**π‘ Problem Formulation:** You’re given a matrix (a list of lists) containing various elements and `None`

values. The task is to sort the rows of the matrix based on the frequency of `None`

values they contain, with the least number of `None`

occurring rows coming first. For instance, [[1, None], [None, None], [3, 4]] should be sorted to [[3, 4], [1, None], [None, None]].

## Method 1: Using a Custom Sort Function

This method involves using a custom key function with the `sorted()`

function or `.sort()`

method, which counts the number of `None`

values in each row. It’s an explicit way to communicate the sorting condition and highly versatile to adapt for variations.

Here’s an example:

matrix = [[None, None], [7, None], [None, 5], [1, 2]] matrix.sort(key=lambda row: row.count(None)) print(matrix)

Output:

[[1, 2], [7, None], [None, 5], [None, None]]

This code snippet sorts the rows of the matrix in place. The sort prioritizes rows with fewer `None`

values by utilizing the `count`

method of lists.

## Method 2: Using the Collections Module

Python’s `collections`

module can be used to efficiently count occurrences. In this method, the `Counter`

class can help count `None`

values in rows, which can then be used for sorting purposes.

Here’s an example:

from collections import Counter matrix = [[3, None], [None, None], [None, 4], [2, 5]] sorted_matrix = sorted(matrix, key=lambda row: Counter(row)[None]) print(sorted_matrix)

Output:

[[2, 5], [3, None], [None, 4], [None, None]]

The code first imports the `Counter`

class, which makes counting fast and easy. The `sorted()`

function is then used with a `lambda`

using the `Counter`

to sort the matrix.

## Method 3: Using NumPy Library

If the data can be converted to a NumPy array, sorting can leverage NumPy’s powerful capabilities. This method is convenient when working with numeric data and can perform complex sorting operations efficiently.

Here’s an example:

import numpy as np def none_sort(matrix): none_counts = np.sum(np.vectorize(lambda x: x is None)(matrix), axis=1) return matrix[np.argsort(none_counts)] matrix = np.array([[None, 9], [5, None], [7, 8], [None, None]]) sorted_matrix = none_sort(matrix) print(sorted_matrix)

Output:

[[7 8] [5 None] [None 9] [None None]]

The example uses NumPy’s vectorization and argsort functions to count `None`

values and sort the array respectively. This takes advantage of NumPy’s high-performance operations.

## Method 4: Using Pandas DataFrames

For those comfortable with DataFrames and possibly dealing with heterogeneous data, using Pandas can be an excellent option. This method has the added benefit of handling non-numeric data seamlessly.

Here’s an example:

import pandas as pd def none_sort_df(matrix): df = pd.DataFrame(matrix) none_counts = df.isnull().sum(axis=1) return df.iloc[none_counts.argsort()] matrix = [[None, 'a'], [3, 4], ['b', None], [None, None]] sorted_matrix = none_sort_df(matrix) print(sorted_matrix)

Output:

0 1 1 3 4 2 b None 0 None a 3 None None

Pandas `isnull()`

method is used to get a count of `None`

values. The rows are then sorted based on these counts using DataFrame’s `iloc`

method along with `argsort()`

.

## Bonus One-Liner Method 5: Using List Comprehension and Count

The power of list comprehensions can be harnessed to perform a concise one-liner sort. This approach is most suitable for simple cases and for those familiar with list comprehension syntax.

Here’s an example:

matrix = [[None, 3], [4, 5], [None, None], [2, None]] sorted_matrix = sorted(matrix, key=lambda row: row.count(None)) print(sorted_matrix)

Output:

[[4, 5], [2, None], [None, 3], [None, None]]

This one-liner uses the list `count()`

function within a lambda to sort the matrix. It provides a quick and efficient solution without needing to define a separate function.

## Summary/Discussion

**Method 1:**Custom Sort Function. Flexible and clear. Requires writing a custom function.**Method 2:**Collections Module. Efficient counting with Counter. Less efficient for tiny datasets.**Method 3:**NumPy Library. Good for numeric data and performance. Requires numerical data and knowledge of NumPy.**Method 4:**Pandas DataFrames. Great for mixed data types. Requires pandas and might be overkill for simple tasks.**Method 5:**List Comprehension One-Liner. Simplest approach. May not be explicit enough for complex cases.