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What is the time complexity of the optimal greedy algorithm for finding the longest wiggle subsequence, and why do some candidates mistakenly believe it is higher?

medium🧠 Conceptual Q5 of Q15

Greedy Algorithms - Wiggle Subsequence

What is the time complexity of the optimal greedy algorithm for finding the longest wiggle subsequence, and why do some candidates mistakenly believe it is higher?

AO(n^2), due to nested loops checking all pairs

BO(n), because it scans the array once updating two counters

CO(n log n), because it involves sorting the array

DO(2^n), since it explores all subsequences recursively

Step-by-Step Solution

Solution:

Step 1: Analyze the algorithm
The greedy approach iterates through the array once, updating 'up' and 'down' counters.
Step 2: Understand common misconceptions
Some think it is O(n^2) because they confuse it with DP solutions or consider all pairs.
Final Answer:
Option B -> Option B
Quick Check:
Single pass linear scan confirms O(n) [OK]

Quick Trick: Greedy uses single pass counters, not nested loops [OK]

Common Mistakes:

MISTAKES

Confusing greedy with DP leading to O(n^2)
Assuming sorting is required
Thinking recursion explores all subsequences

Trap Explanation:

PITFALL

Mistaking DP or brute force for greedy leads to overestimating complexity

Interviewer Note:

CONTEXT

Tests understanding of algorithm complexity and common misconceptions

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