init-commit

internbootcamp/bootcamp/cstrangefunction/cstrangefunction.py

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+"""# 
+
+### 谜题描述
+Let f(i) denote the minimum positive integer x such that x is not a divisor of i.
+
+Compute ∑_{i=1}^n f(i) modulo 10^9+7. In other words, compute f(1)+f(2)+...+f(n) modulo 10^9+7.
+
+Input
+
+The first line contains a single integer t (1≤ t≤ 10^4), the number of test cases. Then t cases follow.
+
+The only line of each test case contains a single integer n (1≤ n≤ 10^{16}).
+
+Output
+
+For each test case, output a single integer ans, where ans=∑_{i=1}^n f(i) modulo 10^9+7.
+
+Example
+
+Input
+
+
+6
+1
+2
+3
+4
+10
+10000000000000000
+
+
+Output
+
+
+2
+5
+7
+10
+26
+366580019
+
+Note
+
+In the fourth test case n=4, so ans=f(1)+f(2)+f(3)+f(4).
+
+  * 1 is a divisor of 1 but 2 isn't, so 2 is the minimum positive integer that isn't a divisor of 1. Thus, f(1)=2. 
+  * 1 and 2 are divisors of 2 but 3 isn't, so 3 is the minimum positive integer that isn't a divisor of 2. Thus, f(2)=3. 
+  * 1 is a divisor of 3 but 2 isn't, so 2 is the minimum positive integer that isn't a divisor of 3. Thus, f(3)=2. 
+  * 1 and 2 are divisors of 4 but 3 isn't, so 3 is the minimum positive integer that isn't a divisor of 4. Thus, f(4)=3. 
+
+
+
+Therefore, ans=f(1)+f(2)+f(3)+f(4)=2+3+2+3=10.
+
+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
+import os
+from io import BytesIO
+
+sys.stdin = BytesIO(os.read(0, os.fstat(0).st_size))
+
+f = sys.stdin
+
+line = lambda: f.readline().strip('\r\n').split()
+
+def solve():
+
+    idx = 0
+    off = 1
+    s = N
+    mul = 1
+     
+    while mul <= N:
+        mul = 1
+        for i in range(idx,-1,-1):
+            f = FACT[i]
+            if mul % f != 0:
+                mul *= f
+         
+        start = mul
+        step = mul
+        
+        d = (N-start)//step + 1
+        off = 1 if idx == 0 else FACT[idx+1] - FACT[idx]
+        s += d * off
+        s %= M
+         
+        idx += 1
+        
+    return str(s)
+
+FACT = [1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43]
+M = 10**9 + 7
+
+T = int(line()[0])
+for test in range(1,T+1):
+    
+    N = int(line()[0])
+    
+    sys.stdout.write(solve())
+    sys.stdout.write(\"\n\")
+    
+f.close()
+```
+
+
+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 Cstrangefunctionbootcamp(Basebootcamp):
+    def __init__(self, min_n=1, max_n=10**16, include_boundary=True):
+        if min_n < 1:
+            raise ValueError("min_n must be at least 1")
+        if max_n < min_n:
+            raise ValueError("max_n must be greater than or equal to min_n")
+        self.min_n = min_n
+        self.max_n = max_n
+        self.include_boundary = include_boundary
+    
+    def case_generator(self):
+        # 生成具有全面覆盖的测试用例
+        if self.include_boundary and random.random() < 0.15:
+            boundary_n = [1, 2, 3, 4, 10, 10000000000000000]
+            n = random.choice(boundary_n)
+        else:
+            r = random.random()
+            if r < 0.3:  # 30%小值
+                n = random.randint(1, 100)
+            elif r < 0.6:  # 30%中等值
+                n = random.randint(10**3, 10**6)
+            elif r < 0.85:  # 25%大值
+                n = random.randint(10**9, 10**12)
+            else:  # 15%极值
+                n = random.randint(10**15, self.max_n)
+            n = max(self.min_n, min(n, self.max_n))
+        return {'n': n}
+    
+    @staticmethod
+    def prompt_func(question_case):
+        n = question_case['n']
+        return f"""请计算∑f(i) mod 1e9+7（1≤i≤{n}），其中f(i)是i的最小非因数。
+规则说明：
+1. f(i)定义为i的最小非除数正整数
+2. 例如f(4)=3，因为1、2是4的因数但3不是
+3. 总和需要对1e9+7取模
+
+输出要求：
+将最终答案放在[answer]标签内，如[answer]123[/answer]"""
+
+    @staticmethod
+    def extract_output(output):
+        # 增强型数字提取逻辑
+        matches = re.findall(r'\[answer\](.*?)\[/answer\]', output, re.DOTALL)
+        if not matches:
+            return None
+        number_str = re.sub(r'[^0-9]', '', matches[-1].strip())
+        try:
+            return int(number_str) % (10**9+7) if number_str else None
+        except:
+            return None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        try:
+            return solution == cls.compute_answer(identity['n'])
+        except:
+            return False
+
+    @staticmethod
+    def compute_answer(n):
+        # 优化后的参考实现
+        FACT = [1,2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43]
+        MOD = 10**9+7
+        res = n % MOD
+        idx = 0
+        
+        while idx < len(FACT):
+            # 计算当前阶乘基
+            product = 1
+            for f in reversed(FACT[:idx+1]):
+                if product % f != 0:
+                    product *= f
+                    if product > n:
+                        break
+            
+            if product > n:
+                break
+            
+            # 计算贡献值
+            offset = FACT[idx+1] - FACT[idx] if idx > 0 else 1
+            count = (n - product) // product + 1
+            res = (res + count * offset) % MOD
+            idx += 1
+        
+        return res