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144 lines
4.3 KiB
Python
Executable file
144 lines
4.3 KiB
Python
Executable file
"""#
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### 谜题描述
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Andrey needs one more problem to conduct a programming contest. He has n friends who are always willing to help. He can ask some of them to come up with a contest problem. Andrey knows one value for each of his fiends — the probability that this friend will come up with a problem if Andrey asks him.
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Help Andrey choose people to ask. As he needs only one problem, Andrey is going to be really upset if no one comes up with a problem or if he gets more than one problem from his friends. You need to choose such a set of people that maximizes the chances of Andrey not getting upset.
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Input
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The first line contains a single integer n (1 ≤ n ≤ 100) — the number of Andrey's friends. The second line contains n real numbers pi (0.0 ≤ pi ≤ 1.0) — the probability that the i-th friend can come up with a problem. The probabilities are given with at most 6 digits after decimal point.
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Output
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Print a single real number — the probability that Andrey won't get upset at the optimal choice of friends. The answer will be considered valid if it differs from the correct one by at most 10 - 9.
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Examples
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Input
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4
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0.1 0.2 0.3 0.8
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Output
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0.800000000000
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Input
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2
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0.1 0.2
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Output
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0.260000000000
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Note
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In the first sample the best strategy for Andrey is to ask only one of his friends, the most reliable one.
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In the second sample the best strategy for Andrey is to ask all of his friends to come up with a problem. Then the probability that he will get exactly one problem is 0.1·0.8 + 0.9·0.2 = 0.26.
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Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
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```python
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m, y, n = input(), 0.0, 1.0
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for p in sorted(map(float, raw_input().split()))[::-1]:
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t = n*p + (1-p)*y
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if t > y: y, n = t, n*(1-p)
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print \"%.9f\" % y
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```
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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。
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"""
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from bootcamp import Basebootcamp
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from bootcamp import Basebootcamp
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import random
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import re
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class Bandreyandproblembootcamp(Basebootcamp):
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def __init__(self, min_n=1, max_n=100):
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self.min_n = min_n
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self.max_n = max_n
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def case_generator(self):
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n = random.randint(self.min_n, self.max_n)
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probs = [round(random.uniform(0, 1), 6) for _ in range(n)]
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sorted_probs = sorted(probs, reverse=True)
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optimal = 0.0
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none_fail = 1.0
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for p in sorted_probs:
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candidate = none_fail * p + (1 - p) * optimal
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if candidate > optimal:
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optimal = candidate
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none_fail *= (1 - p)
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return {
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"n": n,
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"probabilities": probs,
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"expected": optimal
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}
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@staticmethod
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def prompt_func(question_case) -> str:
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probs_str = ' '.join(f"{p:.6f}" for p in question_case["probabilities"])
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return f"""你是安德烈，需要选择一组朋友来最大化恰好得到一个问题的概率。请根据输入数据计算最大概率。
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规则：
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1. 选择任意数量的朋友，每个被选中的朋友独立以给定概率成功
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2. 只有当恰好一个朋友成功时，安德烈不会生气
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3. 需要选择最优的朋友组合使成功概率最大
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输入格式：
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第一行为整数n（朋友数量）
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第二行是n个实数（保留6位小数）
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示例输入1：
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4
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0.1 0.2 0.3 0.8
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示例输出1：
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0.800000000000
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示例输入2：
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2
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0.1 0.2
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示例输出2：
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0.260000000000
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当前问题：
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输入：
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{question_case['n']}
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{probs_str}
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请输出最大概率（必须包含至少9位小数），并将最终答案放在[answer]和[/answer]之间。例如：[answer]0.260000000000[/answer]"""
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@staticmethod
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def extract_output(output):
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matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
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if not matches:
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return None
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last_match = matches[-1].strip()
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try:
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# 处理科学计数法和多余字符
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cleaned = last_match.strip().rstrip('.').replace(',', '')
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return float(cleaned)
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except ValueError:
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return None
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@classmethod
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def _verify_correction(cls, solution, identity):
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if solution is None:
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return False
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try:
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sol = float(solution)
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expected = identity["expected"]
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return abs(sol - expected) <= 1e-9
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except:
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return False
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