Sorting Numbers based on 1 Count in Their Binary Representation Using Python

💡 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 sort(). It is straightforward and readable. However, it mutates the original list.
• Method 2: Lambda Function in sorted(). 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.
• 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.