**π‘ Problem Formulation:** Suppose you have a list of integer elements, and your task is to create a new list where each element is the square of the original elements, sorted in non-decreasing order. For instance, if the input list is `[3, 1, -2]`

, the expected output would be `[1, 4, 9]`

.

## Method 1: Using List Comprehension and Sorted Function

The first method involves squaring each element using a list comprehension and then sorting the resulting list using Python’s built-in `sorted()`

function. This method is efficient and readable, and leverages Python’s concise syntax possibilities. The `sorted()`

function returns a new list containing all elements from the iterable in ascending order.

Here’s an example:

numbers = [3, 1, -2] squared_sorted = sorted([x**2 for x in numbers]) print(squared_sorted)

Output:

[1, 4, 9]

This snippet first creates a new list with the square of each element in the original list using list comprehension. Then, it sorts this list of squared numbers utilizing Python’s `sorted()`

function, which returns a sorted list in ascending order.

## Method 2: Using Map and Sorted Functions

Method 2 combines the `map()`

function to apply the squaring operation to each element and the `sorted()`

function to sort the result. While similar to list comprehensions, `map()`

may be slightly less readable for those unfamiliar with functional programming paradigms in Python.

Here’s an example:

numbers = [3, 1, -2] squared_sorted = sorted(map(lambda x: x**2, numbers)) print(squared_sorted)

Output:

[1, 4, 9]

In this example, `map()`

takes a lambda function that squares its input and applies it to each element of `numbers`

. The map object is then passed to `sorted()`

, which sorts the elements and returns a sorted list.

## Method 3: Using a Custom Function With Sorted’s Key Parameter

Another method employs Python’s `sorted()`

function with a key parameter. By defining a custom squaring function and passing it as the key, the sorting is done based on the squared values, without explicitly creating a list of squared numbers.

Here’s an example:

numbers = [3, 1, -2] squared_sorted = sorted(numbers, key=lambda x: x**2) print(squared_sorted)

Output:

[1, -2, 3]

The key function transforms the items before they are compared for sorting, yet the original elements are preserved in the resulting list. In this case, the items are sorted as if they were squared, resulting in their square values appearing in ascending order.

## Method 4: Using In-Place Sort With a Custom Function

Method 4 modifies the original list in place using the `list.sort()`

method with a key function. The `list.sort()`

method is often faster than `sorted()`

because it doesn’t create a new list. It is suitable when you do not need to retain the original list order.

Here’s an example:

numbers = [3, 1, -2] numbers.sort(key=lambda x: x**2) print(numbers)

Output:

[1, -2, 3]

Here the original list is sorted in-place using the `sort()`

method with a key parameter. As with Method 3, the integers are arranged based on the order of their squares, but the original values are retained in the sorted list.

## Bonus One-Liner Method 5: Using a Generator Expression With Sorted

A one-liner version of Method 1 can be employed using a generator expression within the `sorted()`

function call. This method is more memory efficient than using a list comprehension, especially with large datasets.

Here’s an example:

squared_sorted = sorted(x**2 for x in [3, 1, -2]) print(squared_sorted)

Output:

[1, 4, 9]

This single line of code is essentially performing the same operations as Method 1 but uses a generator expression instead of a list comprehension, yielding elements one by one to be sorted.

## Summary/Discussion

**Method 1:**List Comprehension with Sorted. Straightforward and concise. Memory intensive for large lists.**Method 2:**Map with Sorted. Functional approach. Potentially less readable to those not familiar with`map()`

.**Method 3:**Custom Key Function with Sorted. Preserves original list elements. May cause confusion as the output list elements are not squared.**Method 4:**In-Place Sort with Custom Function. Memory efficient as it modifies the original list. Destroys the initial order of the list which might not be desirable.**Method 5:**Generator with Sorted. Memory efficient. However, generator expressions might be less familiar and therefore less readable for some.