Submit your work as a single Jupyter Notebook file. Please use the following naming convention: StudentName_HW#.ipynb (e.g., 王小明_HW1.ipynb).

• Explanations: Use Markdown cells for all text and prose.
• Mathematics: Use LaTeX for mathematical expressions and formulas.

The notebook must be fully reproducible. Before submission, please “Restart & Run All” to ensure the entire notebook executes from start to finish without errors.

If a specific code block requires significant computation time (> 1 minute), please implement a caching mechanism. The script should check for a local data file; if the file exists, the notebook should load the results rather than re-running the lengthy evaluation.