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internbootcamp/bootcamp/cbinarysearch/cbinarysearch.py

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+"""# 
+
+### 谜题描述
+Andrey thinks he is truly a successful developer, but in reality he didn't know about the binary search algorithm until recently. After reading some literature Andrey understood that this algorithm allows to quickly find a certain number x in an array. For an array a indexed from zero, and an integer x the pseudocode of the algorithm is as follows:
+
+<image>
+
+Note that the elements of the array are indexed from zero, and the division is done in integers (rounding down).
+
+Andrey read that the algorithm only works if the array is sorted. However, he found this statement untrue, because there certainly exist unsorted arrays for which the algorithm find x!
+
+Andrey wants to write a letter to the book authors, but before doing that he must consider the permutations of size n such that the algorithm finds x in them. A permutation of size n is an array consisting of n distinct integers between 1 and n in arbitrary order.
+
+Help Andrey and find the number of permutations of size n which contain x at position pos and for which the given implementation of the binary search algorithm finds x (returns true). As the result may be extremely large, print the remainder of its division by 10^9+7.
+
+Input
+
+The only line of input contains integers n, x and pos (1 ≤ x ≤ n ≤ 1000, 0 ≤ pos ≤ n - 1) — the required length of the permutation, the number to search, and the required position of that number, respectively.
+
+Output
+
+Print a single number — the remainder of the division of the number of valid permutations by 10^9+7.
+
+Examples
+
+Input
+
+
+4 1 2
+
+
+Output
+
+
+6
+
+
+Input
+
+
+123 42 24
+
+
+Output
+
+
+824071958
+
+Note
+
+All possible permutations in the first test case: (2, 3, 1, 4), (2, 4, 1, 3), (3, 2, 1, 4), (3, 4, 1, 2), (4, 2, 1, 3), (4, 3, 1, 2).
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+'''input
+123 42 24
+
+
+'''
+
+from bisect import bisect_right as bl
+from random import randint as R
+RI = lambda : [int(_x) for _x in raw_input().split()]
+mod = 10**9+7
+F = [1]*(1010)
+for i in range(1009):
+	F[i+1]=(F[i]*(i+1))%mod
+
+n,x,p = RI()
+
+l = 0
+r = n
+
+
+big = n-x
+small = x-1
+ans = 1
+
+while l < r:
+	mid = (l+r)/2
+	if mid == p:
+		l = mid + 1
+
+		continue
+	elif mid < p:
+		ans = (ans*small)%mod
+		small -= 1
+		l = mid + 1
+	else:
+		ans = (ans*big)%mod
+		big -= 1
+		r = mid
+
+
+ans = (ans*F[(big+small)])%mod
+
+print ans
+```
+
+
+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
+
+MOD = 10**9 + 7
+
+class Cbinarysearchbootcamp(Basebootcamp):
+    def __init__(self, **params):
+        super().__init__()
+        self.mod = MOD
+        # 预先计算阶乘数组，最多到2000
+        self.max_fact = 2000
+        self.fact = [1] * (self.max_fact + 1)
+        for i in range(1, self.max_fact + 1):
+            self.fact[i] = (self.fact[i-1] * i) % self.mod
+
+    def compute_answer(self, n, x, pos):
+        l = 0
+        r = n
+        big = n - x
+        small = x - 1
+        ans = 1
+        while l < r:
+            mid = (l + r) // 2
+            if mid == pos:
+                l = mid + 1
+                continue
+            elif mid < pos:
+                ans = (ans * small) % self.mod
+                small -= 1
+                l = mid + 1
+            else:
+                ans = (ans * big) % self.mod
+                big -= 1
+                r = mid
+        remaining = big + small
+        if remaining >= 0:
+            ans = (ans * self.fact[remaining]) % self.mod
+        else:
+            ans = 0
+        return ans
+
+    def case_generator(self):
+        # Ensure x is between 1 and n, and pos is between 0 and n-1
+        n = random.randint(1, 1000)
+        x = random.randint(1, n)
+        pos = random.randint(0, n - 1)
+        correct_answer = self.compute_answer(n, x, pos)
+        return {
+            'n': n,
+            'x': x,
+            'pos': pos,
+            'correct_answer': correct_answer
+        }
+
+    @staticmethod
+    def prompt_func(question_case):
+        n = question_case['n']
+        x = question_case['x']
+        pos = question_case['pos']
+        prompt = f"给定n={n}, x={x}, pos={pos}。请计算满足以下条件的排列数目，结果模10^9+7。\n"
+        prompt += "条件如下：\n"
+        prompt += "1. 排列包含1到n的所有整数，每个整数恰好出现一次。\n"
+        prompt += "2. 数字x位于位置pos（数组索引从0开始）。\n"
+        prompt += "3. 使用以下二分查找实现能够找到x并返回True。\n"
+        prompt += "二分查找的伪代码如下：\n"
+        prompt += "函数binary_search(a, x):\n"
+        prompt += "    l = 0\n"
+        prompt += "    r = n\n"
+        prompt += "    while l < r:\n"
+        prompt += "        mid = (l + r) // 2\n"
+        prompt += "        if a[mid] <= x:\n"
+        prompt += "            l = mid + 1\n"
+        prompt += "        else:\n"
+        prompt += "            r = mid\n"
+        prompt += "    return a[l-1] == x\n"
+        prompt += "请将答案放在[answer]和[/answer]标签之间，例如：\n"
+        prompt += "答案：[answer]数值[/answer]"
+        return prompt
+
+    @staticmethod
+    def extract_output(output):
+        pattern = r'\[answer\](\d+)\[/answer\]'
+        matches = re.findall(pattern, output)
+        if matches:
+            return matches[-1]  # 返回最后一个匹配的结果
+        else:
+            return None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        if solution is None:
+            return False
+        expected = identity['correct_answer']
+        try:
+            solution_int = int(solution)
+            return solution_int == expected
+        except (ValueError, TypeError):
+            return False