Solution: Counting Bits
Explore a dynamic programming method to count the number of 1 bits in binary representations of numbers up to n. Learn to optimize the counting process using even and odd number properties and apply bit manipulation techniques. Understand time and space complexity considerations in this practical coding interview problem.
Statement
For a given positive integer, n, your task is to return an array of length such that for each where , result[x] is the count of s in the binary representation of .
Constraints:
Solution
So far, you have probably brainstormed some approaches and have an idea of how to solve this problem. Let’s explore some of these approaches and figure out which one to follow based on considerations such as time complexity and any implementation constraints.
Naive approach
The naive approach for this solution would be to iterate through the string character by character. During the traversal, we convert each number to its binary representation, count the number of
This approach would have a time complexity of