Which approach guarantees an optimal solution with O(n) time and O(1) space complexity?
easy🔍 Pattern Recognition Q11 of Q15
Bit Manipulation - Single Number II (Three Copies)
You are given an array where every element appears exactly three times except for one element which appears only once. Which approach guarantees an optimal solution with O(n) time and O(1) space complexity?
AUse a hash map to count occurrences of each element and return the one with count 1.
BUse bitwise operations to track bits appearing once and twice, resetting bits appearing thrice.
CSort the array and scan to find the unique element by checking neighbors.
DUse a dynamic programming approach to track counts of elements modulo 3.
Step-by-Step Solution
Step 1: Understand the problem constraints
The problem requires identifying the unique element appearing once while others appear thrice, with optimal time and constant space.
Step 2: Evaluate approaches
Hash map uses extra space, sorting is O(n log n), DP is not straightforward here. Bitwise FSM approach tracks bits efficiently in O(n) time and O(1) space.
Final Answer:
Option B -> Option B
Quick Check:
Bitwise FSM approach is known optimal for this problem [OK]
Quick Trick:Bitwise FSM tracks counts mod 3 in constant space [OK]
Common Mistakes:
MISTAKES
Thinking sorting or hash map is optimal for space
Confusing DP applicability here
Trap Explanation:
PITFALL
Hash map counting looks simple and linear time but uses O(n) space, which is not optimal.
Interviewer Note:
CONTEXT
Tests if candidate can identify bitwise FSM pattern beyond brute force
Master "Single Number II (Three Copies)" in Bit Manipulation
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