# Counting Bits

Category

Bit Manipulation

Checkbox

Checkbox

Difficulty

Easy

Index

67

Key Ideas

The key idea to solve this problem is to use dynamic programming to calculate the number of set bits in each number.

Problem Number

338

Problem Summary

The problem "Counting Bits" (Problem Number: 338) is categorized under Bit Manipulation and Dynamic Programming. It requires counting the number of 1's in the binary representation of each number from 0 to a given number. A key pitfall to avoid is mistakenly using a naive approach that counts the bits for each number individually, resulting in a less efficient solution. Instead, utilizing the previously calculated results can lead to an optimized dynamic programming solution.

Solution Summary

To solve the problem "Counting Bits" from LeetCode-75 curated list, the best solution involves using dynamic programming. The key idea is to utilize the fact that the number of set bits in a number can be determined by the number of set bits in its previous power of 2 number. By maintaining an array to store the count of set bits for each number from 0 to n, we can iteratively calculate the count by using the previously computed values. Starting with the base case of 0 having 0 set bits, we use the formula

`dp[i] = dp[i//2] + i%2`

to compute the count for each number. This solution has a time complexity of O(n) as we iterate through all numbers from 0 to n.Tags

Dynamic Programming

Bit Manipulation