Counting Bits
Detailed guide and Python implementation for the 'Counting Bits' problem.
1. Concept Overview
The 'Counting Bits' problem is a key challenge in the Bit Manipulation section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Counting Bits.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Counting Bits carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
Given an integer n, return an array ans of length n + 1 such that for each i (0 <= i <= n), ans[i] is the number of 1's in the binary representation of i.
Write a function countBits(n: int) -> List[int].
- •0 <= n <= 10^5
Examples
n = 2
[0,1,1]
0 -> 0; 1 -> 1; 2 -> 10.
n = 5
[0,1,1,2,1,2]
0 -> 0; 1 -> 1; 2 -> 1; 3 -> 2; 4 -> 1; 5 -> 2.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def count_bits_opt(n):
dp = [0] * (n + 1); offset = 1
for i in range(1, n + 1):
if offset * 2 == i: offset = i
dp[i] = 1 + dp[i - offset]
return dpBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def count_bits_brute(n):
return [bin(i).count("1") for i in range(n + 1)]Algorithm Pattern Checklist
When dealing with Bit Manipulation data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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