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161 lines
4.8 KiB
Python
Executable file
161 lines
4.8 KiB
Python
Executable file
"""#
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### 谜题描述
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On the math lesson a teacher asked each pupil to come up with his own lucky numbers. As a fan of number theory Peter chose prime numbers. Bob was more original. He said that number t is his lucky number, if it can be represented as:
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t = a2 + b2, where a, b are arbitrary positive integers.
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Now, the boys decided to find out how many days of the interval [l, r] (l ≤ r) are suitable for pair programming. They decided that the day i (l ≤ i ≤ r) is suitable for pair programming if and only if the number i is lucky for Peter and lucky for Bob at the same time. Help the boys to find the number of such days.
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Input
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The first line of the input contains integer numbers l, r (1 ≤ l, r ≤ 3·108).
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Output
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In the only line print the number of days on the segment [l, r], which are lucky for Peter and Bob at the same time.
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Examples
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Input
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3 5
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Output
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1
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Input
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6 66
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Output
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7
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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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f = lambda x: int(x**.5)+1
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h,z = map(bytearray,'1\0')
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L,R = map(int,raw_input().split())
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n = f(R); b = n/2*h; b[0] = 0
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for k in xrange(1,f(n)/2):
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if b[k]: p = 2*k+1; s = k*(p+1); b[s::p] = z*len(b[s::p])
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g = ((i*(i+1),2*i+1) for i,v in enumerate(b) if v)
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r = (R+3)/4*h; r[0] = 0
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for s,p in g:
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r[s::p] = z*len(r[s::p])
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print r.count(h,(L+2)/4)+(L<=2<=R)
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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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import random
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import re
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from math import isqrt
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from bootcamp import Basebootcamp
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class Cdoublehappinessbootcamp(Basebootcamp):
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def __init__(self, max_r=10**5):
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"""
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初始化训练场参数，默认最大右边界为1e5以保证生成效率
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:param max_r: 生成区间右端点最大值，默认为100000
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"""
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self.max_r = max_r
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def _sieve(self, l, r):
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"""高效生成区间[l, r]内的质数列表"""
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if r < 2:
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return []
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# 生成基础质数用于筛法
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limit = isqrt(r) + 1
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sieve = [True] * (limit + 1)
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sieve[0:2] = [False, False]
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for i in range(2, isqrt(limit) + 1):
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if sieve[i]:
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sieve[i*i : limit+1 : i] = [False] * len(sieve[i*i : limit+1 : i])
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base_primes = [i for i, prime in enumerate(sieve) if prime]
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# 区间筛法
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segment_size = r - l + 1
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sieve = [True] * segment_size
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for p in base_primes:
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start = max(p * p, ((l + p - 1) // p) * p)
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for i in range(start, r+1, p):
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sieve[i - l] = False
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# 处理小质数的平方
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for i in range(max(2, l), isqrt(r) + 1):
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if sieve[i - l]:
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for j in range(i*i, r+1, i):
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sieve[j - l] = False
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return [i + l for i in range(segment_size) if sieve[i]]
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def case_generator(self):
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"""生成随机区间案例并准确计算答案"""
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while True:
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# 生成有效区间
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l = random.randint(1, self.max_r - 1)
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r = random.randint(l, self.max_r)
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# 获取区间质数
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primes = self._sieve(l, r)
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# 计算有效质数数量
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valid_primes = [p for p in primes if p == 2 or p % 4 == 1]
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# 确保生成有效案例（可包含0个解）
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return {
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'l': l,
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'r': r,
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'answer': len(valid_primes)
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}
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@staticmethod
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def prompt_func(question_case) -> str:
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l = question_case['l']
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r = question_case['r']
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return f"""你是数学课代表，需要帮助Peter和Bob计算在区间[{l}, {r}]内同时满足两个条件的数字：
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1. Peter条件：必须是质数（只能被1和自身整除）
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2. Bob条件：可以表示为两个正整数的平方和（即存在a,b>0使得t=a²+b²）
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重要数学规则：
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- 根据费马定理，质数p可表示为两个平方数之和当且仅当p=2或p≡1(mod4)
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请逐步分析后输出准确答案，并将最终答案放在[answer]和[/answer]标签之间。
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例如：
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当输入为6 66时，正确质数是13,17,29,37,41,53,61，因此输出为7
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当前需要解决的输入：
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l = {l}, r = {r}
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请按照以下格式输出：
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[answer]答案数字[/answer]"""
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@staticmethod
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def extract_output(output):
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matches = re.findall(r'\[answer\]\s*(\d+)\s*\[/answer\]', output, re.IGNORECASE)
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if matches:
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try:
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return int(matches[-1])
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except ValueError:
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return None
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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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return solution == identity['answer']
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