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What is the output of the dynamic programming countBits function when called with n=1?

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Bit Manipulation - Counting Bits (0 to N)
What is the output of the dynamic programming countBits function when called with n=1?
A[0, 0]
B[1, 1]
C[0, 1]
D[1, 0]
Step-by-Step Solution
Solution:

  1. Step 1: Initialize res = [0, 0]

    For i=1, compute res[1] = res[1 >> 1] + (1 & 1) = res[0] + 1 = 0 + 1 = 1.

  2. Step 2: Final res array is [0, 1]

    Output matches counts of set bits for 0 and 1.

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    DP correctly counts bits for n=1 [OK]
Quick Trick: DP uses right shift and bitwise AND to count bits [OK]
Common Mistakes:
MISTAKES
  • Off-by-one in array size
  • Incorrect bit shift direction
  • Misinitializing res array
Trap Explanation:
PITFALL
  • Candidates sometimes forget to initialize res[0] or miscalculate for small n values.
Interviewer Note:
CONTEXT
  • Checks understanding of DP base cases and bitwise operations
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