Bit Manipulation - Subsets Using Bitmask
What is the overall time complexity of generating all subsets of an array of size n using bitmask enumeration?
What is the overall time complexity of generating all subsets of an array of size n using bitmask enumeration?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Number of subsets
There are 2^n subsets for an array of size n.Step 2: Time per subset
For each subset, we check up to n bits to decide which elements to include.Step 3: Total time
Multiplying gives O(n * 2^n).Final Answer:
Option A -> Option AQuick Check:
Each subset requires O(n) to build, total subsets 2^n [OK]
Quick Trick: 2^n subsets, each takes O(n) to build [OK]
Common Mistakes:
MISTAKES- Ignoring the cost to build each subset
- Confusing with O(2^n) only which ignores element iteration
- Mistaking factorial or polynomial complexities
Trap Explanation:
PITFALL- Ignoring the O(n) cost per subset leads to underestimating complexity.
Interviewer Note:
CONTEXT- Tests understanding of time complexity for bitmask subset generation.
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