note/知识图谱/教科书-数学/all/README.md

# 高中数学知识图谱数据库方案

这是一个基于PostgreSQL的高中数学知识图谱数据库系统，支持知识的结构化存储、关系网络分析、全文搜索和个性化推荐。

## 📁 文件结构

```
all/
├── database_schema.sql        # 数据库架构SQL文件
├── data_import.py            # 数据导入脚本
├── config.py                 # 配置文件
├── query_examples.sql        # 常用查询示例
├── analysis_queries.sql      # 分析查询SQL
├── README.md                 # 说明文档（本文件）
├── knowledge-*.json          # 知识点JSON文件
├── method-*.json             # 方法JSON文件
└── problems-*.json           # 题目JSON文件
```

## 🏗️ 数据库架构

### 三层架构设计

1. **Knowledge（知识层）**
   - 知识点定义、原理说明、适用条件
   - 支持前置关系、包含关系、关联内容

2. **Method（方法层）**
   - 解题方法、步骤说明、常见错误
   - 支撑知识点、数学思想、解题策略

3. **Problem（题目层）**
   - 题目内容、题型分类、难度评估
   - 知识点标注、方法标注、来源信息

### 主要数据表

- `knowledge_points` - 知识点主表
- `methods` - 解题方法主表
- `problems` - 题目主表
- `knowledge_relations` - 知识点关系表
- `problem_knowledge_tags` - 题目知识点标注
- `problem_method_tags` - 题目方法标注

## 🚀 快速开始

### 1. 环境准备

```bash
# 安装依赖
pip install psycopg2-binary

# 确保PostgreSQL已启动
pg_ctl -D /usr/local/var/postgres start
```

### 2. 创建数据库

```bash
# 连接到PostgreSQL
psql -U postgres

# 创建数据库
CREATE DATABASE math_knowledge_graph;
\c math_knowledge_graph

# 执行架构脚本
\i database_schema.sql
```

### 3. 配置数据库连接

编辑 `config.py` 文件，修改数据库连接信息：

```python
DATABASE_CONFIG = {
    'host': 'localhost',
    'port': 5432,
    'database': 'math_knowledge_graph',
    'user': 'postgres',
    'password': 'your_actual_password',  # 修改为实际密码
}
```

### 4. 导入数据

```bash
python data_import.py
```

## 📊 使用示例

### 基础查询

```sql
-- 查询所有核心知识点
SELECT code, name, level, importance
FROM knowledge_points
WHERE importance = '核心'
ORDER BY code;

-- 查询特定知识点的详细信息
SELECT * FROM knowledge_detail_view
WHERE code = 'K1-1-1-01';

-- 查询题目及其知识点标注
SELECT p.code, p.stem, kp.name, pkt.tag_type
FROM problems p
JOIN problem_knowledge_tags pkt ON p.id = pkt.problem_id
JOIN knowledge_points kp ON pkt.knowledge_id = kp.id
WHERE p.code = 'T1-1-1-E01';
```

### 关系网络查询

```sql
-- 查询知识点的前置关系
WITH RECURSIVE knowledge_chain AS (
    SELECT k.id, k.code, k.name, 1 as level
    FROM knowledge_points k
    WHERE k.code = 'K1-1-3-01'  -- 目标知识点

    UNION ALL

    SELECT k.id, k.code, k.name, kc.level + 1
    FROM knowledge_points k
    JOIN knowledge_relations kr ON k.id = kr.source_knowledge_id
    JOIN knowledge_chain kc ON kr.target_knowledge_id = kc.id
    WHERE kr.relation_type = '前置知识'
)
SELECT * FROM knowledge_chain ORDER BY level;

-- 查询题目的知识点覆盖度
SELECT
    c.chapter_name,
    COUNT(DISTINCT kp.id) as knowledge_count,
    COUNT(DISTINCT p.id) as problem_count
FROM chapters c
JOIN sections s ON c.id = s.chapter_id
JOIN knowledge_points kp ON s.id = kp.section_id
LEFT JOIN problem_knowledge_tags pkt ON kp.id = pkt.knowledge_id
LEFT JOIN problems p ON pkt.problem_id = p.id
GROUP BY c.id, c.chapter_name;
```

