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You need to find the number of set bits (1s) in the binary representation for every integer from 0 up to a given number n. Which algorithmic pattern best fits this problem?

easy🔍 Pattern Recognition Q1 of Q15
Bit Manipulation - Counting Bits (0 to N)
You need to find the number of set bits (1s) in the binary representation for every integer from 0 up to a given number n. Which algorithmic pattern best fits this problem?
ADynamic Programming using previously computed counts and bit shifts
BGreedy approach selecting bits one by one to maximize count
CTwo Pointers to scan bits from left and right simultaneously
DSliding Window technique to count bits in fixed-size windows
Step-by-Step Solution
Solution:

  1. Step 1: Understand problem requires counts for all numbers 0 to n

    Counting bits for each number individually is inefficient; dynamic programming leverages previous results.

  2. Step 2: Recognize DP relation res[i] = res[i >> 1] + (i & 1]

    This uses right shift to reuse counts, making it optimal for this problem.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    DP with bit shifts is classic for counting bits [OK]
Quick Trick: DP with right shift reuses previous counts efficiently [OK]
Common Mistakes:
MISTAKES
  • Confusing bit counting with sliding window
  • Trying greedy bit selection
  • Using two pointers on bits
Trap Explanation:
PITFALL
  • Candidates often confuse bit counting with unrelated patterns like sliding window or greedy, which don't fit counting bits over a range.
Interviewer Note:
CONTEXT
  • Tests candidate's ability to identify DP pattern in bit manipulation problems
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