#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ 生成/校验「骑士与无赖」(Knights and Knaves)谜题，并导出 puzzles.json。 每道谜题的每句话都用 csp_solver.py 里的结构化 DSL 表示(见该文件顶部说明)， 既能渲染成中文题面(给 LLM 看)，也能直接翻译成 python-constraint 约束来求解。 本脚本用 python-constraint 校验每题「解唯一」后才写出——这确保真值解无歧义， 同时演示了实验 5-2 的核心：把谜题形式化为 CSP 并用求解器离线求解。 约定：骑士(knight)永远说真话，无赖(knave)永远说假话。t[name]=True 表示骑士。 用法： python build_puzzles.py # 导出内置的 12 道精选谜题(默认) python build_puzzles.py --generate 20 # 随机生成 20 道解唯一的谜题 python build_puzzles.py --generate 20 --min-people 3 --max-people 5 --seed 7 python build_puzzles.py --output my.json # 指定输出文件 """ import argparse import json import random from csp_solver import render_nl, solve, solve_labeled # 每题：id, 名字列表, dict{name: 结构化陈述}。中文题面由结构化陈述自动渲染， # 但精选题保留手写的更自然的中文(见 STATEMENTS_NL 覆盖)。 CURATED = [ ("kk01", ["A", "B"], { "A": ["is", "B", "knave"], "B": ["and", ["is", "A", "knave"], ["is", "B", "knave"]]}), ("kk02", ["A", "B"], { "A": ["same", "A", "B"], "B": ["diff", "A", "B"]}), ("kk03", ["A", "B"], { "A": ["count", "knight", ">=", 1], "B": ["is", "A", "knave"]}), ("kk04", ["A", "B", "C"], { "A": ["is", "B", "knave"], "B": ["is", "C", "knave"], "C": ["and", ["is", "A", "knave"], ["is", "B", "knave"]]}), ("kk05", ["A", "B", "C"], { "A": ["is", "B", "knight"], "B": ["is", "C", "knave"], "C": ["same", "A", "B"]}), ("kk06", ["A", "B", "C"], { "A": ["same", "B", "C"], "B": ["is", "A", "knave"], "C": ["same", "C", "A"]}), ("kk07", ["A", "B", "C"], { "A": ["or", ["is", "A", "knave"], ["is", "B", "knight"]], "B": ["is", "A", "knight"], "C": ["is", "B", "knave"]}), ("kk08", ["A", "B", "C", "D"], { "A": ["same", "B", "D"], "B": ["is", "C", "knave"], "C": ["is", "D", "knight"], "D": ["diff", "B", "C"]}), ("kk09", ["A", "B", "C", "D"], { "A": ["is", "B", "knight"], "B": ["is", "C", "knave"], "C": ["is", "D", "knight"], "D": ["diff", "A", "B"]}), ("kk10", ["A", "B", "C", "D"], { "A": ["count", "knave", ">=", 3], "B": ["is", "A", "knave"], "C": ["is", "B", "knight"], "D": ["is", "C", "knave"]}), ("kk11", ["A", "B", "C", "D", "E"], { "A": ["is", "B", "knight"], "B": ["is", "C", "knave"], "C": ["is", "D", "knight"], "D": ["is", "E", "knave"], "E": ["count", "knight", ">=", 2]}), ("kk12", ["A", "B", "C", "D", "E"], { "A": ["is", "B", "knight"], "B": ["is", "C", "knave"], "C": ["is", "D", "knave"], "D": ["is", "E", "knight"], "E": ["same", "A", "C"]}), ] # 精选题的手写中文题面(比自动渲染更自然)。未覆盖的句子回退到 render_nl。 STATEMENTS_NL = { ("kk01", "B"): "我们两人都不是骑士。", ("kk02", "A"): "我和 B 是同一类人（要么都是骑士，要么都是无赖）。", ("kk02", "B"): "我和 A 是不同类人。", ("kk03", "A"): "我们当中至少有一个骑士。", ("kk04", "C"): "A 和 B 都是无赖。", ("kk06", "C"): "我和 A 是同一类人。", ("kk07", "A"): "我是无赖，或者 B 是骑士。", ("kk09", "D"): "A 和 B 不是同一类人。", ("kk10", "A"): "我们四人当中至少有三个无赖。", ("kk11", "E"): "我们五人当中至少有两个骑士。", ("kk12", "E"): "A 和 C 是同一类人。", } def build_puzzle(pid, names, structs, nl_overrides=None): """求解校验(要求解唯一)并组装成写入 puzzles.json 的一条记录。""" sols = solve_labeled(names, structs) if len(sols) != 1: raise ValueError(f"{pid} 解不唯一: {len(sols)} 个解 -> {sols}") solution = sols[0] nl_overrides = nl_overrides or {} statements = {n: nl_overrides.get(n, render_nl(structs[n])) for