**π‘ Problem Formulation:** You are given a list of integers and need to sort them based on the number of 1s in their binary representation, with fewer 1s coming first. For example, given the input `[3, 7, 8, 9]`

, the desired output after sorting based on the binary 1 count would be `[8, 3, 9, 7]`

because their binary forms (1000, 11, 1001, 111) have 1, 2, 2, and 3 ones respectively.

## Method 1: Using the `sort()`

Method with a Custom Key Function

This method involves using Python’s native `sort()`

method and providing a custom key function that calculates the number of 1s in the binary representation of each number. The `bin()`

function gets the binary string, and the `count()`

method finds the number of 1s.

Here’s an example:

def count_ones(x): return bin(x).count('1') numbers = [3, 7, 8, 9] numbers.sort(key=count_ones) print(numbers)

Output: `[8, 3, 9, 7]`

This code defines a function `count_ones()`

that calculates the number of 1s in the binary representation of a number. The list `numbers`

is then sorted using this function as the key. The resulting list is sorted by ascending number of 1s in their binary representations.

## Method 2: Using Lambda Function Inside `sorted()`

The lambda function provides an inline method to define the sorting key, combining the binary conversion and 1 count with Python’s `sorted()`

function to sort the list without modifying the original.

Here’s an example:

numbers = [3, 7, 8, 9] sorted_numbers = sorted(numbers, key=lambda x: bin(x).count('1')) print(sorted_numbers)

Output: `[8, 3, 9, 7]`

This snippet uses a lambda function to succinctly define a custom sorting key that counts the number of binary 1s directly in the `sorted()`

call. The sorted list is output without altering the original `numbers`

list.

## Method 3: Using a Custom Sorting Function

IIn this method, we create a custom sorting function that employs the `sorted()`

function’s key parameter, but explicitly defines the key calculation process within a separate, named function. This aids readability and debuggability.

Here’s an example:

def binary_1_count(x): return bin(x).count('1') numbers = [3, 7, 8, 9] sorted_numbers = sorted(numbers, key=binary_1_count) print(sorted_numbers)

Output: `[8, 3, 9, 7]`

This code has a standalone function `binary_1_count()`

that is used as the key for sorting. The function returns the count of 1s in the binary representation which is used by `sorted()`

to sort the array.

## Method 4: Custom Sort with Tuples

This method uses tuple pairing where each number is paired with its 1 count in binary, sorted by the count, then stripped of the counts to obtain the sorted list.

Here’s an example:

numbers = [3, 7, 8, 9] sorted_numbers = [x for x, _ in sorted((x, bin(x).count('1')) for x in numbers)] print(sorted_numbers)

Output: `[8, 3, 9, 7]`

Here we’ve created tuples pairing each number with its binary 1 count, sorted these tuples with Python’s default tuple sort (which sorts by first elements first), and then discarded the counts during list comprehension to get the sorted list.

## Bonus One-Liner Method 5: Using List Comprehension and `sorted()`

A concise one-liner that encapsulates Method 2, this technique employs list comprehension to define the key in the `sorted()`

function succinctly.

Here’s an example:

print(sorted([3, 7, 8, 9], key=lambda x: bin(x).count('1')))

Output: `[8, 3, 9, 7]`

This single line of code uses a lambda function as a key for the `sorted()`

to count binary 1s. It’s a compact and quick way to sort the list.

## Summary/Discussion

**Method 1: Custom Key Function with**It is straightforward and readable. However, it mutates the original list.`sort()`

.**Method 2: Lambda Function in**It achieves a clean one-liner that’s easy to understand. The original list stays untouched. The downside is that lambdas are sometimes less readable than named functions.`sorted()`

.**Method 3: Custom Sorting Function.**Great for readability and debugging by explicitly defining the key function. Like Method 2, it doesn’t mutate the original list. May be overkill for simple cases.**Method 4: Custom Sort with Tuples.**Using tuples is a Pythonic approach and can be faster due to the way tuples are compared. It is less readable than the others.**Bonus Method 5: List Comprehension One-Liner.**The most concise method; perfect for quick scripts and coding challenges. But in complex programs, it could sacrifice readability.