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internbootcamp/bootcamp/cayoubsfunction/cayoubsfunction.py

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+"""# 
+
+### 谜题描述
+Ayoub thinks that he is a very smart person, so he created a function f(s), where s is a binary string (a string which contains only symbols \"0\" and \"1\"). The function f(s) is equal to the number of substrings in the string s that contains at least one symbol, that is equal to \"1\".
+
+More formally, f(s) is equal to the number of pairs of integers (l, r), such that 1 ≤ l ≤ r ≤ |s| (where |s| is equal to the length of string s), such that at least one of the symbols s_l, s_{l+1}, …, s_r is equal to \"1\". 
+
+For example, if s = \"01010\" then f(s) = 12, because there are 12 such pairs (l, r): (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3), (2, 4), (2, 5), (3, 4), (3, 5), (4, 4), (4, 5).
+
+Ayoub also thinks that he is smarter than Mahmoud so he gave him two integers n and m and asked him this problem. For all binary strings s of length n which contains exactly m symbols equal to \"1\", find the maximum value of f(s).
+
+Mahmoud couldn't solve the problem so he asked you for help. Can you help him? 
+
+Input
+
+The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. The description of the test cases follows.
+
+The only line for each test case contains two integers n, m (1 ≤ n ≤ 10^{9}, 0 ≤ m ≤ n) — the length of the string and the number of symbols equal to \"1\" in it.
+
+Output
+
+For every test case print one integer number — the maximum value of f(s) over all strings s of length n, which has exactly m symbols, equal to \"1\".
+
+Example
+
+Input
+
+
+5
+3 1
+3 2
+3 3
+4 0
+5 2
+
+
+Output
+
+
+4
+5
+6
+0
+12
+
+Note
+
+In the first test case, there exists only 3 strings of length 3, which has exactly 1 symbol, equal to \"1\". These strings are: s_1 = \"100\", s_2 = \"010\", s_3 = \"001\". The values of f for them are: f(s_1) = 3, f(s_2) = 4, f(s_3) = 3, so the maximum value is 4 and the answer is 4.
+
+In the second test case, the string s with the maximum value is \"101\".
+
+In the third test case, the string s with the maximum value is \"111\".
+
+In the fourth test case, the only string s of length 4, which has exactly 0 symbols, equal to \"1\" is \"0000\" and the value of f for that string is 0, so the answer is 0.
+
+In the fifth test case, the string s with the maximum value is \"01010\" and it is described as an example in the problem statement.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+import sys
+ 
+ 
+T = input()
+ 
+ 
+ 
+ 
+ 
+for case in range(T):
+ 
+	n, m = map(int, raw_input().split())
+ 
+	if m >= float(n)/2:
+		A = n*(n + 1)/2 - (n - m)
+	else:
+		# the number of compartments
+		c = m + 1
+		# splitting the zeros into compartments
+		z = n - m
+		f_l = z/c
+		# calculate how many of f_l and f_u there need 
+		n_f_u = z % c
+		n_f_l = c - n_f_u
+ 
+		# calculating A
+		A = n*(n + 1)/2 - (((f_l + 1)*(f_l + 2)/2)*n_f_u + (f_l*(f_l + 1)/2)*n_f_l)
+ 
+	print A
+```
+
+
+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 Cayoubsfunctionbootcamp(Basebootcamp):
+    def __init__(self, n_min=1, n_max=10**9):
+        """
+        支持极大数值范围的初始化参数
+        参数:
+            n_min: 可生成的最小n值 (default=1)
+            n_max: 可生成的最大n值 (default=1e9)
+        """
+        self.n_min = n_min
+        self.n_max = n_max
+    
+    def case_generator(self):
+        # 30%生成特殊边界情况
+        if random.random() < 0.3:
+            n = random.randint(self.n_min, self.n_max)
+            special_cases = [
+                (n, 0),         # 全0字符串
+                (n, n),         # 全1字符串
+                (n, n//2),      # 临界值情况
+                (n, n//2 + 1)   # 临界值+1
+            ]
+            return dict(zip(['n', 'm'], random.choice(special_cases)))
+        
+        # 常规随机生成
+        n = random.randint(max(1, self.n_min), self.n_max)
+        m = random.randint(0, n)
+        return {"n": n, "m": m}
+    
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        n = question_case['n']
+        m = question_case['m']
+        return f"""### Programming Problem Statement
+
+Given a binary string s of length {n} containing exactly {m} '1's, find the maximum possible value of function f(s). 
+
+**Function Definition:**
+f(s) = number of substrings containing at least one '1'
+
+**Substring Definition:**
+A substring is any contiguous sequence of characters from index l to r (1 ≤ l ≤ r ≤ n)
+
+**Examples:**
+1. Input: n=3, m=1 → Output:4
+2. Input: n=5, m=2 → Output:12
+3. Input: n=4, m=0 → Output:0
+
+**Your Task:**
+Compute the maximum f(s) for n={n}, m={m}. 
+
+**Answer Format Requirements:**
+- Return only the integer answer 
+- Enclose your final answer with [answer] and [/answer] tags
+- Example valid response: [answer]42[/answer]"""
+
+    @staticmethod
+    def extract_output(output):
+        # 使用非贪婪匹配并支持跨行内容
+        matches = re.findall(
+            r'\[answer\](.*?)\[/answer\]', 
+            output, 
+            flags=re.IGNORECASE | re.DOTALL
+        )
+        if not matches:
+            return None
+        
+        # 提取最后一个答案并清理空白字符
+        raw_answer = matches[-1].strip()
+        
+        # 处理包含逗号分隔的情况
+        if ',' in raw_answer:
+            raw_answer = raw_answer.replace(',', '')
+        
+        try:
+            return int(raw_answer)
+        except (ValueError, TypeError):
+            return None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        # 处理超大规模数值计算
+        n = identity['n']
+        m = identity['m']
+        
+        if m == 0:
+            return solution == 0
+        
+        # 初始化总子串数
+        total = n * (n + 1) // 2
+        
+        if m >= n / 2.0:
+            expected = total - (n - m)
+            return solution == expected
+        
+        # 分段计算验证
+        c = m + 1
+        z = n - m
+        base, rem = divmod(z, c)
+        
+        sum_zeros = (
+            rem * (base + 1) * (base + 2) // 2 +
+            (c - rem) * base * (base + 1) // 2
+        )
+        expected = total - sum_zeros
+        return solution == expected
+
+    @staticmethod
+    def calculate_answer(n, m):
+        """参考计算方法（用于生成测试答案）"""
+        if m == 0:
+            return 0
+        total = n * (n + 1) // 2
+        if m >= n / 2.0:
+            return total - (n - m)
+        
+        c = m + 1
+        z = n - m
+        base, rem = divmod(z, c)
+        return total - (
+            rem * (base + 1) * (base + 2) // 2 +
+            (c - rem) * base * (base + 1) // 2
+        )