Counting Bits
For every i from 0 to n, return how many 1 bits i has.
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Lesson notes
Try it before you watch
Restate the problem in your own words, list the edge cases, and sketch a solution with its running time. Then play the video and compare.
Reveal the key idea
Reuse earlier answers: bits(i) = bits(i >> 1) + (i & 1).
Pattern: Bit manipulation & math. Use XOR, AND and shifts to work on the binary representation directly.
Complexity
| Measure | Bound |
|---|---|
| Time | O(n) |
| Extra space | O(n) for the output |
Walkthroughs often start from a simpler approach first; aim to reach these bounds. New to Big-O? Read understanding algorithmic complexity.