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internbootcamp/bootcamp/civanandpowersoftwo/civanandpowersoftwo.py

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+"""# 
+
+### 谜题描述
+Ivan has got an array of n non-negative integers a1, a2, ..., an. Ivan knows that the array is sorted in the non-decreasing order. 
+
+Ivan wrote out integers 2a1, 2a2, ..., 2an on a piece of paper. Now he wonders, what minimum number of integers of form 2b (b ≥ 0) need to be added to the piece of paper so that the sum of all integers written on the paper equalled 2v - 1 for some integer v (v ≥ 0). 
+
+Help Ivan, find the required quantity of numbers.
+
+Input
+
+The first line contains integer n (1 ≤ n ≤ 105). The second input line contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ 2·109). It is guaranteed that a1 ≤ a2 ≤ ... ≤ an.
+
+Output
+
+Print a single integer — the answer to the problem.
+
+Examples
+
+Input
+
+4
+0 1 1 1
+
+
+Output
+
+0
+
+
+Input
+
+1
+3
+
+
+Output
+
+3
+
+Note
+
+In the first sample you do not need to add anything, the sum of numbers already equals 23 - 1 = 7.
+
+In the second sample you need to add numbers 20, 21, 22.
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+from math import sqrt as s
+from collections import *
+from fractions import gcd
+n=input()
+arr=map(int,raw_input().split())
+di={}
+for i in arr:
+    j=i
+    if j in di:
+        while j in di:
+            del di[j]
+            j=j+1
+    di[j]=1
+
+#print di
+print max(di)-len(di)+1
+```
+
+
+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
+from bootcamp import Basebootcamp
+import re
+import random
+
+class Civanandpowersoftwobootcamp(Basebootcamp):
+    def __init__(self, **params):
+        self.max_n = params.get('max_n', 1000)
+        self.min_n = params.get('min_n', 1)
+        self.max_a = params.get('max_a', 2 * 10**9)
+    
+    def case_generator(self):
+        n = random.randint(self.min_n, self.max_n)
+        # Generate problem instance with realistic distributions
+        a = [random.randint(0, self.max_a) for _ in range(n)]
+        a.sort()
+        
+        # Simulate optimal merging logic
+        di = {}
+        for num in a:
+            j = num
+            while j in di:
+                del di[j]
+                j += 1
+            di[j] = 1
+        
+        # Calculate expected answer
+        max_j = max(di.keys()) if di else 0
+        len_j = len(di)
+        expected = max_j - len_j + 1
+        
+        return {
+            'n': n,
+            'a': a,
+            'expected': expected
+        }
+    
+    @staticmethod
+    def prompt_func(question_case) -> str:
+        a_str = ' '.join(map(str, question_case['a']))
+        return f"""Ivan's array of exponents (sorted): {a_str}
+
+Task: Determine the minimum number of distinct 2^b terms to add 
+such that total sum equals 2^v -1 for some integer v.
+
+Rules:
+1. Added terms must be distinct (b values are unique)
+2. Original array is sorted non-decreasing
+3. Final sum should be exactly one less than a power of two
+
+Output format: Single integer enclosed in [answer] tags.
+
+Example: For input '3', valid response: [answer]3[/answer]"""
+
+    @staticmethod
+    def extract_output(output):
+        # Robust extraction with error tolerance
+        matches = re.findall(
+            r'\[answer\s*\]\s*(\d+)\s*\[\s*/answer\s*\]', 
+            output, 
+            re.IGNORECASE
+        )
+        if matches:
+            try:
+                return int(matches[-1].strip())
+            except ValueError:
+                return None
+        return None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        return solution == identity.get('expected', -1)