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"""# 谜题训练场开发任务
## 任务概述
你是一位资深程序员我需要你帮我实现一个特定谜题的训练场环境类这个类继承自`Basebootcamp`用于生成谜题实例并验证解答
## 背景说明
我正在开发一系列谜题训练场每个训练场对应一个特定类型的谜题训练场类命名为`{PuzzleName}bootcamp`其中`PuzzleName`是谜题的名称
每个训练场类主要提供两个核心功能
1. 生成该谜题类型的问题实例
2. 验证用户对问题的回答是否正确
## 技术接口规范
### 类方法实现要求
```python
from bootcamp import Basebootcamp
class {PuzzleName}bootcamp(Basebootcamp):
def __init__(self, **params):
\"\"\"
请你自定义params以保存该puzzle相关的参数例如网格大小等参数配有默认值
\"\"\"
pass
def case_generator(self):
\"\"\"
生成谜题实例提示为保证谜题有解可以先生成结果再对结果处理得到谜题
返回一个可JSON序列化的字典避免包含set等无法通过json.dumps处理的数据结构
\"\"\"
pass
@staticmethod
def prompt_func(question_case) -> str:
\"\"\"
将case_generator生成的谜题实例转换为文本形式的问题问题中包含问题背景对谜题规则的介绍具体要解决的谜题实例期望最终答案的格式
例如你是xxxx请你解答yyyy规则如下yyyy最终答案放置在zzzzz
注意请参照提供的谜题描述进行复述规则应当描述详细包括任务背景具体任务操作规则对题目格式和答案格式的含义介绍等
参数:
question_case: 由case_generator生成的谜题实例
返回:
str: 格式化的问题字符串
注意:
1. 需考虑问题的格式以便后续能正确提取
2. 问题描述中应包含期望的答案格式说明以便后续能正确提取为了避免抽取时匹配出干扰项请要求模型将答案放在特定标签如双括号例如[[your answer here]]
\"\"\"
pass
@staticmethod
def extract_output(output):
\"\"\"
从LLM的回复中提取符合格式要求的答案如有多个请抽取最后一个避免使用re.search等只抽取第一个结果的方式
参数:
output: LLM的完整输出包含原始问题和回答
返回:
提取的答案若未找到符合格式的答案则返回None
\"\"\"
pass
@classmethod
def _verify_correction(cls, solution, identity):
\"\"\"
验证提取的答案是否正确注意一个问题可以能有多个解按照谜题规则进行检验不要直接匹配可能的答案
参数:
solution: extract_output提取的答案
identity: case_generator生成的谜题实例
返回:
bool: 答案是否正确
\"\"\"
pass
```
### 验证评分方法(基类已实现)
```python
@classmethod
def verify_score(cls, model_output, identity:dict, format_score=0.1) -> float:
\"\"\"
验证输出结果并评分
参数:
model_output: 模型的完整输出
identity: 谜题实例由case_generator生成
format_score: 答案格式正确时的基础分数
返回:
float: 评分结果0-1之间
\"\"\"
score = 0.
try:
extract_solution = cls.extract_output(model_output)
if extract_solution is None:
return score
else:
score = format_score # 格式正确时的基础分数
if cls._verify_correction(extract_solution, identity):
score = 1. # 答案完全正确时的满分
except Exception as e:
# 处理异常情况
pass
return score
```
### 使用示例
```python
# 初始化谜题训练场
bootcamp = Puzzlebootcamp()
# 生成谜题实例
case = bootcamp.case_generator()
# 将谜题转换为文本问题
prompt = Puzzlebootcamp.prompt_func(case)
# 获取LLM对问题的解答
response = get_response(prompt, \"LLM\")
# 从完整对话中提取答案
extracted_output = Puzzlebootcamp.extract_output(prompt + response)
# 验证答案并评分
score = Puzzlebootcamp.verify_score(extracted_output, case)
```
## 你的任务
请根据以下谜题描述谜题描述可能不完整请先结合你的知识澄清规则实现一个完整的谜题训练场类
### 谜题描述
AB=(A+3B)×(A+B)
A and B are integers.Example questions are as follows:
<example 0>
Compute 23.
Please ensure the answer is a single number and wrap it in double square brackets, like this: [[your answer]].
</example 0>
<example 1>
Compute 72.
