338. Counting Bits

Medium

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Given an integer num, return an array of the number of 1's in the binary representation of every number in the range [0, num].

 

Example 1:

Input: num = 2
Output: [0,1,1]
Explanation:
0 --> 0
1 --> 1
2 --> 10

Example 2:

Input: num = 5
Output: [0,1,1,2,1,2]
Explanation:
0 --> 0
1 --> 1
2 --> 10
3 --> 11
4 --> 100
5 --> 101

 

Constraints:

• 0 <= num <= 105

 

Follow up:

• It is very easy to come up with a solution with run time O(32n). Can you do it in linear time O(n) and possibly in a single pass?
• Could you solve it in O(n) space complexity?
• Can you do it without using any built-in function (i.e., like __builtin_popcount in C++)?