Counting Bits

Given an integer n, count the number of 1’s in the binary representation of every number in the range [0, n].

Return an array output where output[i] is the number of 1’s in the binary representation of i.

Example 1:

Input: n = 4Output: [0,1,1,2,1]

Explanation:
0 --> 0
1 --> 1
2 --> 10
3 --> 11
4 --> 100

Constraints:

0 <= n <= 1000

Solution

If we go through the numbers from $0$ to $n$, we can find that for a binary number $1B$ ($B$ can be any binary sequence), the number of 1 in $B$ is computed and $1B$ has one more 1 compared with $B$. Thus, we can do a dynamic programming, transferring the number of 1 from $B$ to $1B$.

Code

class Solution:def countBits(self, n: int) -> List[int]:power = 1dp = [0]*(n+1)dp[0] = 0for i in range(1, n+1):if i == power*2:power *= 2dp[i] = dp[i-power]+1return dp