Counting Bits

Desicription

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 1:

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

Example 2:

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Input: 5
Output: [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.

Solution

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class Solution {
public:
std::vector<int> countBits(int num) {
auto res = std::vector<int>(num + 1);
for(int i = 0; i <= num; i++) {
res[i] = res[i >> 1] + (i & 1);
}
return res;
}
};