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262 lines
8.4 KiB
Python
Executable file
262 lines
8.4 KiB
Python
Executable file
"""#
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### 谜题描述
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Vasya has written some permutation p_1, p_2, …, p_n of integers from 1 to n, so for all 1 ≤ i ≤ n it is true that 1 ≤ p_i ≤ n and all p_1, p_2, …, p_n are different. After that he wrote n numbers next_1, next_2, …, next_n. The number next_i is equal to the minimal index i < j ≤ n, such that p_j > p_i. If there is no such j let's let's define as next_i = n + 1.
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In the evening Vasya went home from school and due to rain, his notebook got wet. Now it is impossible to read some written numbers. Permutation and some values next_i are completely lost! If for some i the value next_i is lost, let's say that next_i = -1.
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You are given numbers next_1, next_2, …, next_n (maybe some of them are equal to -1). Help Vasya to find such permutation p_1, p_2, …, p_n of integers from 1 to n, that he can write it to the notebook and all numbers next_i, which are not equal to -1, will be correct.
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Input
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The first line contains one integer t — the number of test cases (1 ≤ t ≤ 100 000).
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Next 2 ⋅ t lines contains the description of test cases,two lines for each. The first line contains one integer n — the length of the permutation, written by Vasya (1 ≤ n ≤ 500 000). The second line contains n integers next_1, next_2, …, next_n, separated by spaces (next_i = -1 or i < next_i ≤ n + 1).
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It is guaranteed, that the sum of n in all test cases doesn't exceed 500 000.
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In hacks you can only use one test case, so T = 1.
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Output
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Print T lines, in i-th of them answer to the i-th test case.
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If there is no such permutations p_1, p_2, …, p_n of integers from 1 to n, that Vasya could write, print the only number -1.
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In the other case print n different integers p_1, p_2, …, p_n, separated by spaces (1 ≤ p_i ≤ n). All defined values of next_i which are not equal to -1 should be computed correctly p_1, p_2, …, p_n using defenition given in the statement of the problem. If there exists more than one solution you can find any of them.
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Example
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Input
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6
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3
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2 3 4
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2
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3 3
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3
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-1 -1 -1
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3
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3 4 -1
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1
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2
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4
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4 -1 4 5
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Output
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1 2 3
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2 1
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2 1 3
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-1
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1
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3 2 1 4
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Note
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In the first test case for permutation p = [1, 2, 3] Vasya should write next = [2, 3, 4], because each number in permutation is less than next. It's easy to see, that it is the only satisfying permutation.
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In the third test case, any permutation can be the answer because all numbers next_i are lost.
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In the fourth test case, there is no satisfying permutation, so the answer is -1.
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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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import os
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import sys
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from atexit import register
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from io import BytesIO
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sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
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sys.stdout = BytesIO()
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register(lambda: os.write(1, sys.stdout.getvalue()))
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input = lambda: sys.stdin.readline().rstrip('\r\n')
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t=int(input())
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for u in xrange(t):
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n=int(input())
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a=list(map(int,input().split()))
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long=[]
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lens=0
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fucked=False
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for i in xrange(n):
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if a[i]==-1:
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if lens==0:
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a[i]=i+2
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else:
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a[i]=long[-1]
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else:
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if lens==0 or a[i]<long[-1]:
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long.append(a[i])
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lens+=1
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elif lens>0 and a[i]>long[-1]:
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fucked=True
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if lens>0:
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if i>=long[-1]-2:
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long.pop()
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lens-=1
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if fucked:
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print(-1)
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else:
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back={}
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for i in xrange(n+1):
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back[i+1]=[]
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for i in xrange(n):
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back[a[i]].append(i+1)
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perm=[0]*n
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q=[n+1]
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big=n
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while q!=[]:
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newq=[]
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for guy in q:
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for boi in back[guy]:
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perm[boi-1]=big
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big-=1
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newq+=back[guy]
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q=newq
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perm=[str(guy) for guy in perm]
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print(\" \".join(perm))
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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 Cpermutationrecoverybootcamp(Basebootcamp):
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def __init__(self, **params):
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self.min_n = params.get('min_n', 3)
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self.max_n = params.get('max_n', 6)
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self.prob_negative = params.get('prob_negative', 0.3)
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self.prob_invalid = params.get('prob_invalid', 0.3)
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@staticmethod
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def compute_next(p):
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n = len(p)
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next_list = [n + 1] * n
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stack = []
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for i in range(n):
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while stack and p[i] > p[stack[-1]]:
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j = stack.pop()
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next_list[j] = i + 1
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stack.append(i)
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return next_list
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@classmethod
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def _is_case_invalid(cls, n, next_list):
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long = []
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lens = 0
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fucked = False
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a = next_list.copy()
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for i in range(n):
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if a[i] == -1:
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a[i] = i+2 if lens == 0 else long[-1]
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current = a[i]
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if current != -1:
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if lens > 0 and current > long[-1]:
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fucked = True
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elif lens == 0 or current < long[-1]:
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long.append(current)
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lens += 1
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if lens > 0 and i >= (long[-1]-1):
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long.pop()
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lens -= 1
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return fucked
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def case_generator(self):
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generate_invalid = random.random() < self.prob_invalid
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for _ in range(10): # 多次尝试生成
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n = random.randint(self.min_n, self.max_n)
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p = list(range(1, n+1))
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random.shuffle(p)
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original_next = self.compute_next(p)
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case_next = [
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val if random.random() > self.prob_negative else -1
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for val in original_next
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]
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if not generate_invalid:
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return {'n': n, 'next': case_next}
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else:
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modified_next = case_next.copy()
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valid_modifications = [i for i in range(n) if modified_next[i] != -1]
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random.shuffle(valid_modifications)
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for idx in valid_modifications[:5]: # 最多尝试修改5个有效位置
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i_1based = idx + 1
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current_val = modified_next[idx]
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if random.random() < 0.5:
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# 设置为比i小的值或无效大值
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if current_val <= i_1based:
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continue
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new_val = random.randint(1, i_1based)
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else:
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new_val = random.randint(n+2, n+5)
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modified_next[idx] = new_val
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if self._is_case_invalid(n, modified_next):
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return {'n': n, 'next': modified_next}
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return {'n': n, 'next': case_next}
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return {'n': 3, 'next': [3,4,-1]} # fallback
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@staticmethod
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def prompt_func(question_case) -> str:
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n = question_case['n']
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next_list = question_case['next']
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problem = f"""给定一个长度{n}的next数组，其中-1表示信息丢失。请恢复原始排列，使得非-1的next值满足：
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- next_i是i之后第一个更大元素的最小下标(1-based)
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- 若无则设为{n+1}
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如果解不存在请输出-1。答案请放在[answer]标签内。
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输入：
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n={n}
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next={next_list}
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示例：当n=3且next=[2,3,4]时，排列应为[answer]1 2 3[/answer]"""
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return problem
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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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content = matches[-1].strip()
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if content == '-1':
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return -1
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try:
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return list(map(int, content.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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n = identity['n']
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next_list = identity['next']
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if solution == -1:
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return cls._is_case_invalid(n, next_list)
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if len(solution) != n or set(solution) != set(range(1, n+1)):
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return False
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computed_next = cls.compute_next(solution)
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for i in range(n):
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expected = next_list[i]
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if expected != -1 and computed_next[i] != expected:
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return False
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return True
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