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187 lines
5.9 KiB
Python
Executable file
187 lines
5.9 KiB
Python
Executable file
"""#
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### 谜题描述
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There are n piles of stones, where the i-th pile has a_i stones. Two people play a game, where they take alternating turns removing stones.
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In a move, a player may remove a positive number of stones from the first non-empty pile (the pile with the minimal index, that has at least one stone). The first player who cannot make a move (because all piles are empty) loses the game. If both players play optimally, determine the winner of the game.
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Input
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The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 2t lines contain descriptions of test cases.
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The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of piles.
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The second line of each test case contains n integers a_1,…,a_n (1≤ a_i≤ 10^9) — a_i is equal to the number of stones in the i-th pile.
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It is guaranteed that the sum of n for all test cases does not exceed 10^5.
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Output
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For each test case, if the player who makes the first move will win, output \"First\". Otherwise, output \"Second\".
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Example
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Input
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7
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3
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2 5 4
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8
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1 1 1 1 1 1 1 1
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6
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1 2 3 4 5 6
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6
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1 1 2 1 2 2
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1
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1000000000
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5
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1 2 2 1 1
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3
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1 1 1
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Output
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First
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Second
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Second
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First
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First
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Second
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First
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Note
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In the first test case, the first player will win the game. His winning strategy is:
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1. The first player should take the stones from the first pile. He will take 1 stone. The numbers of stones in piles will be [1, 5, 4].
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2. The second player should take the stones from the first pile. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 5, 4].
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3. The first player should take the stones from the second pile because the first pile is empty. He will take 4 stones. The numbers of stones in piles will be [0, 1, 4].
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4. The second player should take the stones from the second pile because the first pile is empty. He will take 1 stone because he can't take any other number of stones. The numbers of stones in piles will be [0, 0, 4].
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5. The first player should take the stones from the third pile because the first and second piles are empty. He will take 4 stones. The numbers of stones in piles will be [0, 0, 0].
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6. The second player will lose the game because all piles will be empty.
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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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T = int(raw_input())
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for _ in range(T):
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N = int(raw_input())
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stones = [int(v) for v in raw_input().split()]
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winner = N % 2
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for i in range(N):
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if stones[i] > 1:
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winner = (i+1) % 2
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break
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if winner == 0:
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print('Second')
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else:
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print('First')
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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 re
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import random
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from bootcamp import Basebootcamp
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class Bsequentialnimbootcamp(Basebootcamp):
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def __init__(self, min_n=1, max_n=10**5, min_a=1, max_a=10**9, case_type='mixed'):
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self.params = {
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'min_n': max(1, min_n),
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'max_n': max(min_n, max_n),
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'min_a': max(1, min_a),
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'max_a': max(min_a, max_a),
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'case_type': case_type
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}
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def case_generator(self):
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params = self.params
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n = random.randint(params['min_n'], params['max_n'])
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case_type = params['case_type']
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if case_type == 'all_ones':
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a = [1] * n
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elif case_type == 'first_gt1':
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first_gt1 = random.randint(0, n-1)
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a = self._generate_piles_with_key(n, first_gt1)
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else:
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if random.random() < 0.3:
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a = [1] * n
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else:
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first_gt1 = random.randint(0, n-1)
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a = self._generate_piles_with_key(n, first_gt1)
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return {'n': n, 'a': a}
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def _generate_piles_with_key(self, n, key_index):
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a = []
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for _ in range(key_index):
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a.append(1)
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a.append(random.randint(2, self.params['max_a']))
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for _ in range(n - key_index -1):
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a.append(random.randint(1, self.params['max_a']))
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return a
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@staticmethod
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def prompt_func(question_case) -> str:
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input_data = {
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't': 1,
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'n': question_case['n'],
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'a': question_case['a']
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}
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return """## 石子游戏胜负判断
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### 游戏规则
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双方玩家轮流操作，每次必须从第一个非空石堆中取至少一个石子。无法操作者输。胜负判定规则：
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1. 找到第一个石子数>1的石堆（从第1堆开始检查）
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2. 若存在：
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- 该堆位置为奇数 → 先手胜（First）
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- 位置为偶数 → 后手胜（Second）
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3. 若不存在（全为1）：
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- 总堆数奇数 → 先手胜
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- 总堆数偶数 → 后手胜
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### 输入格式
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{t}
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{n}
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{a_vals}
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### 输出要求
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1. 严格按规则分析
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2. 最终答案用[answer]标签包裹，如：[answer]First[/answer]
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请逐步分析当前测试用例：""".format(
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t=input_data['t'],
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n=input_data['n'],
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a_vals=' '.join(map(str, input_data['a']))
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)
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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.I)
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if not matches:
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return None
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last_match = matches[-1].strip().upper()
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return 'First' if last_match.startswith('F') else 'Second'
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@classmethod
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def _verify_correction(cls, solution, identity):
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try:
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n = identity['n']
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a = identity['a']
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gt1_index = next((i for i, x in enumerate(a) if x > 1), None)
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if gt1_index is not None:
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correct = 'First' if (gt1_index % 2 == 0) else 'Second'
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else:
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correct = 'First' if (n % 2 == 1) else 'Second'
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return str(solution).strip().upper() == correct.upper()
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except:
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return False
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