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

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):

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