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198 lines
5.3 KiB
Python
Executable file
198 lines
5.3 KiB
Python
Executable file
"""#
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### 谜题描述
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Sereja has a sequence that consists of n positive integers, a1, a2, ..., an.
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First Sereja took a piece of squared paper and wrote all distinct non-empty non-decreasing subsequences of sequence a. Then for each sequence written on the squared paper, Sereja wrote on a piece of lines paper all sequences that do not exceed it.
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A sequence of positive integers x = x1, x2, ..., xr doesn't exceed a sequence of positive integers y = y1, y2, ..., yr, if the following inequation holds: x1 ≤ y1, x2 ≤ y2, ..., xr ≤ yr.
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Now Sereja wonders, how many sequences are written on the lines piece of paper. Help Sereja, find the required quantity modulo 1000000007 (109 + 7).
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Input
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The first line contains integer n (1 ≤ n ≤ 105). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106).
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Output
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In the single line print the answer to the problem modulo 1000000007 (109 + 7).
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Examples
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Input
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1
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42
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Output
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42
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Input
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3
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1 2 2
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Output
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13
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Input
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5
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1 2 3 4 5
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Output
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719
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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 = input()
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a = map(int, raw_input().split())
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mod = int(1e+9) + 7
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size = max(a)
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tree = [0] * (size + 1)
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def query(index):
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res = 0
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while index:
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res = (res + tree[index]) % mod
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index -= index & -index
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return res
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def update(index, delta):
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while index <= size:
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tree[index] = (tree[index] + delta) % mod
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index += index & -index
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def query_one(index):
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res = tree[index]
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bot = index - (index & -index)
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index -= 1
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while index > bot:
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res -= tree[index]
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if res < 0: res += mod
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index -= index & -index
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return res
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for x in a:
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value = query(x) * x + x
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update(x, value - query_one(x))
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print query(size)
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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 bootcamp import Basebootcamp
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class Eserejaandsubsequencesbootcamp(Basebootcamp):
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def __init__(self, min_n=1, max_n=5, min_val=1, max_val=10, seed=None):
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self.min_n = min_n
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self.max_n = max_n
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self.min_val = min_val
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self.max_val = max_val
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self.seed = seed
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if seed is not None:
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random.seed(seed)
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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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a = [random.randint(self.min_val, self.max_val) for _ in range(n)]
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answer = self.compute_answer(a)
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return {
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'n': n,
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'a': a,
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'answer': answer
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}
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@staticmethod
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def compute_answer(a):
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mod = 10**9 + 7
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if not a:
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return 0
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max_val = max(a)
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tree = [0] * (max_val + 2) # Extra space to avoid index issues
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last = {}
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total = 0
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for x in a:
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# Query sum of all elements <= x
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sum_prev = 0
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idx = x
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while idx > 0:
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sum_prev = (sum_prev + tree[idx]) % mod
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idx -= idx & -idx
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# Calculate new contribution
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new_contrib = (sum_prev * x + x) % mod
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delta = (new_contrib - last.get(x, 0)) % mod
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# Update Fenwick tree
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idx = x
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while idx <= max_val:
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tree[idx] = (tree[idx] + delta) % mod
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idx += idx & -idx
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# Update last and total
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last[x] = new_contrib
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total = (total + delta) % mod
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return total
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@staticmethod
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def prompt_func(question_case):
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n = question_case['n']
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a = question_case['a']
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a_str = ' '.join(map(str, a))
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problem_text = f"""Sereja有一个由n个正整数组成的序列a。你需要解决以下问题：
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问题描述：
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找出所有不同的非空非递减子序列y。然后，对于每个y，计算所有可能的序列x的数量，其中x的长度与y相同，并且每个对应的元素x_i ≤ y_i。所有x的数量的总和模1000000007即为答案。
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子序列定义：
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- 子序列的元素保持原序列中的相对顺序，但可以删除某些元素。
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- 非递减：子序列中的每个元素不小于前一个元素。
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- 不同的子序列由它们的元素序列决定，即相同的元素序列被视为同一个子序列，即使它们来自原序列的不同位置。
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输入格式：
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- 第一行包含整数n（1 ≤ n ≤ 1e5）。
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- 第二行包含n个正整数a_1, a_2, ..., a_n（1 ≤ a_i ≤ 1e6）。
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你的任务：
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给定n和序列a，计算最终的答案并以模1e9+7输出。
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输入样例：
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{n}
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{a_str}
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请按照上述输入样例的格式，计算出正确的答案，并将最终答案用[answer]和[/answer]标签包裹。例如：[answer]42[/answer]。"""
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return problem_text
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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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last_match = matches[-1].strip()
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digits = re.sub(r'\D', '', last_match)
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try:
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return int(digits) % (10**9 + 7)
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except ValueError:
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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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correct_answer = identity.get('answer')
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return solution == correct_answer
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