Leetcode Counting Bits 338

Given a non negative integer number num. For every numbers i in the range 0 ≤ i ≤ num calculate the number of 1’s in their binary representation and return them as an array.

Example:
For num = 5 you should return [0,1,1,2,1,2].

Follow up:

It is very easy to come up with a solution with run time O(n*sizeof(integer)). But can you do it in linear time O(n) /possibly in a single pass?
Space complexity should be O(n).
Can you do it like a boss? Do it without using any builtin function like __builtin_popcount in c++ or in any other language.

题目链接

不让一个一个的计算
不允许使用已经有的库函数

被逼着查看之间的关系

每次添加的一位不是0就是1
vc[i] = vc[i/2] + (i%2)

class Solution {public:    vector<int> countBits(int num) {        vector<int> vc(num+1,0);        for(int i=1;i<=num;i++){            vc[i]=vc[i/2]+(i%2);        }              return vc;    }};