[Solved] You are given an array containing n distinct numbers taken from the... Which approach guarantees finding the missing number in O(n) time and O(1) space without sorting or summation overflow risks? | Bit Manipulation

Bit Manipulation - Find the Missing Number

You are given an array containing n distinct numbers taken from the range 0 to n. Exactly one number in this range is missing from the array. Which approach guarantees finding the missing number in O(n) time and O(1) space without sorting or summation overflow risks?

ASorting the array and scanning for the first index where the value doesn't match the index

BUsing XOR of all indices and array elements to cancel out pairs and find the missing number

CUsing a dynamic programming approach to track missing elements

DUsing a greedy approach to pick the smallest missing number at each step

Step-by-Step Solution

Step 1: Understand the problem constraints
The array contains numbers from 0 to n with exactly one missing. The goal is to find the missing number efficiently.
Step 2: Identify the approach that guarantees O(n) time and O(1) space without overflow
XOR approach works by XORing all indices and all array elements. Since XOR of a number with itself is zero, all pairs cancel out, leaving the missing number.
Final Answer:
Option B -> Option B
Quick Check:
XOR approach avoids sorting overhead and sum overflow [OK]

Quick Trick: XOR cancels pairs to find missing number efficiently [OK]

Common Mistakes:

MISTAKES

Assuming sorting is always optimal
Using sum approach without overflow check
Confusing greedy with XOR logic

Trap Explanation:

PITFALL

Sorting looks intuitive but costs O(n log n). Sum approach risks overflow. XOR is linear and constant space.

Interviewer Note:

CONTEXT

Tests if candidate can recognize optimal bit manipulation pattern under pressure

Master "Find the Missing Number" in Bit Manipulation

3 interactive learning modes - each teaches the same concept differently

Try It Solution Trace

More Bit Manipulation Quizzes

Which approach guarantees finding the missing number in O(n) time and O(1) space without sorting or summation overflow risks?

Step 1: Understand the problem constraints

Step 2: Identify the approach that guarantees O(n) time and O(1) space without overflow

Final Answer:

Quick Check:

Want More Practice?