**π‘ Problem Formulation:** The task is to develop a Python program that identifies the substring that appears to repeat consecutively for exactly k times in a given string sequence. For example, if the input sequence is “abababcc” and k is 3, the output should be “ab” since “ab” is the substring that repeats 3 times consecutively.

## Method 1: Using Nested Loops

This method uses two nested loops to look for all possible substrings in the given sequence. Then, for each substring, it constructs a string made up of k repetitions of that substring and checks if this string is present in the sequence. It is the most straightforward brute-force approach.

Here’s an example:

def max_k_repeat_substring(sequence, k): max_substring = "" for i in range(len(sequence)): for j in range(i+1, len(sequence) + 1): sub = sequence[i:j] if sequence.count(sub * k) > 0 and len(max_substring) < len(sub): max_substring = sub return max_substring print(max_k_repeat_substring("abababcc", 3))

Output:

`"ab"`

This code defines a function that iterates over all substrings of the given sequence and checks for the maximum-length substring that repeats k times consecutively. It updates the `max_substring`

whenever it finds a longer substring that satisfies the criteria.

## Method 2: Using Regular Expressions

Regular expressions can be used to greatly simplify the process of finding repeating substrings. Python’s `re`

module allows us to pattern-match strings. We can create a regex pattern corresponding to any substring repeating k times and use it to find matches.

Here’s an example:

import re def max_k_repeat_substring(sequence, k): regex_pattern = r"(.+?)\1{" + str(k-1) + ",}" matches = re.findall(regex_pattern, sequence) return max(matches, key=len) if matches else "" print(max_k_repeat_substring("abababcc", 3))

Output:

`"ab"`

This code uses the `re.findall()`

function with a pattern that matches any substring that is followed by itself k-1 more times. The `max()`

function is used to find the longest matching substring.

## Method 3: Using itertools.groupby

The `itertools.groupby()`

function is a powerful tool in Python that can be used for iterating over data. In this method, we use `groupby`

to group consecutive repeating substrings and filter out those which meet our criteria of k repetitions.

Here’s an example:

from itertools import groupby def max_k_repeat_substring(sequence, k): return max( ("".join(g) for k, g in groupby(sequence) if len(list(g)) == k), key=len, default="" ) print(max_k_repeat_substring("abababcc", 3))

Output:

`"ab"`

Here, `groupby()`

from the `itertools`

module is used to group the sequence by each unique substring occurrence. A generator expression filters out these groups to keep only those with exactly k characters, and the `max()`

function is then used to find the substring with the maximum length.

## Method 4: Using a Sliding Window

The sliding window technique is a method of array/string manipulation which maintains a subset of data as a window that slides over the data structure to consider subsets of sequences over the array/string. This can be applied to effectively find repeating substrings of a certain length.

Here’s an example:

def max_k_repeat_substring(sequence, k): max_substring = "" for i in range(len(sequence) - k + 1): window = sequence[i:i+k] if (window * k) in sequence and len(window) > len(max_substring): max_substring = window return max_substring print(max_k_repeat_substring("abababcc", 3))

Output:

`"ab"`

A sliding window of size k is used over the sequence. For each position, a window substring is extracted and checked if its k-fold repetition exists in the sequence. The longest such window is kept as the maximum k-repeating substring.

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

By combining list comprehensions with the max function, we can condense our search for the maximum k repeating substring into a concise one-liner. This shows the power of Python’s expressive syntax and built-in functions.

Here’s an example:

max_k_repeat_substring = lambda s, k: max( (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1) if s[i:j]*k in s), key=len, default="" ) print(max_k_repeat_substring("abababcc", 3))

Output:

`"ab"`

In this method, a lambda function is defined, which uses nested list comprehensions to generate all possible substrings and filters them based on our k-repetition criterion, using `max()`

to select the longest.

## Summary/Discussion

**Method 1: Nested Loops.**Straightforward and easy to understand. However, it is inefficient as it checks all possible substrings which leads to O(n^3) time complexity for large n.**Method 2: Regular Expressions.**More sophisticated and much faster than nested loops. But regex can be tricky to understand and create for complex patterns.**Method 3: itertools.groupby.**Pythonic and concise. It provides a clean approach, however, might be less efficient than regex for large input strings.**Method 4: Sliding Window.**Efficient for larger strings compared to nested loops and is easier to understand than regex. However, does not handle overlapping substrings (i.e., cases where the repeating substrings are not adjacent).**Method 5: List Comprehension.**Extremely concise one-liner. It is elegant, but can be less readable for those not familiar with Python’s advanced syntax features, and shares the inefficiency of the nested loops approach.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.