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internbootcamp/bootcamp/dgame/dgame.py

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+"""# 
+
+### 谜题描述
+Allen and Bessie are playing a simple number game. They both know a function f: \{0, 1\}^n → R, i. e. the function takes n binary arguments and returns a real value. At the start of the game, the variables x_1, x_2, ..., x_n are all set to -1. Each round, with equal probability, one of Allen or Bessie gets to make a move. A move consists of picking an i such that x_i = -1 and either setting x_i → 0 or x_i → 1.
+
+After n rounds all variables are set, and the game value resolves to f(x_1, x_2, ..., x_n). Allen wants to maximize the game value, and Bessie wants to minimize it.
+
+Your goal is to help Allen and Bessie find the expected game value! They will play r+1 times though, so between each game, exactly one value of f changes. In other words, between rounds i and i+1 for 1 ≤ i ≤ r, f(z_1, ..., z_n) → g_i for some (z_1, ..., z_n) ∈ \{0, 1\}^n. You are to find the expected game value in the beginning and after each change.
+
+Input
+
+The first line contains two integers n and r (1 ≤ n ≤ 18, 0 ≤ r ≤ 2^{18}).
+
+The next line contains 2^n integers c_0, c_1, ..., c_{2^n-1} (0 ≤ c_i ≤ 10^9), denoting the initial values of f. More specifically, f(x_0, x_1, ..., x_{n-1}) = c_x, if x = \overline{x_{n-1} … x_0} in binary.
+
+Each of the next r lines contains two integers z and g (0 ≤ z ≤ 2^n - 1, 0 ≤ g ≤ 10^9). If z = \overline{z_{n-1} ... z_0} in binary, then this means to set f(z_0, ..., z_{n-1}) → g.
+
+Output
+
+Print r+1 lines, the i-th of which denotes the value of the game f during the i-th round. Your answer must have absolute or relative error within 10^{-6}.
+
+Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if \frac{|a - b|}{max{(1, |b|)}} ≤ 10^{-6}.
+
+Examples
+
+Input
+
+2 2
+0 1 2 3
+2 5
+0 4
+
+
+Output
+
+1.500000
+2.250000
+3.250000
+
+
+Input
+
+1 0
+2 3
+
+
+Output
+
+2.500000
+
+
+Input
+
+2 0
+1 1 1 1
+
+
+Output
+
+1.000000
+
+Note
+
+Consider the second test case. If Allen goes first, he will set x_1 → 1, so the final value will be 3. If Bessie goes first, then she will set x_1 → 0 so the final value will be 2. Thus the answer is 2.5.
+
+In the third test case, the game value will always be 1 regardless of Allen and Bessie's play.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+from fractions import *
+from math import *
+from itertools import *
+from fractions import*
+import string
+import copy
+import random
+import bisect
+from decimal import *
+from collections import deque
+def id_generator(size=20, chars=string.digits):
+    return ''.join(random.choice(chars) for _ in range(size))
+def mp():
+    return map(int,str(raw_input()).split())
+n,r=mp()
+l=list(mp())
+x=pow(2,n)
+s=sum(l)
+print(s/float(x))
+for i in range(r):
+	a,b=mp()
+	s=s-l[a]
+	s+=b
+	l[a]=b
+	print(s/float(x))
+```
+
+
+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 math import isclose
+
+from bootcamp import Basebootcamp
+
+class Dgamebootcamp(Basebootcamp):
+    def __init__(self, **params):
+        self.n = params.get('n', 2)
+        self.r = params.get('r', 0)
+        # 验证n和r的范围
+        if self.n < 1 or self.n > 18:
+            raise ValueError("n must be between 1 and 18")
+        if self.r < 0 or self.r > (2 ** 18):
+            raise ValueError("r must be between 0 and 2^18")
+    
+    def case_generator(self):
+        n = self.n
+        r = self.r
+        size = 2 ** n
+        # 生成初始c数组，考虑边界情况
+        initial_c = [random.randint(0, 10**9) for _ in range(size)]
+        # 确保至少有一次修改，如果r>0
+        updates = []
+        for _ in range(r):
+            z = random.randint(0, size - 1)
+            g = random.randint(0, 10**9)
+            updates.append((z, g))
+        case = {
+            'n': n,
+            'initial_c': initial_c,
+            'r': r,
+            'updates': updates
+        }
+        return case
+    
+    @staticmethod
+    def prompt_func(question_case):
+        n = question_case['n']
+        initial_c = question_case['initial_c']
+        r = question_case['r']
+        prompt = (
+            "Allen和Bessie正在玩一个数字游戏。游戏规则如下：\n"
+            "游戏由一个函数f决定，f接受n个二进制变量，返回一个实数值。"
+            "初始时，所有变量设为-1，每轮随机选择一个玩家设置一个变量为0或1。"
+            "游戏目标是计算在每一轮修改后的期望值，输出r+1个结果，每个结果保留六位小数。\n"
+            "初始函数值为："
+        )
+        prompt += f"{initial_c}\n"
+        prompt += "每次修改操作如下：\n"
+        for i, (z, g) in enumerate(question_case['updates'], 1):
+            prompt += f"第{i}次修改：将f的值{z}修改为{g}\n"
+        prompt += (
+            "请输出每次修改后的期望值，每个值放在[answer]标签内，"
+            "保留六位小数，例如：[answer]1.500000[/answer]。"
+        )
+        return prompt
+    
+    @staticmethod
+    def extract_output(output):
+        pattern = r'\[answer\](.*?)\[\/answer\]'
+        matches = re.findall(pattern, output)
+        if not matches:
+            return None
+        solutions = []
+        for m in matches:
+            m_clean = m.strip()
+            # 处理可能的格式问题，例如多余的空格或换行符
+            if m_clean == "":
+                continue
+            try:
+                num = float(m_clean)
+                solutions.append(num)
+            except ValueError:
+                pass
+        if not solutions:
+            return None
+        return solutions
+    
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        if isinstance(solution, list):
+            solutions = solution
+        else:
+            solutions = [solution]
+        n = identity['n']
+        size = 2 ** n
+        initial_c = identity['initial_c']
+        updates = identity['updates']
+        r = identity['r']
+        correct = []
+        current_sum = sum(initial_c)
+        correct_value = current_sum / size
+        correct.append(correct_value)
+        current_c = initial_c.copy()
+        for z, g in updates:
+            delta = g - current_c[z]
+            current_sum += delta
+            current_c[z] = g
+            correct_value = current_sum / size
+            correct.append(correct_value)
+        if len(solutions) != len(correct):
+            return False
+        for s, c in zip(solutions, correct):
+            if not isclose(s, c, rel_tol=1e-6, abs_tol=1e-6):
+                return False
+        return True