feat(lotto): grade_tickets 매칭 채점 + 등수 매핑

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

lotto/app/backtest.py

@@ -0,0 +1,103 @@
+"""로또 자가학습 백테스트 — 순수 연산 (FastAPI 의존성 0, Windows 이전 대비)."""
+import random
+from typing import Any, Dict, List, Optional, Tuple
+
+from .analyzer import build_analysis_cache, build_number_weights, score_combination
+from .utils import weighted_sample_6
+from .weight_evolver import count_match
+
+
+def grade_tickets(tickets: List[List[int]], winning6: List[int], bonus: int) -> Dict[str, Any]:
+    """티켓 묶음을 당첨번호로 채점 → 매칭 히스토그램 + 보너스 + best_match.
+    2등 판정: 5일치 AND 보너스 번호를 티켓이 포함."""
+    win = set(winning6)
+    hist = {"m3": 0, "m4": 0, "m5": 0, "m6": 0, "bonus_hits": 0}
+    best = 0
+    for t in tickets:
+        c = len(set(t) & win)
+        if c > best:
+            best = c
+        if c == 6:
+            hist["m6"] += 1
+        elif c == 5:
+            hist["m5"] += 1
+            if bonus in t:
+                hist["bonus_hits"] += 1
+        elif c == 4:
+            hist["m4"] += 1
+        elif c == 3:
+            hist["m3"] += 1
+    return {**hist, "best_match": best}
+
+
+def prize_counts(hist: Dict[str, Any]) -> Dict[str, int]:
+    """매칭 히스토그램 → 등수 카운트.
+    1등=m6, 2등=bonus_hits, 3등=m5−bonus_hits, 4등=m4, 5등=m3."""
+    return {
+        "1st": hist.get("m6", 0),
+        "2nd": hist.get("bonus_hits", 0),
+        "3rd": hist.get("m5", 0) - hist.get("bonus_hits", 0),
+        "4th": hist.get("m4", 0),
+        "5th": hist.get("m3", 0),
+    }
+
+
+def generate_pool(cache, number_weights, n: int = 20000,
+                  seed: Optional[int] = None) -> List[List[int]]:
+    """가중 샘플링으로 distinct 후보 풀 생성."""
+    if seed is not None:
+        random.seed(seed)
+    seen, pool = set(), []
+    attempts, cap = 0, n * 4
+    while len(pool) < n and attempts < cap:
+        attempts += 1
+        nums = tuple(sorted(weighted_sample_6(number_weights)))
+        if nums in seen:
+            continue
+        seen.add(nums)
+        pool.append(list(nums))
+    return pool
+
+
+def purchase_tickets(pool, cache, W: List[float], k: int) -> List[List[int]]:
+    """풀을 score_combination(·, W)로 랭킹 → 상위 k장 distinct."""
+    ranked = sorted(pool, key=lambda t: -score_combination(t, cache, W)["score_total"])
+    return ranked[:k]
+
+
+def random_null_tickets(k: int, seed: Optional[int] = None) -> List[List[int]]:
+    """무작위 distinct 티켓 k장 (null-model 대조군)."""
+    if seed is not None:
+        random.seed(seed)
+    seen, out = set(), []
+    while len(out) < k:
+        nums = tuple(sorted(random.sample(range(1, 46), 6)))
+        if nums in seen:
+            continue
+        seen.add(nums)
+        out.append(list(nums))
+    return out
+
+
+def coverage_tickets(k: int, seed: Optional[int] = None) -> List[List[int]]:
+    """greedy 커버리지 — 아직 덜 쓰인 번호를 우선 배치해 번호를 넓게 분산.
+    (휠링/보장설계는 향후. 현재는 distinct + 번호 사용 균등화)"""
+    if seed is not None:
+        random.seed(seed)
+    usage = {n: 0 for n in range(1, 46)}
+    seen, out = set(), []
+    guard = 0
+    while len(out) < k and guard < k * 50:
+        guard += 1
+        ranked = sorted(range(1, 46), key=lambda n: (usage[n], random.random()))
+        nums = tuple(sorted(ranked[:6]))
+        if nums in seen:
+            # 동점 흔들기: 약간 더 깊은 풀에서 샘플
+            nums = tuple(sorted(random.sample(ranked[:12], 6)))
+            if nums in seen:
+                continue
+        seen.add(nums)
+        out.append(list(nums))
+        for n in nums:
+            usage[n] += 1
+    return out