feat: 实现考试分数智能分配

解决题目数量无法整除总分时出现无限小数的问题

后端：
- 新增 ScoreDistributor 分数分配工具类
- 支持整数分配和小数分配两种模式
- 更新 exam_service.py 使用智能分配
- 考试总分固定100分，按题目数量智能分配

前端：
- 新增 scoreFormatter.ts 分数格式化工具
- 提供分数显示、等级判断等辅助函数

示例：100分/6题 = [17,17,17,17,16,16] 总和=100

backend/app/services/exam_service.py

@@ -11,6 +11,7 @@ from app.models.exam import Exam, Question, ExamResult
 from app.models.exam_mistake import ExamMistake
 from app.models.course import Course, KnowledgePoint
 from app.core.exceptions import BusinessException, ErrorCode
+from app.utils.score_distributor import ScoreDistributor
 
 
 class ExamService:
@@ -54,27 +55,38 @@ class ExamService:
             all_questions, min(question_count, len(all_questions))
         )
 
-        # 构建题目数据
+        # 使用智能分数分配器，确保总分为整数且分配合理
+        total_score = 100.0  # 固定总分为100分
+        actual_question_count = len(selected_questions)
+        
+        # 创建分数分配器
+        distributor = ScoreDistributor(total_score, actual_question_count)
+        distributed_scores = distributor.distribute(mode="integer")
+
+        # 构建题目数据，使用分配后的分数
         questions_data = []
-        for q in selected_questions:
+        for i, q in enumerate(selected_questions):
             question_data = {
                 "id": str(q.id),
                 "type": q.question_type,
                 "title": q.title,
                 "content": q.content,
                 "options": q.options,
-                "score": q.score,
+                "score": distributed_scores[i],  # 使用智能分配的分数
             }
             questions_data.append(question_data)
 
+        # 计算及格分数（向上取整，确保公平）
+        pass_score = ScoreDistributor.calculate_pass_score(total_score, 0.6)
+
         # 创建考试记录
         exam = Exam(
             user_id=user_id,
             course_id=course_id,
             exam_name=f"{course.name} - 随机测试",
-            question_count=len(selected_questions),
-            total_score=sum(q.score for q in selected_questions),
-            pass_score=sum(q.score for q in selected_questions) * 0.6,
+            question_count=actual_question_count,
+            total_score=total_score,
+            pass_score=pass_score,
             duration_minutes=60,
             status="started",
             questions={"questions": questions_data},
@@ -140,6 +152,9 @@ class ExamService:
         for question_data in exam.questions["questions"]:
             question_id = question_data["id"]
             question = questions_map.get(question_id)
+            
+            # 使用考试创建时分配的分数（智能分配后的整数分数）
+            allocated_score = question_data.get("score", 10.0)
 
             if not question:
                 continue
@@ -148,7 +163,7 @@ class ExamService:
             is_correct = user_answer == question.correct_answer
 
             if is_correct:
-                total_score += question.score
+                total_score += allocated_score  # 使用分配的分数
                 correct_count += 1
 
             # 创建答题结果记录
@@ -157,7 +172,7 @@ class ExamService:
                 question_id=int(question_id),
                 user_answer=user_answer,
                 is_correct=is_correct,
-                score=question.score if is_correct else 0.0,
+                score=allocated_score if is_correct else 0.0,  # 使用分配的分数
             )
             db.add(exam_result)
 

backend/app/utils/__init__.py

@@ -0,0 +1,14 @@
+"""
+工具模块
+"""
+from app.utils.score_distributor import (
+    ScoreDistributor,
+    distribute_scores,
+    get_question_score,
+)
+
+__all__ = [
+    "ScoreDistributor",
+    "distribute_scores",
+    "get_question_score",
+]

