feat(backend): leitner algorithm with tests

packages/backend/src/services/leitner.test.ts

@@ -0,0 +1,26 @@
+import { describe, it, expect } from 'vitest';
+import { applyResult, BOX_INTERVALS_SEC, MAX_BOX } from './leitner.js';
+
+describe('leitner.applyResult', () => {
+  const now = 1_000_000;
+
+  it('moves correct answer to next box and schedules due', () => {
+    const next = applyResult({ box: 1, correctCount: 0, incorrectCount: 0 }, 'correct', now);
+    expect(next.box).toBe(2);
+    expect(next.nextDueAt).toBe(now + BOX_INTERVALS_SEC[2]!);
+    expect(next.correctCount).toBe(1);
+  });
+
+  it('caps box at MAX_BOX on correct answer', () => {
+    const next = applyResult({ box: MAX_BOX, correctCount: 9, incorrectCount: 0 }, 'correct', now);
+    expect(next.box).toBe(MAX_BOX);
+    expect(next.nextDueAt).toBe(now + BOX_INTERVALS_SEC[MAX_BOX]!);
+  });
+
+  it('resets to box 1 on incorrect', () => {
+    const next = applyResult({ box: 4, correctCount: 3, incorrectCount: 1 }, 'incorrect', now);
+    expect(next.box).toBe(1);
+    expect(next.nextDueAt).toBe(now + BOX_INTERVALS_SEC[1]!);
+    expect(next.incorrectCount).toBe(2);
+  });
+});

packages/backend/src/services/leitner.ts

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+import type { AttemptResult } from '@flashcard/shared';
+
+export const MAX_BOX = 5;
+// index 1..5; index 0 unused
+export const BOX_INTERVALS_SEC: Record<number, number> = {
+  1: 0,
+  2: 1 * 24 * 60 * 60,
+  3: 3 * 24 * 60 * 60,
+  4: 7 * 24 * 60 * 60,
+  5: 14 * 24 * 60 * 60,
+};
+
+export interface ProgressLike {
+  box: number;
+  correctCount: number;
+  incorrectCount: number;
+}
+
+export interface ProgressDelta {
+  box: number;
+  correctCount: number;
+  incorrectCount: number;
+  nextDueAt: number;
+  lastShownAt: number;
+}
+
+export function applyResult(
+  current: ProgressLike,
+  result: AttemptResult,
+  nowSec: number
+): ProgressDelta {
+  let box = current.box;
+  let correctCount = current.correctCount;
+  let incorrectCount = current.incorrectCount;
+  if (result === 'correct') {
+    box = Math.min(MAX_BOX, current.box + 1);
+    correctCount += 1;
+  } else {
+    box = 1;
+    incorrectCount += 1;
+  }
+  return {
+    box,
+    correctCount,
+    incorrectCount,
+    nextDueAt: nowSec + BOX_INTERVALS_SEC[box]!,
+    lastShownAt: nowSec,
+  };
+}