Soyo

May Leetcode Challenge - Day 28

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.

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
    }
}

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