#leetcode#338. Counting Bits

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.

研究规律
位运算
与
与或

class Solution {

public:

    vector<int> countBits(int num) {

        vector<int> cc(num+1,0);

        int i;

        for(i=1;i<=num;i++)

        cc[i]=cc[i>>1]+i%2;

        return cc;

    }

};