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:
Input: 2
Output: [0,1,1]
Example 2:
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
DP with pattern
dp[i] = dp[i - k ^ 2] + 1
class Solution {
func countBits(_ num: Int) -> [Int] {
var dp = [Int](repeating: 0, count: num + 1)
if num == 0 { return dp }
var offset = 1
for i in 1...num {
if i == (offset * 2) {
offset *= 2
}
dp[i] = dp[i - offset] + 1
}
return dp
}
}