Please ensure the answer is a single number and wrap it in double square brackets, like this: [[your answer]].
</example 1>
<example 2>
Compute 234.
Please ensure the answer is a single number and wrap it in double square brackets, like this: [[your answer]].
</example 2>
<example 3>
Compute 632.
Please ensure the answer is a single number and wrap it in double square brackets, like this: [[your answer]].
</example 3>
<example 4>
If X2=60, find X.
The answer should only be given as a number.
The answer may be negative; if so, write it in text format like '-5'.
If there is more than one answer, please separate them with 'or', e.g., 1 or 2.
Ensure that the final answer is wrapped in double square brackets, like this: [[1or2]].
</example 4>
<example 5>
If X5=200, find X.
The answer should only be given as a number.
The answer may be negative; if so, write it in text format like '-5'.
If there is more than one answer, please separate them with 'or', e.g., 1 or 2.
Ensure that the final answer is wrapped in double square brackets, like this: [[1or2]].
</example 5>
<example 6>
If 8X=187, find X.
The answer should only be given as a number.
If the answer is a fraction, write it in 'a/b' text format.Decimals are not allowed.
The answer may be negative; if so, write it in text format like '-5'.
If there is more than one answer, please separate them with 'or', e.g., 1 or 2.
Ensure that the final answer is wrapped in double square brackets, like this: [[1or2]].
</example 6>
<example 7>
If 5(X3)=63, find X.
The answer should only be given as a number.
If the answer contains a root sign, write it in the form \sqrt{x} (x is the number under the root sign).
The answer may be negative; if so, write it in text format like '-5'.
If there is more than one answer, please separate them with 'or', e.g., 1 or 2.
Ensure that the final answer is wrapped in double square brackets, like this: [[1or2]].
</example 7>
<example 8>
Now we make a little change to the rule. Define that A B = (xA + yB) × (A + B),x and y are parameters, Given that 7 2 = 180; 2 3 = 65, solve x and y.
Your answer should be in the format: x= an integer, y= an integer.
Please wrap the answer in double square brackets, like this: [[x=value,y=value]].
</example 8>
<example 9>
Now we make a little change to the rule. Define that A B = (A + 3B) × (xA + yB),x and y are parameters, Given that 7 2 = 208; 2 3 = 77 solve x and y.
Your answer should be in the format: x= an integer, y= an integer.
Please wrap the answer in double square brackets, like this: [[x=value,y=value]].
</example 9>
请完成上述谜题的训练场环境类实现包括所有必要的方法
"""
from bootcamp import Basebootcamp
import re
import random
from fractions import Fraction
from math import isclose
from bootcamp import Basebootcamp
class KorOperationUnicode25cbbootcamp(Basebootcamp):
def __init__(self, **params):
super().__init__(**params)
self.x = params.get('x', 1)
self.y = params.get('y', 3)
def case_generator(self):
problem_type = random.choices(
['compute', 'solve_x', 'solve_xy', 'nested_solve'],
weights=[5, 3, 1, 1],
k=1
)[0]
if problem_type == 'compute':
length = random.choice([2, 3])
numbers = [random.randint(-5, 5) for _ in range(length)]
return {
"type": "compute",
"expr": numbers,
"answer": self._compute_chain(numbers)
}
elif problem_type == 'solve_x':
eq_type = random.choice(["X○B=K", "A○X=K"])
x, y = self.x, self.y
if eq_type == "X○B=K":
B = random.choice([n for n in range(-5,6) if n != 0])
X1 = random.randint(-5, 5)
K = (x*X1 + y*B) * (X1 + B)
