**π‘ Problem Formulation:** Imagine you have a matrix represented as a list of lists in Python, and you need to organize this matrix based on the medians of its rows. The matrix should be sorted such that rows with lower median values come before rows with higher median values. For example, given the input matrix `[[3,1,2],[6,5,4],[9,8,7]]`

, the desired output after sorting by row median would be `[[1,2,3],[4,5,6],[7,8,9]]`

.

## Method 1: Using the Sorted Function

Utilize Python’s `sorted()`

function along with a lambda function to directly sort the rows based on their median using the `statistics.median()`

function. This method provides readability and is straightforward for understanding and maintenance.

Here’s an example:

import statistics matrix = [[3,1,2],[6,5,4],[9,8,7]] sorted_matrix = sorted(matrix, key=lambda row: statistics.median(row)) print(sorted_matrix)

The output of this code snippet:

[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

This code snippet sorts a given matrix by row medians. It imports the `statistics`

module to use the `median()`

function. It then sorts the matrix using the `sorted()`

function with a lambda that computes the median for each row. The result is a new matrix sorted by the median of its rows.

## Method 2: Custom Sort Function

Define a custom function to calculate the median, and then use `sorted()`

with this function. This is useful when more control over the median calculation is required, or when avoiding additional module imports.

Here’s an example:

def row_median(row): sorted_row = sorted(row) mid = len(sorted_row) // 2 return (sorted_row[mid] + sorted_row[~mid]) / 2 matrix = [[3,1,2],[6,5,4],[9,8,7]] sorted_matrix = sorted(matrix, key=row_median) print(sorted_matrix)

The output of this code snippet:

[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

This snippet features a custom function `row_median()`

that finds the median of a row. It is used in conjunction with the `sorted()`

function as the key argument to sort the matrix. The median is obtained by sorting each row and finding the middle value, or the average of the two middle values if the list length is even.

## Method 3: In-place Sort With Decorate-Sort-Undecorate (DSU) Pattern

The Decorate-Sort-Undecorate (DSU) pattern (also known as the Schwartzian transform) involves creating a structure to hold the original rows and their medians, sorting it, and then stripping away the medians. This can be done in-place to save memory.

Here’s an example:

import statistics matrix = [[3,1,2],[6,5,4],[9,8,7]] matrix_with_medians = [(statistics.median(row), row) for row in matrix] matrix_with_medians.sort() sorted_matrix = [row for median, row in matrix_with_medians] print(sorted_matrix)

The output of this code snippet:

[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

Here, a list comprehension creates pairs of row medians and rows. The `sort()`

method is then used to sort these pairs in-place, and a final list comprehension strips the medians, yielding a sorted matrix. This reduces the overhead of calling a key function multiple times for the same row during sorting.

## Method 4: Using NumPy

If working with numerical data, NumPy’s functions can be leveraged for efficient computations. NumPy provides methods for calculating medians and an `argsort()`

function to sort by indices, which can be applied to sort the matrix rows by their medians.

Here’s an example:

import numpy as np matrix = np.array([[3,1,2],[6,5,4],[9,8,7]]) row_medians = np.median(matrix, axis=1) sorted_indices = np.argsort(row_medians) sorted_matrix = matrix[sorted_indices] print(sorted_matrix)

The output of this code snippet:

[[1 2 3] [4 5 6] [7 8 9]]

This code snippet uses NumPy, a powerful numerical computing library. It computes the median of each row of a matrix with `np.median()`

and then sorts the rows by using `np.argsort()`

to obtain the indices that would sort the matrix by the median. Finally, it creates a sorted matrix applying these indices.

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

A one-liner approach combines list comprehension with the `sorted()`

function and `statistics.median()`

, resulting in a compact and expressive way to sort the matrix by row medians.

Here’s an example:

import statistics matrix = [[3,1,2],[6,5,4],[9,8,7]] sorted_matrix = sorted(matrix, key=statistics.median) print(sorted_matrix)

The output of this code snippet:

[[1, 2, 3], [4, 5, 6], [7, 8, 9]]

This succinct code line sorts a matrix by the median of its rows. By passing the `statistics.median()`

function directly to the `key`

parameter of the `sorted()`

function, the matrix rows are sorted in a concise manner.

## Summary/Discussion

**Method 1:**Using the Sorted Function. It is clean and readable. However, it requires importing an additional module.**Method 2:**Custom Sort Function. Offers customization and does not rely on external modules, but is more verbose than one-liners.**Method 3:**In-place Sort With DSU Pattern. Efficient approach that saves computation time, though it can be less intuitive for those unfamiliar with the pattern.**Method 4:**Using NumPy. Highly efficient for large numerical datasets and leverages optimized library functions. However, it requires NumPy and may be overkill for simpler tasks.**Method 5:**Bonus One-Liner. The most concise approach, best for small to medium-sized tasks where brevity is valued. Might be less readable for those who prefer explicitness.