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