"""Heuristic Bayesian knowledge tracing helper.
中文：知识追踪业务逻辑，使用启发式贝叶斯更新掌握度并给出学习顺序建议。
"""
from __future__ import annotations
from collections import defaultdict
from typing import Dict, List
from ...pydantic_models import (
KnowledgeTracingRequest,
KnowledgeTracingResponse,
SkillProgress,
SkillInteraction,
)
def _update_probability(prob: float, interaction: SkillInteraction) -> float:
prob = max(min(prob, 0.999), 0.001)
learning_rate = 0.3
forgetting = 0.4
if interaction.correct:
prob = prob + (1 - prob) * learning_rate
else:
prob = prob * forgetting
if interaction.confidence is not None:
prob = 0.7 * prob + 0.3 * interaction.confidence
if interaction.time_spent_seconds and interaction.time_spent_seconds > 120:
prob -= 0.05 # 过长耗时可能暴露掌握薄弱
return max(min(prob, 1.0), 0.0)
def trace_knowledge(payload: KnowledgeTracingRequest) -> KnowledgeTracingResponse:
prob_map: Dict[str, float] = defaultdict(lambda: 0.5)
prob_map.update(payload.prior_mastery)
history: Dict[str, List[bool]] = defaultdict(list)
for interaction in payload.interactions:
prev = prob_map[interaction.skill]
updated = _update_probability(prev, interaction)
prob_map[interaction.skill] = updated
history[interaction.skill].append(interaction.correct)
skills: List[SkillProgress] = []
for skill, probability in prob_map.items():
recent = history.get(skill, [])
if len(recent) >= 2 and recent[-2:] == [True, True]:
trend = "上升"
elif recent and not recent[-1]:
trend = "下降"
else:
trend = "平稳"
if probability >= 0.85:
action = "安排挑战题巩固迁移。"
elif probability >= 0.6:
action = "保持混合题训练，关注错误类型。"
else:
action = "回到基础例题，配合讲解反馈。"
skills.append(
SkillProgress(
skill=skill,
probability_mastery=round(probability, 3),
trend=trend,
next_action=action,
)
)
recommended_sequence = [item.skill for item in sorted(skills, key=lambda s: s.probability_mastery)]
return KnowledgeTracingResponse(
student_id=payload.student_id,
skills=skills,
recommended_sequence=recommended_sequence,
)
