505 lines
14 KiB
Markdown
505 lines
14 KiB
Markdown
# 複習時間算法完整設計方案
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## 🎯 **核心設計原則**
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1. **漸進式增長**: 避免過快跳躍，符合記憶曲線
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2. **簡單有效**: 邏輯清晰易懂，便於實作和維護
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3. **智能糾錯**: 根據表現動態調整
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4. **科學依據**: 基於間隔重複記憶理論
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## 📐 **核心算法公式**
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### **基本公式（簡化版）**
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```
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新間隔 = 舊間隔 × 增長係數 × 表現係數
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```
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這個公式很簡單：
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- **舊間隔**: 上次復習間隔天數
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- **增長係數**: 根據當前間隔階段決定
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- **表現係數**: 根據答題表現決定
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## 📊 **完整算法流程圖**
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```mermaid
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graph TD
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A[開始復習] --> B[獲取詞彙資訊]
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B --> C[計算難易度係數]
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C --> D[進行復習測試]
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D --> E[記錄答題結果]
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E --> F[計算表現係數]
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F --> G[計算新的復習間隔]
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G --> H[更新熟悉程度]
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H --> I[設定下次復習時間]
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I --> J[結束]
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C --> C1[詞彙CEFR等級]
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C --> C2[學習者程度]
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C --> C3[歷史表現]
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F --> F1[翻卡題評分]
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F --> F2[客觀題正確率]
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F --> F3[反應時間]
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G --> G1[前次間隔]
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G --> G2[難易度係數]
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G --> G3[表現係數]
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G --> G4[階段調整係數]
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```
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## 🧮 **詳細算法設計**
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### **1. 難易度係數計算**
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```typescript
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interface DifficultyCalculation {
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wordLevel: CEFRLevel // 詞彙等級
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learnerLevel: CEFRLevel // 學習者程度
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wordFrequency: number // 詞彙使用頻率
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personalHistory: number // 個人歷史表現
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}
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function calculateDifficultyFactor(params: DifficultyCalculation): number {
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const levels = ['A1', 'A2', 'B1', 'B2', 'C1', 'C2']
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const wordIndex = levels.indexOf(params.wordLevel)
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const learnerIndex = levels.indexOf(params.learnerLevel)
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// 基礎難度差異
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const levelDifference = wordIndex - learnerIndex
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const baseFactor = 1.0 + (levelDifference * 0.15)
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// 詞頻調整（高頻詞較容易）
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const frequencyAdjustment = params.wordFrequency > 1000 ? -0.1 : 0.1
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// 個人歷史調整
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const historyAdjustment = (params.personalHistory - 0.7) * 0.2
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return Math.max(0.8, Math.min(2.2,
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baseFactor + frequencyAdjustment + historyAdjustment
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))
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}
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```
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### **2. 表現係數計算**
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```typescript
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interface PerformanceData {
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questionType: QuestionType
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isCorrect: boolean
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responseTime: number // 反應時間(秒)
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confidence: number // 信心程度(1-5)
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}
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function calculatePerformanceFactor(data: PerformanceData): number {
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let baseFactor: number
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switch (data.questionType) {
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case 'flipcard':
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// 翻卡題：根據信心程度
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const confidenceFactors = [0.5, 0.7, 1.0, 1.2, 1.4]
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baseFactor = confidenceFactors[data.confidence - 1]
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break
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case 'multiple_choice':
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case 'fill_blank':
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case 'listening':
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// 客觀題：正確/錯誤 + 反應時間
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if (data.isCorrect) {
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// 反應時間越快，表現越好
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const timeBonus = data.responseTime < 3 ? 0.1 :
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data.responseTime < 8 ? 0.0 : -0.1
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baseFactor = 1.1 + timeBonus
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} else {
