf nodes, gradient accumulation, and `detach()` for tensor separation. Mastering tensor operations and autograd is foundational for neural network learning.

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Beginner's Guide to PyTorch: Build Your First Neural Network Model Step by Step

This article is an introductory PyTorch tutorial that explains core operations by building a fully connected neural network (MLP) model based on the MNIST dataset. First, install PyTorch (CPU/GPU version), load the MNIST dataset using torchvision, convert it to tensors with ToTensor, normalize with Normalize, and then use DataLoader for batch processing (batch_size=64). The model is defined as an MLP with an input layer of 784 (flattened 28×28 images), a hidden layer of 128 (ReLU activation), and an output layer of 10 (Softmax), implemented by inheriting nn.Module for forward propagation. CrossEntropyLoss is chosen as the loss function, and SGD with lr=0.01 is used as the optimizer. The model is trained for 5 epochs, with forward propagation, loss calculation, backpropagation, and parameter updates executed cyclically, printing the loss every 100 batches. During testing, the model is set to eval mode, gradient computation is disabled, and the accuracy on the test set is calculated. The tutorial also suggests extension directions, such as adjusting the network structure, replacing optimizers, or changing datasets.

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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,

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Farewell 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.

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Frontend 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.

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Data 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.

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Beginners' 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.

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3 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.

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Introduction 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.

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