n in names} lines = [f"{n}: 「{statements[n]}」" for n in names] desc = ( f"这座岛上有 {len(names)} 位居民：{', '.join(names)}。" "每位居民要么是永远说真话的骑士(knight)，要么是永远说假话的无赖(knave)。" "他们各自说了如下的话：\n" + "\n".join(lines) ) return dict(id=pid, num_people=len(names), names=names, statements=statements, statements_struct=structs, description=desc, solution=solution) # ---------------- 随机生成器 ---------------- def _random_stmt(speaker, names, rng): """为 speaker 随机生成一句合法的结构化陈述。""" others = [n for n in names if n != speaker] # Solo resident: only count statements are valid (no "others" to name). if not others: role = rng.choice(["knight", "knave"]) op = rng.choice([">=", "<=", "=="]) return ["count", role, op, rng.randint(1, len(names))] kind = rng.choice(["is", "is", "same", "diff", "count"]) if kind == "is": return ["is", rng.choice(others), rng.choice(["knight", "knave"])] if kind == "same": return ["same", speaker, rng.choice(others)] if kind == "diff": return ["diff", speaker, rng.choice(others)] # count：全体中某角色的人数满足某比较 role = rng.choice(["knight", "knave"]) op = rng.choice([">=", "<=", "=="]) k = rng.randint(1, len(names)) return ["count", role, op, k] def generate(count, min_people, max_people, seed): """随机生成 count 道「解唯一」的谜题(用 python-constraint 过滤)。""" rng = random.Random(seed) names_pool = ["A", "B", "C", "D", "E", "F", "G"] puzzles = [] attempts = 0 while len(puzzles) < count and attempts < count * 2000: attempts += 1 n = rng.randint(min_people, max_people) names = names_pool[:n] structs = {sp: _random_stmt(sp, names, rng) for sp in names} if len(solve(names, structs)) != 1: # 只保留解唯一的谜题 continue pid = f"gen{len(puzzles) + 1:03d}" puzzles.append(build_puzzle(pid, names, structs)) if len(puzzles) < count: print(f"警告：{attempts} 次尝试只生成了 {len(puzzles)}/{count} 道解唯一的谜题。") return puzzles def build_curated(): out = [] for pid, names, structs in CURATED: nl = {n: STATEMENTS_NL[(pid, n)] for n in names if (pid, n) in STATEMENTS_NL} out.append(build_puzzle(pid, names, structs, nl)) return out def main(): ap = argparse.ArgumentParser( description="生成/校验骑士与无赖谜题并导出 puzzles.json" "（用 python-constraint 离线求解，校验每题解唯一）", formatter_class=argparse.RawDescriptionHelpFormatter, epilog=__doc__) ap.add_argument("--generate", type=int, metavar="N", default=0, help="随机生成 N 道解唯一的谜题(默认 0=导出内置 12 道精选题)") ap.add_argument("--min-people", type=int, default=2, help="随机生成时每题最少居民数(默认 2)") ap.add_argument("--max-people", type=int, default=5, help="随机生成时每题最多居民数(难度上限，默认 5)") ap.add_argument("--seed", type=int, default=42, help="随机种子，保证可复现(默认 42)") ap.add_argument("--output", default="puzzles.json", help="输出文件路径(默认 puzzles.json)") args = ap.parse_args() if args.generate > 0: print(f"随机生成 {args.generate} 道谜题" f"({args.min_people}~{args.max_people} 人，seed={args.seed})...") out = generate(args.generate, args.min_people, args.max_people, args.seed) else: out = build_curated() for p in out: print(f"{p['id']}: OK 唯一解 = {p['solution']}") with open(args.output, "w", encoding="utf-8") as f: json.dump(out, f, ensure_ascii=False, indent=2) print(f"\n已写出 {len(out)} 题到 {args.output}") if __name__ == "__main__": main()