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156 lines
5.1 KiB
Python
Executable file
156 lines
5.1 KiB
Python
Executable file
"""#
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### 谜题描述
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The legend of the foundation of Vectorland talks of two integers x and y. Centuries ago, the array king placed two markers at points |x| and |y| on the number line and conquered all the land in between (including the endpoints), which he declared to be Arrayland. Many years later, the vector king placed markers at points |x - y| and |x + y| and conquered all the land in between (including the endpoints), which he declared to be Vectorland. He did so in such a way that the land of Arrayland was completely inside (including the endpoints) the land of Vectorland.
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Here |z| denotes the absolute value of z.
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Now, Jose is stuck on a question of his history exam: \"What are the values of x and y?\" Jose doesn't know the answer, but he believes he has narrowed the possible answers down to n integers a_1, a_2, ..., a_n. Now, he wants to know the number of unordered pairs formed by two different elements from these n integers such that the legend could be true if x and y were equal to these two values. Note that it is possible that Jose is wrong, and that no pairs could possibly make the legend true.
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Input
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The first line contains a single integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of choices.
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The second line contains n pairwise distinct integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9) — the choices Jose is considering.
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Output
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Print a single integer number — the number of unordered pairs \\{x, y\} formed by different numbers from Jose's choices that could make the legend true.
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Examples
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Input
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3
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2 5 -3
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Output
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2
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Input
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2
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3 6
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Output
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1
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Note
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Consider the first sample. For the pair \{2, 5\}, the situation looks as follows, with the Arrayland markers at |2| = 2 and |5| = 5, while the Vectorland markers are located at |2 - 5| = 3 and |2 + 5| = 7:
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<image>
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The legend is not true in this case, because the interval [2, 3] is not conquered by Vectorland. For the pair \{5, -3\} the situation looks as follows, with Arrayland consisting of the interval [3, 5] and Vectorland consisting of the interval [2, 8]:
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<image>
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As Vectorland completely contains Arrayland, the legend is true. It can also be shown that the legend is true for the pair \{2, -3\}, for a total of two pairs.
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In the second sample, the only pair is \{3, 6\}, and the situation looks as follows:
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<image>
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Note that even though Arrayland and Vectorland share 3 as endpoint, we still consider Arrayland to be completely inside of Vectorland.
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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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a = list(map(lambda x: abs(int(x)), raw_input().split()))
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a.sort()
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ans = 0
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from bisect import bisect_right
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for i in xrange(n):
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x = bisect_right(a, 2*a[i])
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ans += x - i - 1
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print ans
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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 bisect
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import random
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import re
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from bootcamp import Basebootcamp
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class Cataleoftwolandsbootcamp(Basebootcamp):
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def __init__(self, max_n=5, min_n=2, min_val=0, max_val=20, allow_negative=True):
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self.max_n = max_n
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self.min_n = min_n
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self.min_val = min_val
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self.max_val = max_val
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self.allow_negative = allow_negative
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def case_generator(self):
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n = random.randint(self.min_n, self.max_n)
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existing = set()
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a = []
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while len(a) < n:
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num = random.randint(self.min_val, self.max_val)
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if self.allow_negative and random.choice([True, False]):
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num *= -1
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if num not in existing:
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a.append(num)
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existing.add(num)
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return {'n': n, 'a': a}
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@staticmethod
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def prompt_func(question_case):
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a_list = question_case['a']
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a_str = ' '.join(map(str, a_list))
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return f"""You are tasked with solving a historical mathematics problem about Vectorland and Arrayland.
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**Problem Statement:**
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Two integers x and y form a valid pair if the Arrayland interval [min(|x|, |y|), max(|x|, |y|)] is fully contained within the Vectorland interval [min(|x−y|, |x+y|), max(|x−y|, |x+y|)].
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**Input Format:**
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- First line: Integer n (2 ≤ n ≤ 2×10^5)
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- Second line: n distinct integers (space-separated)
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**Sample Input 1:**
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3
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2 5 -3
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**Sample Output 1:**
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2
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**Your Input:**
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{question_case['n']}
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{a_str}
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Calculate the answer and put ONLY THE FINAL INTEGER within [answer] tags like: [answer]5[/answer]"""
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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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try:
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return int(matches[-1].strip())
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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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a = list(map(abs, identity['a']))
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a_sorted = sorted(a)
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n = identity['n']
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ans = 0
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for i in range(n):
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threshold = 2 * a_sorted[i]
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pos = bisect.bisect_right(a_sorted, threshold)
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ans += (pos - i - 1)
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return solution == ans
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