**π‘ Problem Formulation:** When working with matrices in Python, it’s occasionally necessary to sort rows based on a custom criterion. Consider the specific task of sorting a matrix by the count of elements that are greater than their immediate predecessor within each row. For example, given the matrix `[[1, 3, 2], [5, 1], [2, 2, 5, 3]]`

, the sorted order, considering the described criterion, should be `[[5, 1], [1, 3, 2], [2, 2, 5, 3]]`

.

## Method 1: Using a Custom Sort Function

This method involves writing a custom function to use as the key in Python’s built-in `sort()`

or `sorted()`

function. The function will calculate the count of elements greater than their preceding element for each row and the sorted function will sort the matrix based on these counts.

Here’s an example:

def count_greater_numbers(row): return sum(x > row[i-1] for i, x in enumerate(row) if i > 0) matrix = [[1, 3, 2], [5, 1], [2, 2, 5, 3]] sorted_matrix = sorted(matrix, key=count_greater_numbers) print(sorted_matrix)

Output:

[[5, 1], [1, 3, 2], [2, 2, 5, 3]]

The code snippet defines a function `count_greater_numbers`

which counts the number of times an element in a row is greater than its predecessor. The matrix is then sorted with the `sorted()`

function using this custom function as a key.

## Method 2: Lambda Function and List Comprehension

In this approach, we avoid defining an explicit function and instead use a lambda function combined with list comprehension directly in the sort key.

Here’s an example:

matrix = [[1, 3, 2], [5, 1], [2, 2, 5, 3]] matrix.sort(key=lambda row: sum(x > row[i-1] for i, x in enumerate(row) if i > 0)) print(matrix)

Output:

[[5, 1], [1, 3, 2], [2, 2, 5, 3]]

In this example, the `sort()`

method takes a lambda function that performs the same computation as the custom function in Method 1. This is a more concise way to sort the rows of the matrix inline without the need for an auxiliary function.

## Method 3: Using a Generator Expression

This method uses a generator expression as a lightweight alternative to list comprehensions for better memory efficiency when dealing with large data sets.

Here’s an example:

matrix = [[1, 3, 2], [5, 1], [2, 2, 5, 3]] sorted_matrix = sorted(matrix, key=lambda row: sum(x > row[i-1] for i, x in enumerate(row) if i > 0)) print(sorted_matrix)

Output:

[[5, 1], [1, 3, 2], [2, 2, 5, 3]]

This code uses a lambda function with a generator expression as the sorting key. The generator does not build an intermediate list, thus saving memory when sorting the matrix, especially beneficial for large matrices.

## Method 4: In-place Sorting with Custom Key

Comparable to Method 1, this strategy sorts the matrix in-place using a custom key function, affecting the original matrix directly.

Here’s an example:

def count_greater_numbers(row): return sum(x > row[i-1] for i, x in enumerate(row) if i > 0) matrix = [[1, 3, 2], [5, 1], [2, 2, 5, 3]] matrix.sort(key=count_greater_numbers) print(matrix)

Output:

[[5, 1], [1, 3, 2], [2, 2, 5, 3]]

This example modifies the original `matrix`

list instead of creating a new sorted list. The in-place sorting may be a desirable feature when memory optimization is a concern, and there’s no need to preserve the original order.

## Bonus One-Liner Method 5: Using Itemgetter

Utilize Python’s operator module and its `itemgetter()`

function in a one-liner to achieve the same result.

Here’s an example:

from operator import itemgetter matrix = [[1, 3, 2], [5, 1], [2, 2, 5, 3]] greater_counts = [sum(x > row[i-1] for i, x in enumerate(row) if i > 0) for row in matrix] sorted_matrix = [x for _, x in sorted(zip(greater_counts, matrix), key=itemgetter(0))] print(sorted_matrix)

Output:

[[5, 1], [1, 3, 2], [2, 2, 5, 3]]

In this one-liner, we create a list of counts and use the `zip`

function to pair each count with its corresponding row. The resultant pairs are sorted by the first item (the count), and the matrix rows are then arranged accordingly.

## Summary/Discussion

**Method 1:**Custom Sort Function. Intuitive and clear for understanding sorting criteria. Potentially less efficient due to function call overhead.**Method 2:**Lambda Function and List Comprehension. Concise and functional with no need for separate function definition. May be less readable for complex criteria.**Method 3:**Generator Expression. Memory-efficient, good for large matrices. Similar to Method 2, but slightly less readable due to generator syntax.**Method 4:**In-place Sorting. Directly modifies the input matrix, saving memory. Care required since original data ordering is lost after sorting.**Method 5:**One-Liner using Itemgetter. Concise and clever. May sacrifice some readability and be less straightforward for Python novices.