feat(backend): leitner algorithm with tests

packages/backend/src/services/leitner.ts

@@ -0,0 +1,49 @@
+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,
+  };
+}