class Solution:

def count_bits(self, n: int) -> list[int]:

"""

Optimized version with better variable naming and comments.

Time: O(n)

Space: O(1) excluding output array

"""

if n == 0:

return [0]

bits_count = [0] * (n + 1)

for num in range(1, n + 1):

# For any number, the count of 1s equals:

# count of 1s in (num >> 1) + whether the last bit is 1

bits_count[num] = bits_count[num >> 1] + (num & 1)

return bits_count