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212 lines
6.2 KiB
Python
Executable file
212 lines
6.2 KiB
Python
Executable file
"""#
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### 谜题描述
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Mahmoud has an array a consisting of n integers. He asked Ehab to find another array b of the same length such that:
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* b is lexicographically greater than or equal to a.
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* bi ≥ 2.
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* b is pairwise coprime: for every 1 ≤ i < j ≤ n, bi and bj are coprime, i. e. GCD(bi, bj) = 1, where GCD(w, z) is the greatest common divisor of w and z.
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Ehab wants to choose a special array so he wants the lexicographically minimal array between all the variants. Can you find it?
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An array x is lexicographically greater than an array y if there exists an index i such than xi > yi and xj = yj for all 1 ≤ j < i. An array x is equal to an array y if xi = yi for all 1 ≤ i ≤ n.
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Input
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The first line contains an integer n (1 ≤ n ≤ 105), the number of elements in a and b.
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The second line contains n integers a1, a2, ..., an (2 ≤ ai ≤ 105), the elements of a.
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Output
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Output n space-separated integers, the i-th of them representing bi.
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Examples
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Input
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5
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2 3 5 4 13
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Output
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2 3 5 7 11
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Input
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3
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10 3 7
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Output
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10 3 7
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Note
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Note that in the second sample, the array is already pairwise coprime so we printed it.
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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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MAX_NUM = 2000000
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prime_str = ('2 3 5 7 11 13 17 19 23 29 '
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+ '31 37 41 43 47 53 59 61 67 71 '
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+ '73 79 83 89 97 101 103 107 109 113 '
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+ '127 131 137 139 149 151 157 163 167 173 '
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+ '179 181 191 193 197 199 211 223 227 229 '
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+ '233 239 241 251 257 263 269 271 277 281 '
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+ '283 293 307 311 313 317 '
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)
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prime_list = [int(p) for p in prime_str.split()]
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used = [False] * MAX_NUM
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n = input()
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a = list(map(int,raw_input().split()))
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def record(x):
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t = []
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for p in prime_list:
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if x % p == 0:
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while x % p == 0:
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x = x // p
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t.append(p)
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if x == 1:
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break
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if x != 1:
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t.append(x)
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for ti in t:
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for i in range(ti, MAX_NUM, ti):
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used[i] = True
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b = []
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for ai in a:
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if not used[ai]:
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b.append(ai)
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record(ai)
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else:
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temp = ai + 1
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while used[temp]:
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temp += 1
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b.append(temp)
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record(temp)
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break
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temp = 2
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while len(b) < len(a):
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while used[temp]:
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temp += 1
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b.append(temp)
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record(temp)
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print(' '.join(str(x) for x in b))
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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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from bootcamp import Basebootcamp
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class Dmahmoudandehabandanotherarrayconstructiontaskbootcamp(Basebootcamp):
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def __init__(self, max_n=10, max_ai=100):
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self.max_n = max_n
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self.max_ai = max_ai
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@staticmethod
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def generate_b(a):
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MAX_NUM = 2000000
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prime_str = ('2 3 5 7 11 13 17 19 23 29 '
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'31 37 41 43 47 53 59 61 67 71 '
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'73 79 83 89 97 101 103 107 109 113 '
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'127 131 137 139 149 151 157 163 167 173 '
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'179 181 191 193 197 199 211 223 227 229 '
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'233 239 241 251 257 263 269 271 277 281 '
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'283 293 307 311 313 317')
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prime_list = [int(p) for p in prime_str.split()]
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used = [False] * (MAX_NUM + 1)
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n = len(a)
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b = []
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def record(x):
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t = []
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tmp_x = x
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for p in prime_list:
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if tmp_x % p == 0:
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while tmp_x % p == 0:
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tmp_x = tmp_x // p
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t.append(p)
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if tmp_x == 1:
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break
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if tmp_x != 1:
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t.append(tmp_x)
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for ti in t:
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if ti > MAX_NUM:
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continue
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for i in range(ti, MAX_NUM + 1, ti):
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used[i] = True
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for ai in a:
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if ai <= MAX_NUM and not used[ai]:
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b.append(ai)
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record(ai)
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else:
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temp = ai + 1
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while temp <= MAX_NUM and used[temp]:
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temp += 1
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if temp > MAX_NUM:
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temp = ai + 1
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b.append(temp)
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record(temp)
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break # Break after first replacement
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temp = 2
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while len(b) < len(a):
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while temp <= MAX_NUM and used[temp]:
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temp += 1
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if temp > MAX_NUM:
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break
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b.append(temp)
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record(temp)
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temp += 1
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return b
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def case_generator(self):
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n = random.randint(1, self.max_n)
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a = [random.randint(2, self.max_ai) for _ in range(n)]
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expected_b = self.generate_b(a)
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return {
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'n': n,
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'a': a,
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'expected_b': expected_b
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}
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@staticmethod
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def prompt_func(question_case):
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a_str = ' '.join(map(str, question_case['a']))
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return (
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f"You are given an array a of {question_case['n']} integers. Your task is to construct the lexicographically smallest array b that meets the following conditions:\n\n"
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"1. The array b is lexicographically greater than or equal to a.\n"
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"2. Each element in b is at least 2.\n"
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"3. All elements in b are pairwise coprime (their GCD must be 1).\n\n"
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f"Input array a: {a_str}\n\n"
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"Output the space-separated elements of array b. Enclose your answer within [answer] and [/answer] tags."
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)
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@staticmethod
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def extract_output(output):
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import re
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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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try:
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return list(map(int, last_answer.split()))
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except:
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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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expected_b = identity.get('expected_b', [])
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return solution == expected_b
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