Easy

Given an integer n, return an array ans of length n + 1 such that for each i (0 <= i <= n), ans[i] is the number of 1's in the binary representation of i.

Example 1:

Input: n = 2

Output: [0,1,1]

Explanation:

0 --> 0
1 --> 1
2 --> 10 

Example 2:

Input: n = 5

Output: [0,1,1,2,1,2]

Explanation:

0 --> 0
1 --> 1
2 --> 10
3 --> 11
4 --> 100
5 --> 101 

Constraints:

• 0 <= n <= 105

Follow up:

• It is very easy to come up with a solution with a runtime of O(n log n). Can you do it in linear time O(n) and possibly in a single pass?
• Can you do it without using any built-in function (i.e., like __builtin_popcount in C++)?

# @param {Integer} num
# @return {Integer[]}
def count_bits(num)
  result = Array.new(num + 1, 0)
  border_pos = 1
  incr_pos = 1

  (1..num).each do |i|
    # when we reach pow of 2, reset border_pos and incr_pos
    if incr_pos == border_pos
      result[i] = 1
      incr_pos = 1
      border_pos = i
    else
      result[i] = 1 + result[incr_pos]
      incr_pos += 1
    end
  end

  result
end