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What is the time complexity of the XOR partitioning approach to find two missing numbers from 1 to n given an array of size n-2?

medium🪤 Complexity Trap Q13 of Q15
Bit Manipulation - Find Two Missing Numbers
What is the time complexity of the XOR partitioning approach to find two missing numbers from 1 to n given an array of size n-2?
AO(n²) due to nested loops over the range and array
BO(n) because it iterates over the range and array a constant number of times
CO(n log n) due to bitwise operations on each element
DO(1) since XOR operations are constant time
Step-by-Step Solution

  1. Step 1: Identify loops in the algorithm

    The algorithm iterates over the range 1 to n once and over the input array once, each in separate loops.

  2. Step 2: Analyze operations inside loops

    Each iteration performs constant time XOR and bitwise operations, so total time is proportional to n.

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Two linear passes -> O(n) time [OK]
Quick Trick: Count loops and operations per iteration carefully [OK]
Common Mistakes:
MISTAKES
  • Assuming nested loops cause O(n²)
  • Thinking bitwise ops add log n factor
  • Confusing constant time with O(1) overall
Trap Explanation:
PITFALL
  • Bitwise ops are constant time, so no log factor; no nested loops means no quadratic time.
Interviewer Note:
CONTEXT
  • Checks if candidate understands complexity beyond superficial code reading.
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