feat: implement SM-2 spaced repetition algorithm

Implements sm2_schedule() following Wozniak (1990):
- quality < 3: reset interval to 1, repetitions to 0
- quality >= 3: interval grows (1 → 6 → interval × ease_factor)
- ease_factor adjusts per quality, floored at 1.3

Author: prithaxdev

apps/api/app/algorithms/sm2.py

@@ -0,0 +1,57 @@
+"""SM-2 Spaced Repetition Algorithm.
+
+Reference: Wozniak, P.A. (1990). SuperMemo 2 algorithm.
+https://www.supermemo.com/en/archives1990-2015/english/ol/sm2
+"""
+
+
+def sm2_schedule(
+    quality: int,
+    repetitions: int,
+    ease_factor: float,
+    interval: int,
+) -> tuple[int, int, float]:
+    """Calculate the next review schedule using the SM-2 algorithm.
+
+    Args:
+        quality: Rating of recall quality from 0 to 5.
+                 0-2: complete failure / incorrect response
+                 3:   correct response with serious difficulty
+                 4:   correct response after hesitation
+                 5:   perfect response
+        repetitions: Number of times this item has been successfully recalled.
+        ease_factor: Difficulty multiplier, minimum 1.3. Default starts at 2.5.
+        interval: Current interval in days before the next review.
+
+    Returns:
+        A tuple of (new_interval, new_repetitions, new_ease_factor).
+    """
+    if not (0 <= quality <= 5):
+        raise ValueError(f"quality must be between 0 and 5, got {quality}")
+    if repetitions < 0:
+        raise ValueError(f"repetitions must be >= 0, got {repetitions}")
+    if ease_factor < 1.3:
+        raise ValueError(f"ease_factor must be >= 1.3, got {ease_factor}")
+    if interval < 1:
+        raise ValueError(f"interval must be >= 1, got {interval}")
+
+    if quality < 3:
+        # Forgot — reset progress
+        new_repetitions = 0
+        new_interval = 1
+    else:
+        # Remembered — advance schedule
+        new_repetitions = repetitions + 1
+
+        if repetitions == 0:
+            new_interval = 1
+        elif repetitions == 1:
+            new_interval = 6
+        else:
+            new_interval = round(interval * ease_factor)
+
+    # Adjust ease factor based on quality (applies regardless of pass/fail)
+    new_ease_factor = ease_factor + (0.1 - (5 - quality) * (0.08 + (5 - quality) * 0.02))
+    new_ease_factor = max(1.3, round(new_ease_factor, 4))
+
+    return new_interval, new_repetitions, new_ease_factor