| """Original corpus and exact scoring; MIT. Generated problem corpus: CC0-1.0.""" |
| import itertools |
| import json |
| import random |
| import re |
| from pathlib import Path |
|
|
| ROOT = Path(__file__).resolve().parent |
| SEED = 20260912 |
|
|
|
|
| def enumerate_optimum(items, capacity): |
| best, winners = -1, [] |
| for mask in itertools.product((0, 1), repeat=len(items)): |
| chosen = [x for x, take in zip(items, mask) if take] |
| if sum(x['weight'] for x in chosen) > capacity: |
| continue |
| value = sum(x['value'] for x in chosen) |
| ids = [x['id'] for x in chosen] |
| if value > best: |
| best, winners = value, [ids] |
| elif value == best: |
| winners.append(ids) |
| return best, winners |
|
|
|
|
| def dp_optimum(items, capacity): |
| dp = [0] * (capacity + 1) |
| for item in items: |
| for c in range(capacity, item['weight'] - 1, -1): |
| dp[c] = max(dp[c], dp[c - item['weight']] + item['value']) |
| return dp[capacity] |
|
|
|
|
| def make_corpus(): |
| rng = random.Random(SEED) |
| families, attempts = [], 0 |
| while len(families) < 4: |
| attempts += 1 |
| if attempts > 10000: |
| raise RuntimeError('Corpus selection did not converge') |
| items = [dict(id=chr(65+i), weight=rng.randint(2, 9), value=rng.randint(3, 24)) for i in range(6)] |
| capacity = sum(x['weight'] for x in items) // 2 |
| a, b = [enumerate_optimum(items, c) for c in (capacity, capacity+1)] |
| if len(a[1]) != 1 or len(b[1]) != 1 or a[0] == b[0]: |
| continue |
| families.append((items, capacity)) |
| cases = [] |
| for family, (items, base) in enumerate(families, 1): |
| for increment in (0, 1): |
| capacity = base + increment |
| optimum, sets = enumerate_optimum(items, capacity) |
| assert optimum == dp_optimum(items, capacity) |
| for lang in ('en', 'zh'): |
| if lang == 'en': |
| text = f'Select a subset of these six indivisible items. Each item may be selected at most once. Total weight must be at most {capacity}. Maximize total value.\nID | weight | value\n' |
| tail = '\nExplain your calculation briefly, then give exactly one final line using this format (example only): FINAL_JSON: {"value": 12, "items": ["A", "C"]}. Report the maximum value and one optimal subset.' |
| else: |
| text = f'从以下六个不可分割的物品中选择一个子集。每个物品最多选一次，总重量不能超过{capacity}。请使总价值最大。\n编号 | 重量 | 价值\n' |
| tail = '\n简要说明计算过程，然后严格用以下格式给出唯一的最终行（仅为格式示例）：FINAL_JSON: {"value": 12, "items": ["A", "C"]}。报告最大价值和一个最优子集。' |
| text += '\n'.join(f"{x['id']} | {x['weight']} | {x['value']}" for x in items) |
| cases.append(dict(id=f'f{family}-c{increment}-{lang}', family=family, increment=increment, language=lang, items=items, capacity=capacity, optimum=optimum, optimal_sets=sets, prompt=text+tail)) |
| return dict(seed=SEED, rejected_candidates=attempts-4, cases=cases) |
|
|
|
|
| def score(case, text, thinking, truncated): |
| result = dict(strict_correct=False, parsed=False, feasible=False, value_consistent=False, optimal=False, truncated=truncated) |
| if thinking and '</think>' not in text: |
| return {**result, 'reason': 'no_final_channel'} |
| final = text.rsplit('</think>', 1)[-1] |
| markers = list(re.finditer(r'(?m)^\s*FINAL_JSON:\s*', final)) |
| if len(markers) != 1: |
| return {**result, 'reason': 'missing_or_ambiguous_marker'} |
| try: |
| answer, end = json.JSONDecoder().raw_decode(final[markers[0].end():]) |
| suffix = final[markers[0].end()+end:].strip() |
| if suffix not in ('', '```'): |
| raise ValueError('trailing content') |
| if not isinstance(answer, dict) or set(answer) != {'value', 'items'}: |
| raise ValueError('schema') |
| ids = answer['items'] |
| if type(answer['value']) is not int or not isinstance(ids, list) or not all(isinstance(x, str) for x in ids): |
| raise ValueError('types') |
| lookup = {x['id']:x for x in case['items']} |
| if len(ids) != len(set(ids)) or not set(ids) <= set(lookup): |
| raise ValueError('invalid or repeated ID') |
| except (ValueError, TypeError) as exc: |
| return {**result, 'reason': 'invalid_final_json: '+str(exc)} |
| weight = sum(lookup[x]['weight'] for x in ids) |
| value = sum(lookup[x]['value'] for x in ids) |
| result.update(parsed=True, answer=answer, actual_weight=weight, actual_value=value, |
| feasible=weight<=case['capacity'], value_consistent=value==answer['value'], optimal=value==case['optimum']) |
| result['strict_correct'] = all(result[x] for x in ('feasible', 'value_consistent', 'optimal')) and not truncated |
| result['reason'] = 'correct' if result['strict_correct'] else ('budget_exhausted' if truncated else 'incorrect_solution') |
| return result |
|
|
|
|
| if __name__ == '__main__': |
| target = ROOT/'corpus.json' |
| data = json.dumps(make_corpus(), ensure_ascii=False, indent=2)+'\n' |
| if target.exists() and target.read_text(encoding='utf-8') != data: |
| raise SystemExit('Existing corpus differs; refusing to overwrite') |
| target.write_text(data, encoding='utf-8') |
| print(f'{len(make_corpus()["cases"])} prompts written; enumeration agrees with independent DP') |
|
|
