problem-analysis

# 赛题分析与方法检索 Competition problem: $ARGUMENTS ## Constants - **METHOD_LIBRARY** — Local directory containing reference materials (past solutions, method notes). Check these paths in order: 1. `data/` in the current project directory 2. `reference/` in the current project directory 3. Custom path specified by user in `CLAUDE.md` under `## Method Library` - **MAX_LOCAL_REFS = 10** — Maximum number of local reference files to scan. If more are found, prioritize by filename relevance to the problem. - **SEARCH_DEPTH = standard** — When `deep`, perform extended web search for similar competition problems and classic methods. When `standard` (default), focus on the most relevant methods and past solutions. > 💡 Overrides: > - `/problem-analysis "赛题" — method library: ~/my_refs/` — custom reference path > - `/problem-analysis "赛题" — sources: local` — only search local references > - `/problem-analysis "赛题" — sources: web` — only search the web (skip local) > - `/problem-analysis "赛题" — sources: local, web` — search local + web > - `/problem-analysis "赛题" — search depth: deep` — extended search for similar problems and methods ## Data Sources This skill checks multiple sources **in priority order**. All are optional — if a source is not configured or not available, skip it silently. ### Source Selection Parse `$ARGUMENTS` for a `— sources:` directive: - **If `— sources:` is specified**: Only search the listed sources (comma-separated). Valid values: `local`, `web`, `all`. - **If not specified**: Default to `all` — search every available source in priority order. Examples: ``` /problem-analysis "赛题描述" → all (default) /problem-analysis "赛题描述" — sources: all → all (default) /problem-analysis "赛题描述" — sources: local → local references only /problem-analysis "赛题描述" — sources: web → web search only /problem-analysis "赛题描述" — sources: local, web → local + web ``` ### Source Table | Priority | Source | ID | How to detect | What it provides | |----------|--------|----|---------------|-----------------| | 1 | **Local references** | `local` | `Glob: data/**/*.*, reference/**/*.*` | 赛题数据文件、参考资料、过往优秀论文 | | 2 | **Web search** | `web` | Always available (WebSearch) | 数模优秀论文库、CNKI、经典教材方法、赛题案例库 | > **Graceful degradation**: If no local references exist, the skill still works via web search alone. ## Workflow ### Step 0a: 读取赛题与数据 1. **读取赛题描述**: 从 `$ARGUMENTS` 或 `PROBLEM_BRIEF.md` 获取完整赛题文本 2. **扫描数据文件**: 检查 `data/` 目录下的数据文件（.csv, .xlsx, .txt 等） ``` Glob: data/**/*.{csv,xlsx,xls,txt,dat,json} ``` 3. **初步数据概览**: 对每个数据文件，快速提取： - 文件名、大小、行数/列数 - 列名/字段名 - 数据类型和基本统计量 4. **识别赛题类型**: 判断属于哪一类数模问题（优化、预测、评价、分类、调度、博弈等） > 📋 赛题数据是建模的基础——先理解数据结构，再决定建模方法。 ### Step 0b: 扫描本地参考资料 检查用户是否已有相关参考资料： 1. **Locate references**: Check METHOD_LIBRARY paths for reference files ``` Glob: reference/**/*.{pdf,md,txt,docx}, data/**/*.{pdf,md,txt} ``` 2. **Filter by relevance**: Match filenames and content against the competition problem. Skip clearly unrelated files. 3. **Summarize relevant references**: For each relevant file (up to MAX_LOCAL_REFS): - Read content (first 3 pages for PDFs) - Extract: title, core method, applicability to current problem - Flag references that are directly related vs tangentially related 4. **Build local knowledge base**: Compile summaries into a "references you already have" section. This becomes the starting point — web search fills the gaps. > 📚 If no local references are found, skip to Step 1. If the user has relevant materials, the web search can be more targeted (focus on what's missing). ### Step 1: 检索经典方法与类似赛题 (external) - Use WebSearch to find classic modeling methods for this type of problem - Search for: 数模竞赛优秀论文, CNKI 数学建模, 经典教材方法, 赛题案例库 - Focus on: (1) classic textbook methods, (2) past competition winning solutions, (3) applicable mathematical techniques - **De-duplicate**: Skip methods already found in local references **Web search strategy** (multi-query): ``` Query 1: "[问题类型] 数学建模方法" (e.g., "优化问题 数学建模方法") Query 2: "[关键词] 数学建模竞赛 优秀论文" (e.g., "交通流 数学建模竞赛 优秀论文") Query 3: "[问题类型] mathematical modeling approach" (English search for international methods) Query 4: "CUMCM/MCM [类似赛题关键词]" (search for similar past competition problems) ``` For each search, extract: - Method name and category (统计/优化/微分方程/图论/机器学习/模拟) - Key references or textbook sources - Applicability to the current problem - Complexity and implementation difficulty **Method categorization**: Organize found methods into a **方法地图** (method map): | Category | Methods | Applicability | Difficulty | |----------|---------|--------------|------------| | 统计分析 | 回归分析, 时间序列, 主成分分析... | | | | 优化方法 | 线性规划, 整数规划, 动态规划... | | | | 微分方程 | ODE, PDE, 差分方程... | | | | 图论/网络 | 最短路, 网络流, 图着色... | | | | 机器学习 | 分类, 聚类, 神经网络... | | | | 模拟仿真 | Monte Carlo, 元胞自动机, Agent-based... | | | ### Step 2: 分析赛题结构 For each sub-problem identified, extract: - **问题类型**: 属于哪类数学问题（优化/预测/评价/分类/调度/博弈等） - **关键变量**: 决策变量、参数、约束条件 - **数据需求**: 需要哪些数据，现有数据是否满足 - **可行方法**: 基于 Step 1 的方法地图，列出候选方法 - **难点**: 该子问题的主要建模难点 ### Step 3: 综合分析 - Group methods by problem type and applicability - Identify which methods are most suitable for each sub-problem - Find potential innovation points (方法组合、改进、创新应用) - Assess data-method compatibility (数据是否支持所选方法) ### Step 4: Output Save as `PROBLEM_ANALYSIS.md`: ``` | 子问题 | 问题类型 | 候选方法 | 推荐方法 | 难度 | 创新空间 | |--------|---------|---------|---------|------|---------| ``` Plus a narrative analysis (3-5 paragraphs) covering: 1. 赛题整体解读 2. 子问题之间的逻辑关系 3. 推荐的建模路线（主方法 + 备选方法） 4. 潜在的创新点和加分项 Include a simple reference list for methods and sources consulted. ### Step 5: Save - Save `PROBLEM_ANALYSIS.md` to the project root - Update any reference materials in `reference/` - Log the analysis in project memory for downstream skills ## Key Rules - Always cite method sources (textbook, past competition paper, or reference) - Distinguish between classic methods (well-established) and novel approaches (higher risk, higher reward) - Be honest about limitations of each method for this specific problem - Note which methods are commonly used in award-winning papers for similar problems - **Never fail because local references are missing** — always fall back gracefully to web search - Prioritize methods that match the available data and time constraints of the competition