300 lines
10 KiB
Markdown
300 lines
10 KiB
Markdown
基于你的需求，我来重新梳理一下需要设计的表结构。总共需要**7张核心表**，使用 PostgreSQL 语法：
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## 知识图谱相关表（3张）
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### 1. knowledge（知识点表）
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```sql
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CREATE TABLE knowledge (
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id VARCHAR(20) PRIMARY KEY, -- K3-1-1-01
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name VARCHAR(100) NOT NULL, -- 函数的三要素
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type VARCHAR(20), -- 概念/定理/公式
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definition TEXT, -- 定义内容
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core_features TEXT[], -- PostgreSQL 数组类型 ["任意性", "唯一性"]
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prerequisites TEXT[], -- PostgreSQL 数组类型 ["K1-1-01", "K1-2-01"]
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importance VARCHAR(10), -- 核心/重要/基础
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textbook_location VARCHAR(100), -- 必修1 P62
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created_at TIMESTAMP DEFAULT NOW()
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);
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-- 数组字段的 GIN 索引，支持高效的包含查询
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CREATE INDEX idx_knowledge_core_features ON knowledge USING GIN(core_features);
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CREATE INDEX idx_knowledge_prerequisites ON knowledge USING GIN(prerequisites);
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```
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### 2. method（方法表）
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```sql
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CREATE TABLE method (
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id VARCHAR(20) PRIMARY KEY, -- M3-1-1-01
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name VARCHAR(100) NOT NULL, -- 分式型定义域求解法
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type VARCHAR(20), -- 解题方法/计算技巧
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scenario VARCHAR(200), -- 适用场景
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steps TEXT, -- 方法步骤描述，纯文本
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supported_knowledge TEXT[], -- PostgreSQL 数组类型 ["K3-1-1-02"]
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common_errors TEXT[], -- PostgreSQL 数组类型 ["遗漏分母"]
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difficulty_level INT, -- 1-5
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created_at TIMESTAMP DEFAULT NOW()
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);
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-- 数组字段的 GIN 索引
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CREATE INDEX idx_method_supported_knowledge ON method USING GIN(supported_knowledge);
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CREATE INDEX idx_method_common_errors ON method USING GIN(common_errors);
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```
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### 3. problem（题目表）
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```sql
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CREATE TABLE problem (
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id VARCHAR(20) PRIMARY KEY, -- T3-1-1-E02
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problem_type VARCHAR(20), -- 例题/练习题/习题
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content TEXT NOT NULL, -- 完整题目内容
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problem_category VARCHAR(50), -- 函数基础
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difficulty INT, -- 1-5
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source VARCHAR(100), -- 必修1 P65 例2
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created_at TIMESTAMP DEFAULT NOW()
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);
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-- 题目-知识点映射表
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CREATE TABLE problem_knowledge_mapping (
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problem_id VARCHAR(20),
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question_part VARCHAR(10), -- 小题1/小题2/整体
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knowledge_id VARCHAR(20),
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is_primary BOOLEAN DEFAULT TRUE, -- 是否为主要考查点
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weight DECIMAL(3,2) DEFAULT 1.0, -- 权重(0.1-1.0)
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PRIMARY KEY (problem_id, question_part, knowledge_id),
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FOREIGN KEY (problem_id) REFERENCES problem(id),
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FOREIGN KEY (knowledge_id) REFERENCES knowledge(id)
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);
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-- 题目-方法映射表
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CREATE TABLE problem_method_mapping (
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problem_id VARCHAR(20),
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question_part VARCHAR(10),
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method_id VARCHAR(20),
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is_primary BOOLEAN DEFAULT TRUE,
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weight DECIMAL(3,2) DEFAULT 1.0,
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PRIMARY KEY (problem_id, question_part, method_id),
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FOREIGN KEY (problem_id) REFERENCES problem(id),
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FOREIGN KEY (method_id) REFERENCES method(id)
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);
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-- 性能索引
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CREATE INDEX idx_problem_knowledge_problem ON problem_knowledge_mapping(problem_id);
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CREATE INDEX idx_problem_knowledge_knowledge ON problem_knowledge_mapping(knowledge_id);
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CREATE INDEX idx_problem_method_problem ON problem_method_mapping(problem_id);
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CREATE INDEX idx_problem_method_method ON problem_method_mapping(method_id);
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```
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---
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## 学生评分相关表（4张）
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### 4. student（学生表）
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```sql
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CREATE TABLE student (
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id VARCHAR(20) PRIMARY KEY, -- S001
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name VARCHAR(50) NOT NULL,
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grade VARCHAR(10), -- 高一/高二/高三
