Bit Manipulation - Counting Bits (0 to N)
What is the space complexity of the dynamic programming approach that uses right shift to count bits for all numbers from 0 to n?
What is the space complexity of the dynamic programming approach that uses right shift to count bits for all numbers from 0 to n?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: DP uses an array of size n+1 to store counts
This requires O(n) space for the result array.Step 2: Each computation uses constant extra space, no recursion stack
But if implemented recursively without memoization, stack could be O(log n).Step 3: The auxiliary space includes the DP array and any temporary variables
Overall space is O(n), but some candidates confuse with recursion stack or auxiliary structures.Final Answer:
Option D -> Option DQuick Check:
DP array dominates space usage [OK]
Quick Trick: DP array size n+1 dominates space [OK]
Common Mistakes:
MISTAKES- Confusing recursion stack with DP array
- Assuming constant space
- Overestimating auxiliary space
Trap Explanation:
PITFALL- Candidates often forget the DP array space or confuse recursion stack with iterative DP space.
Interviewer Note:
CONTEXT- Checks understanding of space usage in DP vs recursion
Master "Counting Bits (0 to N)" in Bit Manipulation
Want More Practice?
15+ quiz questions · All difficulty levels · Free
Free Signup - Practice All QuestionsMore Bit Manipulation Quizzes