Problem

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

Dynamic

Main idea - dynamic programming :

Create resulting array k with len num. Set solution ofr 0 and 1.

Create variablem where we will save next pow of 2 -> cmp. Init with value == 2. Walk throw resulting array and write to idx position value k[idx-cmp/2]+1.

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func countBits(num int) []int {
    k := make([]int,num+1)
    k[0] = 0
    if num == 0 {
        return k
    }
    cmp:=1
    for idx:=1; idx<=num; idx++ {
        if idx == 1 {
            k[1] = 1
            cmp = 2
            continue
        }
        if cmp == idx {
            cmp *=2
        }
        k[idx] = k[idx-cmp/2]+1
        
    }
    return k
}