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201 lines
5.3 KiB
Python
Executable file
201 lines
5.3 KiB
Python
Executable file
"""#
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### 谜题描述
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To become the king of Codeforces, Kuroni has to solve the following problem.
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He is given n numbers a_1, a_2, ..., a_n. Help Kuroni to calculate ∏_{1≤ i<j≤ n} |a_i - a_j|. As result can be very big, output it modulo m.
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If you are not familiar with short notation, ∏_{1≤ i<j≤ n} |a_i - a_j| is equal to |a_1 - a_2|⋅|a_1 - a_3|⋅ ... ⋅|a_1 - a_n|⋅|a_2 - a_3|⋅|a_2 - a_4|⋅ ... ⋅|a_2 - a_n| ⋅ ... ⋅ |a_{n-1} - a_n|. In other words, this is the product of |a_i - a_j| for all 1≤ i < j ≤ n.
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Input
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The first line contains two integers n, m (2≤ n ≤ 2⋅ 10^5, 1≤ m ≤ 1000) — number of numbers and modulo.
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The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).
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Output
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Output the single number — ∏_{1≤ i<j≤ n} |a_i - a_j| mod m.
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Examples
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Input
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2 10
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8 5
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Output
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3
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Input
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3 12
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1 4 5
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Output
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0
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Input
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3 7
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1 4 9
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Output
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1
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Note
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In the first sample, |8 - 5| = 3 ≡ 3 mod 10.
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In the second sample, |1 - 4|⋅|1 - 5|⋅|4 - 5| = 3⋅ 4 ⋅ 1 = 12 ≡ 0 mod 12.
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In the third sample, |1 - 4|⋅|1 - 9|⋅|4 - 9| = 3 ⋅ 8 ⋅ 5 = 120 ≡ 1 mod 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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from collections import defaultdict as dd, Counter, OrderedDict as od, deque
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from itertools import combinations as comb, permutations as perm
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from functools import reduce
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from math import log, ceil, floor
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from fractions import gcd
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import os, sys
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#sys.stdin = open(\"pb.txt\", \"r\")
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raw_input = sys.stdin.readline
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int_input = lambda : int(raw_input())
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list_input = lambda : list(raw_input().strip())
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explode_input = lambda sep :raw_input().split(sep)
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format_input = lambda object : map(object, raw_input().split())
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n, m = format_input(int)
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a = format_input(int)
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if n > m:
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print 0
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else:
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cum = 1
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n_itr1 = 0
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while cum > 0 and n_itr1 < n:
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for n_itr2 in xrange(n_itr1 + 1, n):
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cum = (cum * abs(a[n_itr1] - a[n_itr2])) % m
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n_itr1 += 1
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print cum
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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 collections import defaultdict
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from bootcamp import Basebootcamp
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class Ckuroniandimpossiblecalculationbootcamp(Basebootcamp):
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def __init__(self, **params):
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self.min_n = params.get('min_n', 2)
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self.max_n = params.get('max_n', 20)
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self.min_m = params.get('min_m', 1)
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self.max_m = params.get('max_m', 1000)
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self.a_min = params.get('a_min', 0)
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self.a_max = params.get('a_max', 10**9)
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self.n_gt_m_prob = params.get('n_gt_m_prob', 0.5)
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def case_generator(self):
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if random.random() < self.n_gt_m_prob:
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# 确保m的取值范围适配当前max_n
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m_upper = min(self.max_m, self.max_n-1)
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if m_upper < self.min_m:
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m = self.max_n # 当无法满足则转为生成n <= m模式
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n = random.randint(self.min_n, min(self.max_n, m))
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else:
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m = random.randint(self.min_m, m_upper)
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n = random.randint(m+1, self.max_n)
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a = [random.randint(self.a_min, self.a_max) for _ in range(n)]
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return {
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'n': n,
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'm': m,
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'a': a,
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'expected': 0
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}
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else:
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# 生成n <= m的案例
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m = random.randint(self.min_m, self.max_m)
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n = random.randint(self.min_n, min(self.max_n, m))
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mods = defaultdict(int)
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duplicates = False
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a = []
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for _ in range(n):
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val = random.randint(self.a_min, self.a_max)
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mod = val % m
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if mods[mod] >= 1:
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duplicates = True
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mods[mod] += 1
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a.append(val)
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expected = 0 if duplicates else self._safe_compute(n, m, a)
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return {
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'n': n,
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'm': m,
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'a': a,
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'expected': expected
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}
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def _safe_compute(self, n, m, a):
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"""安全计算模式（限制n不超过100）"""
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if n > 100:
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return 0
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product = 1
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for i in range(n):
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for j in range(i+1, n):
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product = (product * abs(a[i]-a[j])) % m
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return product
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@staticmethod
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def prompt_func(question_case) -> str:
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input_case = f"{question_case['n']} {question_case['m']}\n{' '.join(map(str, question_case['a']))}"
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return f"""编程竞赛题目：
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计算所有两两绝对差值的乘积模m
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输入格式：
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第一行：n m（2≤n≤2e5，1≤m≤1000）
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第二行：a_1 a_2 ... a_n（0≤a_i≤1e9）
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示例说明：
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当n>m时结果为0，否则计算各对差值的乘积取模
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当前题目：
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输入：
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{input_case}
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请将最终答案用[answer]标签包裹，例如：[answer]0[/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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return solution == identity['expected']
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