I was confused by all of this, lol. But after some review of lambda. I specifically didnt understand why you needed the (seemingly additional) , nums) in (count_set_bits(num), num)). NiperGPT helped explain so I thought I'd make a note of it for anyone else currious.

#per NiperGPT

Args:

• lambda x: This defines an anonymous function that takes a single argument, which is named 'x'. 'x' will represent each element of the arr list as sorted() iterates through it.

How the Sorting Works:

• The sorted() function uses the key function to determine the order of the elements. Here's how the comparison process happens:

  1. For each element x in arr, the lambda function is called, and it returns a tuple: (count_bits(x), x).

  2. Python's sorting algorithm then compares these tuples element by element. Python tuples are compared lexicographically (like words in a dictionary). This means:

     • First, it compares the first elements of the tuples (the count_bits(x)
       values). If these are different, the elements are sorted based on the number of set bits. Elements with fewer set bits come earlier in the sorted list.

     • If the first elements of the tuples are the same (i.e., two numbers have the same number of set bits), then the second elements of the tuples are compared (the original x
       values). This means that if two numbers have the same number of set bits, they are sorted in their natural numerical order.

Here's how the sorting would proceed:

input = [5, 3, 7, 10, 1]

1. 5: count_bits(5) returns 2. The tuple is (2, 5).
2. 3: count_bits(3) returns 2. The tuple is (2, 3).
3. 7: count_bits(7) returns 3. The tuple is (3, 7).
4. 10: count_bits(10) returns 2. The tuple is (2, 10).
5. 1: count_bits(1) returns 1. The tuple is (1, 1).

Now, Python sorts based on these tuples:

• (1, 1) comes first because 1 < 2 and 1 < 3.
• (2, 3), (2, 5), and (2, 10) all have the same first element (2). So, they are sorted based on the second element (3, 5, and 10), resulting in the order 3, 5, 10.
• (3, 7) comes last because 3 > 2 and 3 > 1.

Therefore, the final sorted list array_sorted
would be: [1, 3, 5, 10, 7]