Which approach guarantees finding these two unique elements in linear time and constant space?
easy🔍 Pattern Recognition Q11 of Q15
Bit Manipulation - Single Number III (Two Singles)
You are given an array where exactly two elements appear only once and all the other elements appear exactly twice. Which approach guarantees finding these two unique elements in linear time and constant space?
AUse XOR of all elements, then partition the array by a set bit of the XOR result and XOR partitions separately.
BSort the array and scan linearly to find the two unique elements.
CUse a hash map to count occurrences and then collect elements with count one.
DUse a greedy approach to pick elements that appear once by checking neighbors.
Step-by-Step Solution
Step 1: Understand the problem constraints
Two unique elements appear once, others appear twice. We want O(n) time and O(1) space.
Step 2: Identify the approach that uses XOR partitioning
XOR all elements to get xor = num1 ^ num2. Find a set bit in xor to partition elements into two groups, each containing one unique number. XOR each group separately to find the unique numbers.
Final Answer:
Option A -> Option A
Quick Check:
Sorting is O(n log n), hash map uses extra space, greedy fails on duplicates [OK]
Quick Trick:XOR partitioning splits unique numbers by differing bit [OK]
Common Mistakes:
MISTAKES
Assuming sorting is linear time
Using hash map violates O(1) space
Greedy fails on duplicates
Trap Explanation:
PITFALL
Sorting looks plausible but is O(n log n), hash map uses extra space, greedy doesn't handle duplicates correctly.
Interviewer Note:
CONTEXT
Tests if candidate recognizes XOR partitioning pattern for two unique numbers.
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