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internbootcamp/bootcamp/cfadiandlcm/cfadiandlcm.py

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+"""# 
+
+### 谜题描述
+Today, Osama gave Fadi an integer X, and Fadi was wondering about the minimum possible value of max(a, b) such that LCM(a, b) equals X. Both a and b should be positive integers.
+
+LCM(a, b) is the smallest positive integer that is divisible by both a and b. For example, LCM(6, 8) = 24, LCM(4, 12) = 12, LCM(2, 3) = 6.
+
+Of course, Fadi immediately knew the answer. Can you be just like Fadi and find any such pair?
+
+Input
+
+The first and only line contains an integer X (1 ≤ X ≤ 10^{12}).
+
+Output
+
+Print two positive integers, a and b, such that the value of max(a, b) is minimum possible and LCM(a, b) equals X. If there are several possible such pairs, you can print any.
+
+Examples
+
+Input
+
+
+2
+
+
+Output
+
+
+1 2
+
+
+Input
+
+
+6
+
+
+Output
+
+
+2 3
+
+
+Input
+
+
+4
+
+
+Output
+
+
+1 4
+
+
+Input
+
+
+1
+
+
+Output
+
+
+1 1
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+def gcd(a,b):
+    while b:
+        a,b=b,a%b
+    return a
+n=input()
+maxx=n
+for i in range(1,int(n**(0.5)+1)):
+    if n%i==0:
+        s=n/i
+        x=gcd(i,s)
+        m=max(i,s)
+        m*=x
+        maxx=min(maxx,m)
+a=maxx
+b=n/maxx
+b*=gcd(a,b)
+print min(a,b),max(a,b)
+```
+
+
+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 math
+from math import gcd
+from bootcamp import Basebootcamp
+
+class Cfadiandlcmbootcamp(Basebootcamp):
+    def __init__(self, min_X=1, max_X=10**6):
+        self.min_X = min_X
+        self.max_X = max_X
+    
+    def case_generator(self):
+        # 增加特殊案例生成逻辑
+        if random.random() < 0.3:  # 30%概率生成边界案例
+            candidates = [
+                1,  # 最小边界
+                random.choice([2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31]),  # 小质数
+                int(math.sqrt(self.max_X))**2,  # 最大平方数
+                2**random.randint(1, 20),  # 2的幂次方
+                2 * 3  # 两个质数的乘积
+            ]
+            X = random.choice(candidates)
+            X = max(self.min_X, min(X, self.max_X))
+        else:
+            X = random.randint(self.min_X, self.max_X)
+        return {'X': X}
+    
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        X = question_case['X']
+        prompt = f"""Given X = {X}, find two positive integers a and b such that:
+1. LCM(a, b) = X
+2. max(a, b) is minimized
+
+Output format: [answer]a b[/answer]"""
+        return prompt
+    
+    @staticmethod
+    def extract_output(output):
+        import re
+        matches = re.findall(r'\[answer\]\s*(\d+\s+\d+)\s*\[/answer\]', output)
+        return matches[-1] if matches else None
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        X = identity['X']
+        
+        # 解析答案
+        try:
+            a, b = map(int, solution.split())
+            if a <= 0 or b <= 0:
+                return False
+        except:
+            return False
+        
+        # 验证LCM正确性
+        current_gcd = gcd(a, b)
+        if a * b // current_gcd != X:
+            return False
+        
+        # 计算最优解
+        min_max = math.inf
+        sqrt_x = int(math.sqrt(X))
+        for i in range(1, sqrt_x + 1):
+            if X % i == 0:
+                j = X // i
+                pair_gcd = gcd(i, j)
+                candidate_max = max(i, j) * pair_gcd  # 关键优化点
+                min_max = min(min_max, candidate_max)
+        
+        return max(a, b) == min_max