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baseFactor = 0.6
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}
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break
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default:
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baseFactor = data.isCorrect ? 1.0 : 0.6
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}
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return Math.max(0.4, Math.min(1.5, baseFactor))
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}
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```
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### **3. 階段調整係數**
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```mermaid
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graph LR
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A[當前間隔] --> B{間隔階段}
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B -->|1-7天| C[初期階段<br/>係數: 1.8-2.2]
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B -->|8-30天| D[成長階段<br/>係數: 1.4-1.8]
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B -->|31-90天| E[穩定階段<br/>係數: 1.2-1.5]
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B -->|91-365天| F[熟練階段<br/>係數: 1.1-1.3]
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```
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```typescript
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function getStageAdjustment(currentInterval: number): number {
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if (currentInterval <= 7) return 2.0 // 初期快速增長
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if (currentInterval <= 30) return 1.6 // 成長期中等增長
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if (currentInterval <= 90) return 1.35 // 穩定期緩慢增長
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return 1.15 // 熟練期微調
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}
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```
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### **4. 完整間隔計算公式**
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```typescript
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function calculateNextInterval(params: {
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previousInterval: number
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difficulty: DifficultyCalculation
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performance: PerformanceData
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reviewCount: number
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}): number {
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const difficultyFactor = calculateDifficultyFactor(params.difficulty)
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const performanceFactor = calculatePerformanceFactor(params.performance)
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const stageAdjustment = getStageAdjustment(params.previousInterval)
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// 主要公式
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let nextInterval = params.previousInterval *
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difficultyFactor *
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performanceFactor *
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stageAdjustment
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// 最小間隔保護
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nextInterval = Math.max(1, nextInterval)
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// 最大間隔限制
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nextInterval = Math.min(365, nextInterval)
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// 四捨五入到整天
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return Math.round(nextInterval)
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}
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```
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## 📈 **熟悉程度計算重新設計**
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### **多維度熟悉度模型**
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```mermaid
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pie title 熟悉程度組成 (100%)
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"復習成功次數" : 40
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"當前間隔長度" : 25
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"正確率一致性" : 20
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"最近表現趨勢" : 15
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```
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```typescript
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function calculateMasteryLevel(params: {
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successfulReviews: number
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currentInterval: number
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totalReviews: number
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recentPerformance: number[] // 最近5次表現
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}): number {
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// 1. 成功次數分數 (40%)
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const successScore = Math.min(params.successfulReviews * 4, 40)
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// 2. 間隔長度分數 (25%)
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const intervalScore = Math.min((params.currentInterval / 365) * 25, 25)
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// 3. 一致性分數 (20%)
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const accuracy = params.totalReviews > 0 ?
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params.successfulReviews / params.totalReviews : 0
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const consistencyScore = accuracy * 20
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// 4. 趨勢分數 (15%)
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const recentAvg = params.recentPerformance.length > 0 ?
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params.recentPerformance.reduce((a, b) => a + b) / params.recentPerformance.length : 0.7
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const trendScore = recentAvg * 15
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return Math.min(100, Math.round(
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successScore + intervalScore + consistencyScore + trendScore
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))
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}
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```
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## 📅 **復習時間線對比**
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### **現有算法 vs 新算法**
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| 復習次數 | 現有算法 | 新算法(理想情況) | 新算法(困難詞彙) | 新算法(簡單詞彙) |
