**π‘ Problem Formulation:** When dealing with binary data, a common problem is to verify whether all occurrences of the digit ‘1’ are consecutive. In Python, there are various ways to approach this problem. For instance, given the input `'00111110010'`

, the desired output is `False`

because not all ‘1’s are adjacent. However, for the input `'00011111000'`

, the output should be `True`

, signifying all ‘1’s are consecutive.

## Method 1: Iterative Check

This method involves iterating over the string and checking for sequences of ‘1’s. If a ‘1’ is found after a sequence of non-‘1’s, the function returns false; otherwise, it returns true at the end. This method is very straightforward and does not require importing any additional modules.

Here’s an example:

def are_ones_consecutive(data): found_one = False for char in data: if char == '1': if found_one is None: found_one = True elif not found_one: return False else: found_one = False return True # Example usage: print(are_ones_consecutive('00111110010')) # Should return False print(are_ones_consecutive('00011111000')) # Should return True

Output:

False True

This code snippet defines a function, `are_ones_consecutive()`

, that takes a string of binary data as input. It uses a flag `found_one`

to keep track of whether a ‘1’ has been encountered and ensures that no non-‘1’ characters appear after a ‘1’ until all ‘1’s are checked consecutively.

## Method 2: Using Regular Expressions

The regular expressions module, `re`

, can be used to solve this problem by searching for a pattern that does not match consecutive ‘1’s. This method is more sophisticated and can be faster for larger strings.

Here’s an example:

import re def are_ones_consecutive_re(data): return not re.search('10+1', data) # Example usage: print(are_ones_consecutive_re('00111110010')) # Should return False print(are_ones_consecutive_re('00011111000')) # Should return True

Output:

False True

This code snippet employs the Python `re`

module to define the function `are_ones_consecutive_re()`

. It utilizes a regular expression `'10+1'`

to search for a ‘1’ followed by one or more ‘0’s, followed by another ‘1’, which would indicate non-consecutive ‘1’s. If no such pattern is found, all ‘1’s are consecutive.

## Method 3: Using the Split Method

The split method can be used to divide the string into a list using ‘0’ as the delimiter. After the split, the list should not contain any ‘1’s, indicating that all ‘1’s were consecutive before the split.

Here’s an example:

def are_ones_consecutive_split(data): return '1' not in ''.join(data.split('0')) # Example usage: print(are_ones_consecutive_split('00111110010')) # Should return False print(are_ones_consecutive_split('00011111000')) # Should return True

Output:

False True

The function `are_ones_consecutive_split()`

splits the string using ‘0’ as the delimiter and then joins it back. If the resulting string contains a ‘1’, it means there were non-consecutive ‘1’s, otherwise, all ‘1’s were consecutive.

## Method 4: Using String Methods

Python string methods can be utilized to locate sequences of ‘1’s and compare them to the original string. This is less efficient than other methods but still demonstrates the versatility of Python’s string handling abilities.

Here’s an example:

def are_ones_consecutive_str(data): return '1' * data.count('1') in data # Example usage: print(are_ones_consecutive_str('00111110010')) # Should return False print(are_ones_consecutive_str('00011111000')) # Should return True

Output:

False True

This function `are_ones_consecutive_str()`

creates a string of ‘1’s that is as long as the count of ‘1’s in the input data and checks if this string is a substring of the input string, indicating consecutive ‘1’s.

## Bonus One-Liner Method 5: Using List Comprehension and all()

A concise one-liner using list comprehension and the `all()`

built-in function can check for consecutive ‘1’s by comparing adjacent characters for being ‘1’s.

Here’s an example:

are_ones_consecutive_one_liner = lambda data: all(data[i] == '1' or data[i+1] != '1' for i in range(len(data)-1)) # Example usage: print(are_ones_consecutive_one_liner('00111110010')) # Should return False print(are_ones_consecutive_one_liner('00011111000')) # Should return True

Output:

False True

The one-liner lambda function `are_ones_consecutive_one_liner`

iterates through each character in the string (except the last one) and checks that if a character is ‘1’, the next character must also be ‘1’. If this is always true, then all ‘1’s are consecutive.

## Summary/Discussion

**Method 1: Iterative Check.**This technique is simple and easy to understand, making it suitable for beginners. However, its performance may degrade with very long strings.**Method 2: Using Regular Expressions.**It’s more compact and can be faster than the iterative method, particularly on larger datasets. But it may not be as readable for those unfamiliar with regex.**Method 3: Using the Split Method.**An elegant and readable option. It can perform well but may use more memory compared to regex as it creates new lists.**Method 4: Using String Methods.**Demonstrates the power of Python’s string methods but might not be the most efficient solution in terms of time complexity.**Bonus Method 5: One-Liner.**Extremely concise and uses list comprehension neatly. However, it’s not as reader-friendly as the other methods and may be challenging for beginners to understand at first glance.