What is the time complexity of the optimal XOR and partition approach to find two unique numbers in an array of size n?

medium🪤 Complexity Trap Q13 of Q15

Bit Manipulation - Single Number III (Two Singles)

AO(n log n) due to sorting step

BO(n) because it traverses the array a constant number of times

CO(n^2) because of nested loops in partitioning

DO(n) but uses O(n) extra space for partitions

Step-by-Step Solution

Step 1: Identify loops in the algorithm
The algorithm traverses the array twice: once to XOR all elements, once to partition and XOR groups.
Step 2: Analyze time and space complexity
Each traversal is O(n), no nested loops. Space used is constant (variables only), no extra arrays.
Final Answer:
Option B -> Option B
Quick Check:
Two linear passes, constant space [OK]

Quick Trick: Two passes over array -> O(n) time, O(1) space [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Sorting or nested loops seem plausible but are not part of the optimal approach.

Interviewer Note:

CONTEXT

Checks if candidate understands linear time and constant space of XOR partitioning.

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