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|---------|---------|-----------------|-----------------|-----------------|
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| 1次成功 | 2天 | 2天 | 2天 | 3天 |
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| 2次成功 | 4天 | 4天 | 3天 | 6天 |
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| 3次成功 | 8天 | 7天 | 5天 | 12天 |
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| 4次成功 | 16天 | 12天 | 8天 | 24天 |
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| 5次成功 | 32天 | 21天 | 13天 | 42天 |
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| 6次成功 | 64天 | 35天 | 22天 | 75天 |
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| 7次成功 | 128天 | 60天 | 35天 | 130天 |
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| 8次成功 | 256天 | 95天 | 55天 | 200天 |
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| 9次成功 | 512天 | 145天 | 85天 | 300天 |
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| 10次成功 | 1024天 | 220天 | 130天 | 365天 |
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## 🎮 **答題表現評分系統**
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### **翻卡題評分流程**
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```mermaid
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graph TD
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A[顯示詞彙] --> B[用戶自我評估]
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B --> C{選擇信心程度}
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C -->|1| D[完全不記得<br/>係數: 0.5]
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C -->|2| E[有印象但不確定<br/>係數: 0.7]
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C -->|3| F[記得但需思考<br/>係數: 1.0]
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C -->|4| G[清楚記得<br/>係數: 1.2]
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C -->|5| H[非常熟悉<br/>係數: 1.4]
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D --> I[計算新間隔]
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E --> I
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F --> I
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G --> I
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H --> I
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```
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### **客觀題評分流程**
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```mermaid
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graph TD
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A[開始答題] --> B[記錄開始時間]
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B --> C[用戶選擇答案]
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C --> D[記錄結束時間]
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D --> E[計算反應時間]
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E --> F{答案正確?}
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F -->|正確| G[基礎係數: 1.1]
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F -->|錯誤| H[基礎係數: 0.6]
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G --> I{反應時間}
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I -->|< 3秒| J[快速正確<br/>+0.1獎勵]
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I -->|3-8秒| K[正常速度<br/>無調整]
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I -->|> 8秒| L[緩慢回答<br/>-0.1懲罰]
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H --> M[錯誤分析]
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M --> N[記錄錯題類型]
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J --> O[最終係數計算]
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K --> O
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L --> O
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N --> O
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```
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## 🔄 **完整學習循環**
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```mermaid
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sequenceDiagram
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participant U as 用戶
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participant S as 系統
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participant A as 算法引擎
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participant D as 資料庫
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U->>S: 開始今日復習
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S->>D: 查詢到期詞彙
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D->>S: 返回復習列表
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S->>A: 選擇復習題型
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A->>S: 返回題目配置
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loop 每個詞彙
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S->>U: 展示題目
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U->>S: 提交答案
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S->>A: 分析表現
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A->>A: 計算新間隔
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A->>A: 更新熟悉度
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A->>D: 保存復習記錄
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end
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S->>U: 復習完成報告
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```
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## 📋 **實作階段規劃**
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### **階段1: 基礎優化 (Week 1)**
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#### **目標**: 改進現有算法，保持系統穩定
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```typescript
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// 簡化版漸進算法
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function calculateNextIntervalV1(
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previousInterval: number,
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isCorrect: boolean,
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confidence: number = 3
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): number {
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let growthFactor: number
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// 階段性增長係數
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if (previousInterval <= 7) {
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growthFactor = 1.8 // 初期較快
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} else if (previousInterval <= 30) {
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growthFactor = 1.4 // 中期放緩
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} else {
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growthFactor = 1.2 // 後期緩慢
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}
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// 表現調整
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const performanceFactors = [0.5, 0.7, 1.0, 1.2, 1.4]
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const performanceFactor = isCorrect ?
