**π‘ Problem Formulation:** When working with lists of numbers or strings in Python, you might encounter a situation where you need to sort the elements based on the frequency of a specific digit they contain. For instance, given a list of numbers `[123, 45, 11415, 78, 901]`

, you may wish to sort them by the number of ‘1’s each element contains, yielding the sorted list `[45, 78, 901, 123, 11415]`

.

## Method 1: Using a Custom Sort Function

This method involves defining a custom function that counts the occurrences of the desired digit within each element, then using this function as a key in the `sorted()`

function or `list.sort()`

method. This approach provides clarity and flexibility, allowing to sort any iterable based on the count of a particular digit.

Here’s an example:

def count_digit(number, digit): return str(number).count(str(digit)) numbers = [123, 45, 11415, 78, 901] sorted_numbers = sorted(numbers, key=lambda x: count_digit(x, 1)) print(sorted_numbers)

Output:

[45, 78, 901, 123, 11415]

This code snippet defines a function `count_digit`

that takes a number and a digit and returns the count of the digit in the number. Then, it uses this function as the sorting key for the `sorted()`

function, passing each number as an argument to the lambda function, which in turn calls `count_digit`

.

## Method 2: Using List Comprehensions

List comprehensions in Python provide a concise way to sort based on complex criteria without defining separate functions. In this method, we’ll embed the digit counting within a list comprehension to generate the sort keys for each element, which will be used by the `sorted()`

function.

Here’s an example:

numbers = [123, 45, 11415, 78, 901] sorted_numbers = sorted(numbers, key=lambda x: str(x).count('1')) print(sorted_numbers)

Output:

[45, 78, 901, 123, 11415]

Here, we have a one-liner lambda function that is directly counting ‘1’s in each element, turned into a string, using `str.count()`

. The sorting is then based on these counts.

## Method 3: Using the map Function

The `map()`

function applies a given function to every item of an iterable and returns a list of the results. We’ll use `map()`

to create a list of tuples containing the digit counts and original elements, which we’ll then sort.

Here’s an example:

numbers = [123, 45, 11415, 78, 901] count_tuples = list(map(lambda x: (str(x).count('1'), x), numbers)) sorted_numbers = [num for count, num in sorted(count_tuples)] print(sorted_numbers)

Output:

[45, 78, 901, 123, 11415]

In this code snippet, we create a list of tuples using map, where each tuple contains the count of ‘1’s and the original number. We then sort this list of tuples (which Python does by the first element of the tuples by default) and extract the original numbers from the sorted list.

## Method 4: Using a Custom Class with __lt__ Method

Defining a custom class with an overridden `__lt__()`

method enables object comparison based on a customizable criterion. In this case, we will compare objects based on their digit count.

Here’s an example:

class Number: def __init__(self, value): self.value = value def __lt__(self, other): return str(self.value).count('1') < str(other.value).count('1') numbers = [Number(123), Number(45), Number(11415), Number(78), Number(901)] sorted_numbers = sorted(numbers, key=lambda x: x.value) print([num.value for num in sorted_numbers])

Output:

[45, 78, 901, 123, 11415]

This code snippet defines a class `Number`

with an `__lt__()`

method that compares two instances of the class by counting ‘1’s in their values. The list is then sorted based on this custom comparison, and we extract the `value`

attributes for the output.

## Bonus One-Liner Method 5: Using functools and cmp_to_key

`functools.cmp_to_key()`

is a utility from Python’s `functools`

module that converts a comparison function into a key function. This method enables a one-liner sort using a custom comparison for digit counting.

Here’s an example:

from functools import cmp_to_key numbers = [123, 45, 11415, 78, 901] sorted_numbers = sorted(numbers, key=cmp_to_key(lambda x, y: str(x).count('1') - str(y).count('1'))) print(sorted_numbers)

Output:

[45, 78, 901, 123, 11415]

The code uses `functools.cmp_to_key()`

to convert a lambda that implements a custom comparison based on ‘1’s count into a key function for sorting. The lambda subtracts the count results to follow traditional comparison result patterns.

## Summary/Discussion

**Method 1:**Custom Sort Function. Provides clear separation of logic. Requires additional code for the function definition.**Method 2:**List Comprehensions. Offers concise one-liners. Can become unreadable with more complex logics.**Method 3:**map Function. Useful for pre-computing sort keys. Could be less performant due to tuple creation and extra iterations.**Method 4:**Custom Class with`__lt__`

Method. Offers the most object-oriented approach. Overkill for simple use cases and can be less readable.**Bonus One-Liner Method 5:**Using`cmp_to_key`

. Provides crisp, functional style sorting. The comparison logic can be more complex to reason about than using key functions.