**π‘ Problem Formulation:** This article addresses the challenge of sorting a matrix based on the count of palindromes in each row. A palindrome is a sequence that reads the same backward as forward. Given a matrix where each row contains a list of strings, we aim to sort the rows in ascending order according to the number of palindromic strings found in them. For example, if the input is [[“aba”, “xyz”], [“abc”, “def”], [“pop”, “mom”, “dad”]], the desired output is [[“abc”, “def”], [“aba”, “xyz”], [“pop”, “mom”, “dad”]], since the second row contains no palindromes, the first row contains one, and the third row contains three.

## Method 1: Basic Function with Sorted()

This method involves writing a function that takes a matrix, counts the number of palindromes for each row, and sorts the rows accordingly by using Python’s built-in sorted() function. This approach is clear and allows for easy customization of the sorting criteria.

Here’s an example:

def is_palindrome(s): return s == s[::-1] def sort_matrix_by_palindrome(matrix): return sorted(matrix, key=lambda row: sum(is_palindrome(word) for word in row)) matrix = [["aba", "xyz"], ["abc", "def"], ["pop", "mom", "dad"]] sorted_matrix = sort_matrix_by_palindrome(matrix) print(sorted_matrix)

Output: [[‘abc’, ‘def’], [‘aba’, ‘xyz’], [‘pop’, ‘mom’, ‘dad’]]

This code defines a function `is_palindrome()`

that checks if a string is a palindrome. The main function `sort_matrix_by_palindrome()`

sorts the rows of the matrix based on the count of palindromic strings each row contains, in ascending order. Finally, we print the sorted matrix.

## Method 2: Using a Custom Class

By creating a custom class that overrides the comparison methods, we can sort the matrix according to the number of palindromes found. This is particularly useful if we wish to sort objects other than just strings or want to keep track of the palindrome count within the object.

Here’s an example:

class Row: def __init__(self, words): self.words = words self.palindrome_count = sum(is_palindrome(word) for word in words) def __lt__(self, other): return self.palindrome_count < other.palindrome_count matrix = [Row(["aba", "xyz"]), Row(["abc", "def"]), Row(["pop", "mom", "dad"])] sorted_matrix = sorted(matrix, key=lambda row: row.palindrome_count) print([[word for word in row.words] for row in sorted_matrix])

Output: [[‘abc’, ‘def’], [‘aba’, ‘xyz’], [‘pop’, ‘mom’, ‘dad’]]

The `Row`

class encapsulates a list of words along with its palindrome count. It defines the `__lt__()`

method, which is used by sorted(). After creating instances of the `Row`

class for each row in the matrix, the sorted() function is used to sort these instances.

## Method 3: In-Place Sort with List.sort()

The list.sort() method provides an in-place sort that modifies the original matrix. We can use this to sort the matrix internally, without creating a new sorted matrix, saving on memory when dealing with large datasets.

Here’s an example:

def sort_matrix_by_palindrome_in_place(matrix): matrix.sort(key=lambda row: sum(is_palindrome(word) for word in row)) matrix = [["aba", "xyz"], ["abc", "def"], ["pop", "mom", "dad"]] sort_matrix_by_palindrome_in_place(matrix) print(matrix)

Output: [[‘abc’, ‘def’], [‘aba’, ‘xyz’], [‘pop’, ‘mom’, ‘dad’]]

In this snippet, we define a function that applies the `list.sort()`

method to sort the matrix in place. This avoids extra memory allocation but alters the original dataset.

## Method 4: Using Pandas DataFrame

Integrating with the powerful Pandas library, we can convert the matrix into a DataFrame and leverage DataFrame’s sorting capabilities. This method is particularly efficient for large datasets and offers extensive functionality for data analysis.

Here’s an example:

import pandas as pd def sort_matrix_with_pandas(matrix): df = pd.DataFrame({'row': matrix}) df['palindrome_count'] = df['row'].apply(lambda x: sum(is_palindrome(word) for word in x)) return df.sort_values('palindrome_count')['row'].tolist() matrix = [["aba", "xyz"], ["abc", "def"], ["pop", "mom", "dad"]] sorted_matrix = sort_matrix_with_pandas(matrix) print(sorted_matrix)

Output: [[‘abc’, ‘def’], [‘aba’, ‘xyz’], [‘pop’, ‘mom’, ‘dad’]]

Here, we create a DataFrame from the matrix and then add a column ‘palindrome_count’ where we calculate the count for each row. We then sort the DataFrame by this column and convert it back to a list format.

## Bonus One-Liner Method 5: Lambda and List Comprehension

For a succinct solution, Python’s lambda functions combined with list comprehension can achieve the same result in a single line of code, which is elegant and highly readable for those familiar with Python’s functional programming features.

Here’s an example:

sorted_matrix = sorted(matrix, key=lambda row: sum(word == word[::-1] for word in row)) print(sorted_matrix)

Output: [[‘abc’, ‘def’], [‘aba’, ‘xyz’], [‘pop’, ‘mom’, ‘dad’]]

This code uses a lambda function within the sorted() call to count palindromes in a concise manner. A list comprehension checks each word for the palindrome property inline without the need for an auxiliary function, providing a clean and efficient one-liner.

## Summary/Discussion

**Method 1: Basic Function with Sorted().**Offers customization and clarity. Not the most succinct or Pythonic approach.**Method 2: Using a Custom Class.**Provides an object-oriented approach. It may be excessive for simple tasks but is highly expandable.**Method 3: In-Place Sort with List.sort().**Saves memory by sorting in place. It alters the original data, which may not always be desirable.**Method 4: Using Pandas DataFrame.**Leverages powerful data manipulation features. Depends on external libraries and might be an overkill for small tasks.**Bonus One-Liner Method 5:**Lambda and List Comprehension. Concise and efficient. Potentially less readable for those less familiar with Python’s syntax.