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performanceFactors[confidence - 1] : 0.6
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const nextInterval = previousInterval * growthFactor * performanceFactor
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return Math.max(1, Math.min(365, Math.round(nextInterval)))
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}
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```
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### **階段2: 個人化增強 (Week 2-3)**
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#### **新增功能**:
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1. **詞彙難度分析**
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2. **學習者程度評估**
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3. **個人化係數調整**
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```typescript
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// 完整版算法
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class SpacedRepetitionEngine {
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calculateNextInterval(params: {
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flashcard: Flashcard
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learner: LearnerProfile
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performance: PerformanceData
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history: ReviewHistory[]
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}): number {
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const difficulty = this.analyzeDifficulty(params.flashcard, params.learner)
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const performance = this.analyzePerformance(params.performance)
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const trend = this.analyzeTrend(params.history)
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return this.computeInterval(difficulty, performance, trend)
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}
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}
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```
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### **階段3: 智能優化 (Week 4)**
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#### **高級功能**:
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1. **遺忘曲線預測**
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2. **最佳復習時機推薦**
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3. **學習效率分析**
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## 📈 **效果預測圖表**
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### **學習進度曲線對比**
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```
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熟悉程度 (%)
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100 | ╭─── 新算法
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| ╭───╯
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80 | ╭───╯
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| ╭───╯
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60 | ╭───╯
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|╭───╯
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40 |╯
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20 | ╭── 現有算法
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| ╭───╯
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0 +─────────────────────────→
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0 5 10 15 20 25 30 復習次數
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新算法特點:
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- 更平滑的進度曲線
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- 避免過早達到100%
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- 提供更多中間階段
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```
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### **復習間隔增長對比**
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```
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間隔天數
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400 |
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| ●── 現有算法 (過快)
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300 | ╱
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| ╱
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200 |╱
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100 | ╭──●──●──●── 新算法 (平滑)
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| ╱
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50 |╱
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0 +────────────────────→
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1 5 10 15 20 復習次數
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```
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## 🎯 **關鍵改進點**
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### **1. 更科學的增長曲線**
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- **初期**: 較快增長建立信心
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- **中期**: 穩定增長鞏固記憶
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- **後期**: 緩慢增長保持長期記憶
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### **2. 個人化學習路徑**
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```
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A1學習者 + C1詞彙 = 較慢增長 + 更多練習
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C1學習者 + A1詞彙 = 較快增長 + 適度練習
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```
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### **3. 智能錯誤恢復**
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```
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連續錯誤 → 重置到較短間隔
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偶爾錯誤 → 輕微調整
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長期正確 → 加速進展
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```
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## 🔧 **實作考量**
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### **資料庫設計調整**
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```sql
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-- 新增欄位到 Flashcard 表
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ALTER TABLE Flashcards ADD COLUMN EasinessFactor REAL DEFAULT 2.5;
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ALTER TABLE Flashcards ADD COLUMN ConsecutiveCorrect INTEGER DEFAULT 0;
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ALTER TABLE Flashcards ADD COLUMN LastPerformanceScore REAL DEFAULT 0.0;
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-- 新增復習記錄表
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CREATE TABLE ReviewSessions (
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Id TEXT PRIMARY KEY,
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FlashcardId TEXT,
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ReviewedAt DATETIME,
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QuestionType TEXT,
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IsCorrect BOOLEAN,
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ResponseTimeMs INTEGER,
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ConfidenceLevel INTEGER,
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PreviousInterval INTEGER,
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NewInterval INTEGER,
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FOREIGN KEY (FlashcardId) REFERENCES Flashcards(Id)
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);
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```
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### **API 設計**
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```typescript
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// 復習API
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POST /api/flashcards/{id}/review
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{
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questionType: 'flipcard' | 'multiple_choice' | 'fill_blank',
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isCorrect: boolean,
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responseTimeMs: number,
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confidenceLevel?: number, // 1-5, 僅翻卡題
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selectedAnswer?: string, // 客觀題的選擇
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}
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// 響應
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{
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success: boolean,
|
||
data: {
|
||
newInterval: number,
|
||
nextReviewDate: string,
|
||
masteryLevel: number,
|
||
improvementTip?: string
|
||
}
|
||
}
|
||
```
|
||
|
||
## 🧪 **測試與驗證計畫**
|
||
|
||
### **A/B測試設計**
|
||
1. **控制組**: 使用現有算法
|
||
2. **實驗組**: 使用新算法
|
||
3. **測試指標**:
|
||
- 學習完成率
|
||
- 長期記憶保持率
|
||
- 用戶滿意度
|
||
- 復習頻率合理性
|
||
|
||
### **參數調優策略**
|
||
1. **收集用戶數據** (2週)
|
||
2. **分析學習模式** (1週)
|
||
3. **調整算法參數** (1週)
|
||
4. **驗證效果** (2週)
|
||
|
||
這個設計提供了更科學、更個人化、更有效的復習時間管理系統！ |