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class_name VARCHAR(20), -- 班级
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created_at TIMESTAMP DEFAULT NOW()
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);
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```
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### 5. learning_record（学习记录表 - 核心流水表）
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```sql
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CREATE TABLE learning_record (
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id BIGSERIAL PRIMARY KEY, -- PostgreSQL 自增类型
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student_id VARCHAR(20) NOT NULL,
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problem_id VARCHAR(20) NOT NULL, -- T3-1-1-E02
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knowledge_id VARCHAR(20) NOT NULL, -- K3-1-1-02
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method_id VARCHAR(20), -- M3-1-1-01 (可选)
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question_part VARCHAR(10), -- 小题1/小题2/整体
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is_correct BOOLEAN NOT NULL, -- 正确/错误
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score DECIMAL(5,2), -- 得分(0-100)
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max_score DECIMAL(5,2) NOT NULL, -- 该题/该小题的满分
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exam_id VARCHAR(20) NOT NULL, -- 该场考试的id或名称
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exam_date DATE, -- 考试/练习日期
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response_time_ms INT, -- 响应时间（毫秒）
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created_at TIMESTAMP DEFAULT NOW(),
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FOREIGN KEY (student_id) REFERENCES student(id),
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FOREIGN KEY (problem_id) REFERENCES problem(id),
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FOREIGN KEY (knowledge_id) REFERENCES knowledge(id),
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FOREIGN KEY (method_id) REFERENCES method(id)
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);
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-- 分区表（按月分区，提高查询性能）
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CREATE TABLE learning_record_y2024m01 PARTITION OF learning_record
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FOR VALUES FROM ('2024-01-01') TO ('2024-02-01');
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-- 性能索引
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CREATE INDEX idx_learning_record_student_knowledge ON learning_record(student_id, knowledge_id);
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CREATE INDEX idx_learning_record_exam_date ON learning_record(exam_date);
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CREATE INDEX idx_learning_record_student_exam ON learning_record(student_id, exam_date DESC);
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```
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### 6. knowledge_mastery（知识点掌握度表 - 汇总表）
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```sql
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CREATE TABLE knowledge_mastery (
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student_id VARCHAR(20),
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knowledge_id VARCHAR(20),
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mastery_score DECIMAL(5,2) DEFAULT 100.0, -- 掌握度分数(0-100)
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total_attempts INT DEFAULT 0, -- 总尝试次数
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correct_attempts INT DEFAULT 0, -- 正确次数
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avg_response_time DECIMAL(8,2), -- 平均答题时间
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last_practiced DATE, -- 最后练习日期
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confidence_level DECIMAL(3,2), -- 置信度(0-1)
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updated_at TIMESTAMP DEFAULT NOW(),
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PRIMARY KEY (student_id, knowledge_id),
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FOREIGN KEY (student_id) REFERENCES student(id),
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FOREIGN KEY (knowledge_id) REFERENCES knowledge(id)
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);
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-- 性能索引
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CREATE INDEX idx_knowledge_mastery_score ON knowledge_mastery(mastery_score);
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CREATE INDEX idx_knowledge_mastery_updated ON knowledge_mastery(updated_at);
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```
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### 7. method_mastery（方法掌握度表 - 汇总表）
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```sql
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CREATE TABLE method_mastery (
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student_id VARCHAR(20),
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method_id VARCHAR(20),
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mastery_score DECIMAL(5,2) DEFAULT 100.0,
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total_usage INT DEFAULT 0, -- 总使用次数
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successful_usage INT DEFAULT 0, -- 成功使用次数
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avg_success_rate DECIMAL(5,2), -- 平均成功率
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updated_at TIMESTAMP DEFAULT NOW(),
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PRIMARY KEY (student_id, method_id),
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FOREIGN KEY (student_id) REFERENCES student(id),
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FOREIGN KEY (method_id) REFERENCES method(id)
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);
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```
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---
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## PostgreSQL 特有的查询优势
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### **1. 数组查询示例**
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```sql
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-- 查找包含特定特征的知识点
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SELECT * FROM knowledge
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WHERE '任意性' = ANY(core_features);
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-- 查找前置知识点包含 K1-1-01 的所有知识点
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SELECT id, name FROM knowledge
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WHERE 'K1-1-01' = ANY(prerequisites);
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-- 查找支持特定知识点的方法
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SELECT id, name FROM method
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WHERE 'K3-1-1-02' = ANY(supported_knowledge);
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-- 查找常见错误的方法
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SELECT id, name FROM method