X2 = (-B*(x + y) - X1*y) // x
return {
"type": "solve_x",
"equation": f"X○{B} = {K}",
"solutions": sorted([X1, X2])
}
else:
A = random.randint(1, 5)
X1 = random.randint(-5, 5)
K = (x*A + y*X1) * (A + X1)
X2 = Fraction(-A*(x + y) - x*A, y)
return {
"type": "solve_x",
"equation": f"{A}○X = {K}",
"solutions": sorted([X1, float(X2)])
}
elif problem_type == 'solve_xy':
x = random.randint(-3, 3)
y = random.randint(-3, 3)
equations = []
for _ in range(2):
while True:
A, B = random.randint(1,5), random.randint(1,5)
if (A + B) != 0:
break
K = (A*x + B*y) * (A + B)
equations.append(f"{A}{B} = {K}")
return {
"type": "solve_xy",
"equations": equations,
"solution": (x, y)
}
elif problem_type == 'nested_solve':
# 生成有效嵌套方程A○(X○B)=C
A = random.randint(1, 5)
B = random.randint(1, 5)
X = random.randint(-5, 5)
# 计算内部表达式值
inner_val = self._compute_op(X, B, self.x, self.y)
# 计算最终结果C
C = self._compute_op(A, inner_val, self.x, self.y)
return {
"type": "nested_solve",
"equation": f"{A}○(X○{B}) = {C}",
"solution": X,
"params": (self.x, self.y),
"B": B,
"A": A
}
def _compute_chain(self, numbers):
res = numbers[0]
for n in numbers[1:]:
res = (self.x*res + self.y*n) * (res + n)
return res
@staticmethod
def _compute_op(a, b, x, y):
return (x*a + y*b) * (a + b)
@staticmethod
def prompt_func(case):
if case['type'] == 'compute':
expr = ''.join(map(str, case['expr']))
return (
f"计算表达式:{expr}\n"
"运算符○定义为A○B = (xA + yB)(A + B)其中x={x}y={y}\n"
"答案请用[[结果]]包裹,例如[[25]]"
).format(x=case.get('x',1), y=case.get('y',3))
elif case['type'] == 'solve_x':
return (
f"解方程:{case['equation']}\n"
"运算符○定义为A○B = (xA + yB)(A + B)其中x={x}y={y}\n"
"可能有多个解,答案格式:[[解1 or 解2]]\n"
"支持分数如5/3和负数示例[[-3/2 or 4]]"
).format(x=case.get('x',1), y=case.get('y',3))
elif case['type'] == 'solve_xy':
return (
"已知以下方程:\n" +
'\n'.join(case['equations']) +
"\n求参数x和y的值答案格式[[x=值,y=值]]"
)
elif case['type'] == 'nested_solve':
return (
f"解嵌套方程:{case['equation']}\n"
"运算符○定义为A○B = (xA + yB)(A + B)其中x={x}y={y}\n"
"答案用[[数值]]包裹,示例:[[5]]"
).format(x=case['params'][0], y=case['params'][1])
@staticmethod
def extract_output(text):
patterns = [
# 参数解
r'\[\[x\s*=\s*(-?\d+)\s*,\s*y\s*=\s*(-?\d+)\]\]',
# 带分数/根号的多解
r'\[\[((?:-?\d+/\d+|\d+|-\d+|\\sqrt{\d+})(?:\s+or\s+[-?\d+/\d+|\d+|\\sqrt{\d+}]+)+)\]\]',
# 单值解
r'\[\[(-?\d+/\d+|\d+|-\d+|\\sqrt{\d+})\]\]'
]
for pattern in patterns:
matches = re.findall(pattern, text)
if matches:
last_match = matches[-1]
if isinstance(last_match, tuple):
return f"x={last_match[0]},y={last_match[1]}"
return last_match
return None
@classmethod
def _verify_correction(cls, answer, case):
try:
if case['type'] == 'compute':
return int(answer) == case['answer']
elif case['type'] == 'solve_x':
expected = set(case['solutions'])
# 解析答案
parts = answer.split(' or ')
solutions = []
for p in parts:
if '/' in p:
solutions.append(float(Fraction(p)))
elif 'sqrt' in p:
solutions.append(eval(p.replace('\\sqrt', 'math.sqrt')))
else:
solutions.append(float(p))
# 允许浮点误差
return all(any(isclose(s, e, rel_tol=1e-9) for e in expected) for s in solutions) and len(solutions) == len(expected)
elif case['type'] == 'solve_xy':
x = int(re.search(r'x=(-?\d+)', answer).group(1))
y = int(re.search(r'y=(-?\d+)', answer).group(1))
return (x, y) == case['solution']
elif case['type'] == 'nested_solve':
X = float(answer)
# 验证嵌套计算
inner = cls._compute_op(X, case['B'], *case['params'])
final = cls._compute_op(case['A'], inner, *case['params'])
return isclose(final, int(case['equation'].split('=')[-1]), rel_tol=1e-9)
return False
except:
return False