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internbootcamp/bootcamp/eserejaandsubsequences/eserejaandsubsequences.py

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+"""# 
+
+### 谜题描述
+Sereja has a sequence that consists of n positive integers, a1, a2, ..., an. 
+
+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.
+
+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.
+
+Now Sereja wonders, how many sequences are written on the lines piece of paper. Help Sereja, find the required quantity modulo 1000000007 (109 + 7). 
+
+Input
+
+The first line contains integer n (1 ≤ n ≤ 105). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106).
+
+Output
+
+In the single line print the answer to the problem modulo 1000000007 (109 + 7).
+
+Examples
+
+Input
+
+1
+42
+
+
+Output
+
+42
+
+
+Input
+
+3
+1 2 2
+
+
+Output
+
+13
+
+
+Input
+
+5
+1 2 3 4 5
+
+
+Output
+
+719
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+n = input()
+a = map(int, raw_input().split())
+mod = int(1e+9) + 7
+size = max(a)
+tree = [0] * (size + 1)
+
+def query(index):
+  res = 0
+  while index:
+    res = (res + tree[index]) % mod
+    index -= index & -index
+  return res
+
+def update(index, delta):
+  while index <= size:
+    tree[index] = (tree[index] + delta) % mod
+    index += index & -index
+
+def query_one(index):
+  res = tree[index]
+  bot = index - (index & -index)
+  index -= 1
+  while index > bot:
+    res -= tree[index]
+    if res < 0: res += mod
+    index -= index & -index
+  return res
+
+
+for x in a:
+  value = query(x) * x + x
+  update(x, value - query_one(x))
+print query(size)
+```
+
+
+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。
+"""
+
+from bootcamp import Basebootcamp
+import random
+import re
+from bootcamp import Basebootcamp
+
+class Eserejaandsubsequencesbootcamp(Basebootcamp):
+    def __init__(self, min_n=1, max_n=5, min_val=1, max_val=10, seed=None):
+        self.min_n = min_n
+        self.max_n = max_n
+        self.min_val = min_val
+        self.max_val = max_val
+        self.seed = seed
+        if seed is not None:
+            random.seed(seed)
+    
+    def case_generator(self):
+        n = random.randint(self.min_n, self.max_n)
+        a = [random.randint(self.min_val, self.max_val) for _ in range(n)]
+        answer = self.compute_answer(a)
+        return {
+            'n': n,
+            'a': a,
+            'answer': answer
+        }
+    
+    @staticmethod
+    def compute_answer(a):
+        mod = 10**9 + 7
+        if not a:
+            return 0
+        max_val = max(a)
+        tree = [0] * (max_val + 2)  # Extra space to avoid index issues
+        last = {}
+        total = 0
+        
+        for x in a:
+            # Query sum of all elements <= x
+            sum_prev = 0
+            idx = x
+            while idx > 0:
+                sum_prev = (sum_prev + tree[idx]) % mod
+                idx -= idx & -idx
+            
+            # Calculate new contribution
+            new_contrib = (sum_prev * x + x) % mod
+            delta = (new_contrib - last.get(x, 0)) % mod
+            
+            # Update Fenwick tree
+            idx = x
+            while idx <= max_val:
+                tree[idx] = (tree[idx] + delta) % mod
+                idx += idx & -idx
+            
+            # Update last and total
+            last[x] = new_contrib
+            total = (total + delta) % mod
+        
+        return total
+    
+    @staticmethod
+    def prompt_func(question_case):
+        n = question_case['n']
+        a = question_case['a']
+        a_str = ' '.join(map(str, a))
+        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：
+
+问题描述：
+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。
+
+子序列定义：
+- 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。
+- 非递减：子序列中的每个元素不小于前一个元素。
+- 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。
+
+输入格式：
+- 第一行包含整数n（1 ≤ n ≤ 1e5）。
+- 第二行包含n个正整数a_1, a_2, ..., a_n（1 ≤ a_i ≤ 1e6）。
+
+你的任务：
+给定n和序列a，计算最终的答案并以模1e9+7输出。
+
+输入样例：
+{n}
+{a_str}
+
+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]。"""
+        return problem_text
+    
+    @staticmethod
+    def extract_output(output):
+        matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
+        if not matches:
+            return None
+        last_match = matches[-1].strip()
+        digits = re.sub(r'\D', '', last_match)
+        try:
+            return int(digits) % (10**9 + 7)
+        except ValueError:
+            return None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        correct_answer = identity.get('answer')
+        return solution == correct_answer