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WHERE array_length(common_errors, 1) > 2;
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```
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### **2. 规范化查询示例**
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```sql
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-- 查找考查 K3-1-1-02 的所有题目
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SELECT DISTINCT p.* FROM problem p
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JOIN problem_knowledge_mapping pkm ON p.id = pkm.problem_id
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WHERE pkm.knowledge_id = 'K3-1-1-02';
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-- 查找小题1考查特定知识点的题目
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SELECT p.* FROM problem p
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JOIN problem_knowledge_mapping pkm ON p.id = pkm.problem_id
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WHERE pkm.knowledge_id = 'K3-1-1-02' AND pkm.question_part = '小题1';
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-- 查找使用特定方法的所有题目
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SELECT DISTINCT p.* FROM problem p
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JOIN problem_method_mapping pmm ON p.id = pmm.problem_id
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WHERE pmm.method_id = 'M3-1-1-01';
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-- 获取题目的完整知识点映射
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SELECT p.content, pkm.question_part, k.name as knowledge_name, pkm.is_primary, pkm.weight
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FROM problem p
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JOIN problem_knowledge_mapping pkm ON p.id = pkm.problem_id
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JOIN knowledge k ON pkm.knowledge_id = k.id
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WHERE p.id = 'T3-1-1-E02'
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ORDER BY pkm.question_part;
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-- 全文搜索方法步骤
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SELECT id, name, steps FROM method
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WHERE steps LIKE '%识别分母%' AND steps LIKE '%令≠0%';
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```
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### **3. 复杂关联查询**
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```sql
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-- 获取某个学生的薄弱知识点（掌握度低于60且尝试次数大于5）
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SELECT k.id, k.name, km.mastery_score, km.total_attempts
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FROM knowledge k
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JOIN knowledge_mastery km ON k.id = km.knowledge_id
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WHERE km.student_id = 'S001'
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AND km.mastery_score < 60
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AND km.total_attempts >= 5
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ORDER BY km.mastery_score ASC;
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-- 获取推荐题目（基于薄弱知识点）
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SELECT DISTINCT p.*, pkm.question_part, pkm.weight
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FROM problem p
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JOIN problem_knowledge_mapping pkm ON p.id = pkm.problem_id
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WHERE pkm.knowledge_id IN (
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SELECT knowledge_id
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FROM knowledge_mastery
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WHERE student_id = 'S001' AND mastery_score < 60
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)
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ORDER BY p.difficulty, pkm.weight DESC;
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-- 统计知识点考查频率
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SELECT k.id, k.name, COUNT(*) as question_count, AVG(p.difficulty) as avg_difficulty
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FROM knowledge k
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JOIN problem_knowledge_mapping pkm ON k.id = pkm.knowledge_id
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JOIN problem p ON pkm.problem_id = p.id
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GROUP BY k.id, k.name
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ORDER BY question_count DESC;
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```
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## 表关系说明
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```
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知识图谱层：
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knowledge ← (一对多) → problem (通过knowledge_mapping关联)
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method ← (一对多) → problem (通过method_mapping关联)
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学生评分层：
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student ← (一对多) → learning_record (流水记录)
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student ← (一对多) → knowledge_mastery (汇总统计)
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student ← (一对多) → method_mastery (汇总统计)
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learning_record 同时关联：
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- student_id (哪个学生)
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- problem_id (哪道题)
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- knowledge_id (哪个知识点)
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- method_id (哪个方法)
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```
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---
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## 数据流向
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```
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学生答题 → learning_record (记录原始数据)
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↓
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定时任务 → knowledge_mastery (计算掌握度)
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↓
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查询分析 → 个性化推荐
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```
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## 核心优势
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1. **数据完整性** - 记录了每个学生的详细学习轨迹
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2. **实时更新** - learning_record实时记录，mastery表定期汇总
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3. **灵活查询** - 可以按学生、知识点、方法、时间等多个维度分析
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4. **扩展性强** - 支持后续的智能推荐和预测分析
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5. **PostgreSQL 优势**：
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- 数组类型简化了多值字段的存储和查询
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- 分区表特性优化了大数据量的查询性能
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- GIN 索引支持复杂的包含查询
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这7张表构成了完整的知识图谱+个性化评分系统。需要我帮你设计具体的SQL插入示例或API接口吗？ |