Counting Bits
Difficulty: Easy
Category: DSA
Topics: Dynamic Programming, Bit Manipulation
Asked at: Amazon, Blizzard
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++)?