Practice: Counting Bits

Problem: https://leetcode.com/problems/counting-bits/

Recognition reminder: you return the set-bit count for every integer from 0 to n. Bits handled directly, plus a “build each answer from a smaller one” smell, is a bit cue with a Week 13 DP flavor.

Before you start (the five-beat rhythm)

  1. Your three Pattern Cards for this week are already written.
  2. Name the pattern aloud (which of the three, and why) and write your approach as a plain-English comment before any code.
  3. Struggle floor: 25 minutes unaided. No hints, no AI, no Discuss tab.
  4. If stuck past the floor, ask the tutor for a hint. Six rungs, one per ask.
  5. Debrief in your commit message before moving to the next problem.

Your target

Fill these in yourself before you look at anyone else’s solution:

Target time complexity:  ____
Target space complexity: ____

Computing every count independently is O(n log n); a single pass that reuses an earlier answer for each i brings it to O(n) time, with O(n) space for the output array. Ask which already-computed entry the count for i can be built from, and know why that makes the DP faster than recomputing.

Where your code goes

Write your solution in your own work repo (see getting-started.md), not in this folder. This folder ships only the problem spec and a provided-example test (tests/test_provided.py) so you can check the given cases locally before you submit to LeetCode’s judge. The judge is the oracle; the tutor will not confirm your answer by reading it.

Debrief (paste into your commit message) 

1. What pattern did this turn out to be?
2. What was the trigger phrase or input shape that should have made me reach for it?
3. What was the time and space complexity, and what would dominate at scale?
4. What edge case would have broken my first attempt?
5. What would I do differently in three days when I see this cold?