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Given an array of size n-2 containing distinct integers from 1 to n with two missing numbers, which technique allows finding the missing numbers in O(n) time and constant space?

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Bit Manipulation - Find Two Missing Numbers

Given an array of size n-2 containing distinct integers from 1 to n with two missing numbers, which technique allows finding the missing numbers in O(n) time and constant space?

AUsing XOR operations to partition and isolate missing numbers

BSorting the array and scanning for gaps

CUsing a hash set to track presence of numbers

DBrute force checking each number from 1 to n

Step-by-Step Solution

Solution:

Step 1: Compute XOR of all numbers from 1 to n and XOR of array elements
This yields XOR of the two missing numbers.
Step 2: Find a set bit in the XOR result to partition numbers
Partition numbers into two groups based on this bit and XOR separately to find each missing number.
Final Answer:
Option A -> Option A
Quick Check:
Time is linear and space is constant [OK]

Quick Trick: XOR partitions missing numbers efficiently [OK]

Common Mistakes:

MISTAKES

Assuming sorting is O(n) time
Using extra space like hash sets unnecessarily
Not partitioning XOR correctly

Trap Explanation:

PITFALL

Sorting or hash sets seem intuitive but don't meet O(1) space requirement

Interviewer Note:

CONTEXT

Tests knowledge of XOR-based algorithm for missing numbers

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