AlgoSolveoRoadmap › Stage 10: Tries & Bits › Pattern 53 of 53
DSA pattern guide
Bit Manipulation — Subsets & XOR
Enumerate subsets, XOR over ranges.
Use it when
Enumerate subsets, XOR over ranges.
Key idea
A mask from 0 to 2ⁿ−1 represents a subset. Prefix XOR answers range XOR in O(1).
Practice problems, in order
- SubsetsMedium
- Subsets IIMedium
- XOR Queries of a SubarrayMedium
- Maximum XOR of Two Numbers in ArrayMedium
- Maximum XOR With an Element From ArrayHard
How to practise this pattern
- Read the problem and look for the signal above before writing any code.
- Say the brute force out loud, with its time complexity, then ask what work it repeats.
- Apply the key idea and write the optimised version yourself.
- If you're stuck for more than 10 minutes, take one small hint, not the full solution.
- Move to the next problem only when you can explain why this pattern fits.
Stuck on one of these?
The AlgoSolveo extension (free, launching soon) sits beside the LeetCode problem and gives the smallest hint that gets you moving, never the full answer. Solved problems tick off on your roadmap.
Join the extension waitlistTrack it on the roadmap