Solution: Counting Bits
Explore how to apply dynamic programming techniques to count the number of 1 bits in binary representations of integers up to n. Understand the use of previous computations for even and odd numbers to optimize the solution. This lesson helps you implement an efficient algorithm that improves on naive approaches by reducing time complexity to linear and minimizing space usage.
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