Question
Formatted question description: https://leetcode.ca/all/338.html
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 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.
@tag-dp
Algorithm
DP: countAtNum[i] = countAtNum[i>>1] + (i&1);
Code
Java
public class Counting_Bits {
class Solution {
public int[] countBits(int num) {
int[] countAtNum = new int[num + 1];
if (num <= 0) {
return countAtNum;
}
countAtNum[0] = 0; // to be explicit
countAtNum[1] = 1;
for (int i = 2; i <= num; i++) {
// @note @memorize : & operator lower than +, so should be in ()
countAtNum[i] = countAtNum[i>>1] + (i&1);
}
return countAtNum;
}
}
}