[Solved] You are given an array containing n-2 distinct integers from the range 1 to n.... Which algorithmic approach guarantees finding these two missing numbers in O(n) time and O(1) extra space? | Bit Manipulation

Bit Manipulation - Find Two Missing Numbers

You are given an array containing n-2 distinct integers from the range 1 to n. Exactly two numbers are missing from the array. Which algorithmic approach guarantees finding these two missing numbers in O(n) time and O(1) extra space?

AUse XOR partitioning to separate numbers based on a set bit and find missing numbers.

BUse a greedy approach to pick missing numbers by scanning the array once.

CUse dynamic programming to build a table of sums and identify missing numbers.

DUse a brute force nested loop to check all pairs of missing numbers.

Step-by-Step Solution

Step 1: Understand problem constraints
We have an array missing exactly two numbers from 1 to n, and need an efficient solution.
Step 2: Identify suitable algorithm
XOR partitioning leverages bitwise properties to find missing numbers in linear time and constant space, unlike brute force or DP which are slower or use extra space.
Final Answer:
Option A -> Option A
Quick Check:
XOR partitioning runs in O(n) time and O(1) space [OK]

Quick Trick: XOR partitioning splits numbers by set bit efficiently [OK]

Common Mistakes:

MISTAKES

Assuming brute force is efficient enough
Confusing DP with sum-based methods
Thinking greedy can find missing pairs

Trap Explanation:

PITFALL

Brute force looks straightforward but is O(n²), DP is unrelated here, greedy fails because missing numbers are not necessarily consecutive.

Interviewer Note:

CONTEXT

Tests if candidate can recognize the optimal bit manipulation pattern under time constraints.

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More Bit Manipulation Quizzes

Which algorithmic approach guarantees finding these two missing numbers in O(n) time and O(1) extra space?

Step 1: Understand problem constraints

Step 2: Identify suitable algorithm

Final Answer:

Quick Check:

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