### 全文搜索

```sql
-- 搜索知识点
SELECT code, name, importance
FROM knowledge_points
WHERE search_vector @@ to_tsquery('chinese', '函数 & 定义')
ORDER BY ts_rank(search_vector, to_tsquery('chinese', '函数 & 定义')) DESC;

-- 搜索题目
SELECT code, problem_type, stem
FROM problems
WHERE search_vector @@ to_tsquery('chinese', '定义域')
ORDER BY ts_rank(search_vector, to_tsquery('chinese', '定义域')) DESC;
```

### 数据分析

```sql
-- 难度分布统计
SELECT
    type,
    COUNT(*) as count,
    AVG(difficulty_level) as avg_difficulty
FROM methods
GROUP BY type
ORDER BY avg_difficulty;

-- 知识点考查频次统计
SELECT
    kp.name,
    COUNT(pkt.id) as problem_count,
    AVG(p.difficulty_info->>'整体难度')::float as avg_problem_difficulty
FROM knowledge_points kp
LEFT JOIN problem_knowledge_tags pkt ON kp.id = pkt.knowledge_id
LEFT JOIN problems p ON pkt.problem_id = p.id
WHERE pkt.tag_type = '主要考查'
GROUP BY kp.id, kp.name
HAVING COUNT(pkt.id) > 0
ORDER BY problem_count DESC
LIMIT 10;
```

## 🛠️ 数据维护

### 数据备份

```bash
# 备份数据库
pg_dump -U postgres math_knowledge_graph > backup.sql

# 恢复数据库
psql -U postgres math_knowledge_graph < backup.sql
```

### 索引重建

```sql
-- 重建搜索向量索引
UPDATE knowledge_points SET search_vector =
    setweight(to_tsvector('chinese', COALESCE(name, '')), 'A') ||
    setweight(to_tsvector('chinese', COALESCE(core_content::text, '')), 'B');

-- 重建所有索引
REINDEX DATABASE math_knowledge_graph;
```

### 性能优化

```sql
-- 分析查询性能
EXPLAIN ANALYZE SELECT * FROM knowledge_points WHERE importance = '核心';

-- 更新表统计信息
ANALYZE knowledge_points;
ANALYZE methods;
ANALYZE problems;
```

## 📈 扩展功能

### 个性化学习路径

```sql
-- 基于知识点关系的学习路径推荐
WITH RECURSIVE learning_path AS (
    SELECT k.id, k.code, k.name, k.level, 0 as step, ARRAY[k.id] as path_ids
    FROM knowledge_points k
    WHERE k.importance = '核心' AND k.level = '二级'

    UNION ALL

    SELECT k.id, k.code, k.name, k.level, lp.step + 1, lp.path_ids || k.id
    FROM knowledge_points k
    JOIN knowledge_relations kr ON k.id = kr.source_knowledge_id
    JOIN learning_path lp ON kr.target_knowledge_id = lp.id
    WHERE kr.relation_type = '前置知识'
    AND k.id != ALL(lp.path_ids)
    AND lp.step < 5
)
SELECT code, name, level, step
FROM learning_path
WHERE step <= 3
ORDER BY step, name;
```

### 错误模式分析

```sql
-- 常见错误类型统计
SELECT
    m.name as method_name,
    COUNT(mce.id) as error_count,
    ARRAY_AGG(DISTINCT mce.error_description) as error_types
FROM methods m
LEFT JOIN method_common_errors mce ON m.id = mce.method_id
GROUP BY m.id, m.name
HAVING COUNT(mce.id) > 0
ORDER BY error_count DESC;
```

## 🔍 故障排除

### 常见问题

1. **连接失败**
   - 检查PostgreSQL服务是否启动
   - 验证数据库配置信息
   - 确认防火墙设置

2. **导入失败**
   - 检查JSON文件格式是否正确
   - 验证文件编码（应为UTF-8）
   - 查看导入日志文件

3. **查询缓慢**
   - 检查索引是否创建
   - 分析查询执行计划
   - 考虑优化SQL语句

### 日志文件

```bash
# 查看导入日志
tail -f data_import.log

# 查看PostgreSQL日志
tail -f /usr/local/var/postgres.log
```

## 📞 技术支持

如有问题，请检查：
1. PostgreSQL版本要求：≥ 12
2. Python版本要求：≥ 3.7
3. 所需Python包：psycopg2-binary

## 📄 许可证

本项目采用MIT许可证，详见LICENSE文件。