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136 lines
4.2 KiB
Python
Executable file
136 lines
4.2 KiB
Python
Executable file
"""#
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### 谜题描述
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Vladik and Chloe decided to determine who of them is better at math. Vladik claimed that for any positive integer n he can represent fraction <image> as a sum of three distinct positive fractions in form <image>.
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Help Vladik with that, i.e for a given n find three distinct positive integers x, y and z such that <image>. Because Chloe can't check Vladik's answer if the numbers are large, he asks you to print numbers not exceeding 109.
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If there is no such answer, print -1.
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Input
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The single line contains single integer n (1 ≤ n ≤ 104).
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Output
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If the answer exists, print 3 distinct numbers x, y and z (1 ≤ x, y, z ≤ 109, x ≠ y, x ≠ z, y ≠ z). Otherwise print -1.
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If there are multiple answers, print any of them.
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Examples
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Input
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3
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Output
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2 7 42
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Input
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7
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Output
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7 8 56
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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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n = int(raw_input())
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z = 0
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if(n==1):
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print -1
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else:
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for x in xrange(2,1000000001):
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for y in xrange(x+1,1000000001):
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if((1/float(x)+1/float(y))>=2/float(n)):
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break
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z = float(n*x*y)/float(2*x*y-n*y-n*x)
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if z==float(int(z)) and z!=x and z!=y:
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print x, y, int(z)
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break
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else:
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if(z<y):
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z = 0
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break
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z = 0
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if(z>0):
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break
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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 Cvladikandfractionsbootcamp(Basebootcamp):
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def __init__(self, **params):
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super().__init__(**params) # 显式调用基类初始化
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self.max_n = params.get('max_n', 10000) # 默认上限为10^4
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def case_generator(self):
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# 生成n的范围为1到max_n，包含所有可能的问题实例
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# 当n=1时答案应为-1，其他n≥2根据题目逻辑应有解
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n = random.randint(1, self.max_n)
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return {"n": n}
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@staticmethod
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def prompt_func(question_case):
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n = question_case["n"]
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problem_text = (
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f"Vladik and Chloe are determining who is better at math. Vladik claims that for any positive integer n, "
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f"the fraction 2/n can be expressed as the sum of three distinct positive unit fractions. Help Vladik prove this "
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f"by finding three distinct positive integers x, y, z such that 1/x + 1/y + 1/z = 2/{n}. The numbers x, y, z must "
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f"not exceed 1e9. If it's impossible, output -1.\n\n"
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"Provide your answer as three space-separated integers or -1 enclosed within [answer] and [/answer] tags. "
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"Example: [answer]2 7 42[/answer] or [answer]-1[/answer] if no solution exists."
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)
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return problem_text
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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_answer = matches[-1].strip()
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if last_answer == '-1':
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return -1
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parts = last_answer.split()
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if len(parts) != 3:
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return None
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try:
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x, y, z = map(int, parts)
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return (x, y, z)
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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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n = identity["n"]
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if n == 1:
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return solution == -1 # n=1时只有-1正确
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else:
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# 其他n必须返回有效三元组
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if solution == -1:
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return False # n≥2时不接受-1
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if not isinstance(solution, tuple) or len(solution) != 3:
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return False
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x, y, z = solution
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if x <= 0 or y <= 0 or z <= 0:
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return False
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if x > 1e9 or y > 1e9 or z > 1e9:
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return False
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if x == y or x == z or y == z:
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return False
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# 关键数学验证：n(xy + yz + zx) == 2xyz
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left = n * (x * y + y * z + z * x)
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right = 2 * x * y * z
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return left == right
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