backend/app/utils/score_distributor.py

@@ -0,0 +1,218 @@
+"""
+分数分配工具
+
+解决题目分数无法整除的问题，确保：
+1. 所有题目分数之和精确等于总分
+2. 题目分数差异最小化（最多相差1分）
+3. 支持整数分配和小数分配两种模式
+"""
+from typing import List, Tuple
+from decimal import Decimal, ROUND_HALF_UP
+import math
+
+
+class ScoreDistributor:
+    """
+    智能分数分配器
+    
+    使用示例：
+        distributor = ScoreDistributor(total_score=100, question_count=6)
+        scores = distributor.distribute()
+        # 结果: [17, 17, 17, 17, 16, 16]  总和=100
+    """
+    
+    def __init__(self, total_score: float, question_count: int):
+        """
+        初始化分配器
+        
+        Args:
+            total_score: 总分（如 100）
+            question_count: 题目数量（如 6）
+        """
+        if question_count <= 0:
+            raise ValueError("题目数量必须大于0")
+        if total_score <= 0:
+            raise ValueError("总分必须大于0")
+            
+        self.total_score = total_score
+        self.question_count = question_count
+    
+    def distribute_integer(self) -> List[int]:
+        """
+        整数分配模式
+        
+        将总分分配为整数，前面的题目分数可能比后面的多1分
+        
+        Returns:
+            分数列表，如 [17, 17, 17, 17, 16, 16]
+            
+        示例：
+            100分 / 6题 = [17, 17, 17, 17, 16, 16]
+            100分 / 7题 = [15, 15, 14, 14, 14, 14, 14]
+        """
+        total = int(self.total_score)
+        count = self.question_count
+        
+        # 基础分数（向下取整）
+        base_score = total // count
+        # 需要额外加1分的题目数量
+        extra_count = total % count
+        
+        # 生成分数列表
+        scores = []
+        for i in range(count):
+            if i < extra_count:
+                scores.append(base_score + 1)
+            else:
+                scores.append(base_score)
+        
+        return scores
+    
+    def distribute_decimal(self, decimal_places: int = 1) -> List[float]:
+        """
+        小数分配模式
+        
+        将总分分配为小数，最后一题用于补齐差额
+        
+        Args:
+            decimal_places: 小数位数，默认1位
+            
+        Returns:
+            分数列表，如 [16.7, 16.7, 16.7, 16.7, 16.7, 16.5]
+        """
+        count = self.question_count
+        
+        # 计算每题分数并四舍五入
+        per_score = self.total_score / count
+        rounded_score = round(per_score, decimal_places)
+        
+        # 前 n-1 题使用四舍五入的分数
+        scores = [rounded_score] * (count - 1)
+        
+        # 最后一题用总分减去前面的和，确保总分精确
+        last_score = round(self.total_score - sum(scores), decimal_places)
+        scores.append(last_score)
+        
+        return scores
+    
+    def distribute(self, mode: str = "integer") -> List[float]:
+        """
+        分配分数
+        
+        Args:
+            mode: 分配模式
+                - "integer": 整数分配（推荐）
+                - "decimal": 小数分配
+                - "decimal_1": 保留1位小数
+                - "decimal_2": 保留2位小数
+                
+        Returns:
+            分数列表
+        """
+        if mode == "integer":
+            return [float(s) for s in self.distribute_integer()]
+        elif mode == "decimal" or mode == "decimal_1":
+            return self.distribute_decimal(1)
+        elif mode == "decimal_2":
+            return self.distribute_decimal(2)
+        else:
+            return [float(s) for s in self.distribute_integer()]
+    
+    def get_score_for_question(self, question_index: int, mode: str = "integer") -> float:
+        """
+        获取指定题目的分数
+        
+        Args:
+            question_index: 题目索引（从0开始）
+            mode: 分配模式
+            
+        Returns:
+            该题目的分数
+        """
+        scores = self.distribute(mode)
+        if 0 <= question_index < len(scores):
+            return scores[question_index]
+        raise IndexError(f"题目索引 {question_index} 超出范围 [0, {self.question_count})")
+    
+    def validate(self) -> Tuple[bool, str]:
+        """
+        验证分配结果
+        
+        Returns:
+            (是否有效, 信息)
+        """
+        scores = self.distribute()
+        total = sum(scores)
+        
+        if abs(total - self.total_score) < 0.01:
+            return True, f"分配有效：{scores}，总分={total}"
+        else:
+            return False, f"分配无效：{scores}，总分={total}，期望={self.total_score}"
+    
+    @staticmethod
+    def format_score(score: float, decimal_places: int = 1) -> str:
+        """
+        格式化分数显示
+        
+        Args:
+            score: 分数
+            decimal_places: 小数位数
+            
+        Returns:
+            格式化的分数字符串
+        """
+        if score == int(score):
+            return str(int(score))
+        return f"{score:.{decimal_places}f}"
+    
+    @staticmethod
+    def calculate_pass_score(total_score: float, pass_rate: float = 0.6) -> float:
+        """
+        计算及格分数
+        
+        Args:
+            total_score: 总分
+            pass_rate: 及格率，默认60%
+            
+        Returns:
+            及格分数（整数）
+        """
+        return math.ceil(total_score * pass_rate)
+
+
+def distribute_scores(total_score: float, question_count: int, mode: str = "integer") -> List[float]:
+    """
+    便捷函数：分配分数
+    
+    Args:
+        total_score: 总分
+        question_count: 题目数量
+        mode: 分配模式（integer/decimal）
+        
+    Returns:
+        分数列表
+    """
+    distributor = ScoreDistributor(total_score, question_count)
+    return distributor.distribute(mode)
+
+
+def get_question_score(
+    total_score: float, 
+    question_count: int, 
+    question_index: int,
+    mode: str = "integer"
+) -> float:
+    """
+    便捷函数：获取指定题目的分数
+    
+    Args:
+        total_score: 总分
+        question_count: 题目数量
+        question_index: 题目索引（从0开始）
+        mode: 分配模式
+        
+    Returns:
+        该题目的分数
+    """
+    distributor = ScoreDistributor(total_score, question_count)
+    return distributor.get_score_for_question(question_index, mode)