Bit Manipulation - Find Two Missing Numbers
What is the overall time complexity of the XOR partitioning method to find two missing numbers from an array of size
n-2 containing numbers from 1 to n?What is the overall time complexity of the XOR partitioning method to find two missing numbers from an array of size n-2 containing numbers from 1 to n?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: XOR all numbers from 1 to n
This requires iterating through n numbers once.Step 2: XOR all elements in the array
Iterate through n-2 elements once.Step 3: Partition and XOR subsets
Again linear passes over the array and range.Final Answer:
Option C -> Option CQuick Check:
Each step is a single pass over n elements [OK]
Quick Trick: XOR approach requires linear passes only [OK]
Common Mistakes:
MISTAKES- Assuming sorting is involved increasing complexity
- Thinking partitioning doubles complexity
- Confusing with quadratic or logarithmic complexities
Trap Explanation:
PITFALL- Misunderstanding partitioning as nested loops inflating complexity
Interviewer Note:
CONTEXT- Checks understanding of time complexity of XOR-based solution
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