refactor: extract utils to fix circular import and enable smart generator

backend/app/utils.py

@@ -0,0 +1,59 @@
+from typing import List, Dict, Any, Tuple
+
+def calc_metrics(numbers: List[int]) -> Dict[str, Any]:
+    nums = sorted(numbers)
+    s = sum(nums)
+    odd = sum(1 for x in nums if x % 2 == 1)
+    even = len(nums) - odd
+    mn, mx = nums[0], nums[-1]
+    rng = mx - mn
+
+    # 1-10, 11-20, 21-30, 31-40, 41-45
+    buckets = {
+        "1-10": 0,
+        "11-20": 0,
+        "21-30": 0,
+        "31-40": 0,
+        "41-45": 0,
+    }
+    for x in nums:
+        if 1 <= x <= 10:
+            buckets["1-10"] += 1
+        elif 11 <= x <= 20:
+            buckets["11-20"] += 1
+        elif 21 <= x <= 30:
+            buckets["21-30"] += 1
+        elif 31 <= x <= 40:
+            buckets["31-40"] += 1
+        else:
+            buckets["41-45"] += 1
+
+    return {
+        "sum": s,
+        "odd": odd,
+        "even": even,
+        "min": mn,
+        "max": mx,
+        "range": rng,
+        "buckets": buckets,
+    }
+
+def calc_recent_overlap(numbers: List[int], draws: List[Tuple[int, List[int]]], last_k: int) -> Dict[str, Any]:
+    """
+    draws: [(drw_no, [n1..n6]), ...] 오름차순
+    last_k: 최근 k회 기준 중복
+    """
+    if last_k <= 0:
+        return {"last_k": 0, "repeats": 0, "repeated_numbers": []}
+
+    recent = draws[-last_k:] if len(draws) >= last_k else draws
+    recent_set = set()
+    for _, nums in recent:
+        recent_set.update(nums)
+
+    repeated = sorted(set(numbers) & recent_set)
+    return {
+        "last_k": len(recent),
+        "repeats": len(repeated),
+        "repeated_numbers": repeated,
+    }