0

What is the time complexity of the optimal greedy algorithm for the wiggle subsequence problem, and why might some candidates mistakenly think it is higher?

medium🪤 Complexity Trap Q13 of Q15

Greedy Algorithms - Wiggle Subsequence

What is the time complexity of the optimal greedy algorithm for the wiggle subsequence problem, and why might some candidates mistakenly think it is higher?

AO(n) because it scans the list once, updating counters based on difference signs

BO(2^n) because it explores all subsequences recursively

CO(n log n) due to sorting or binary search steps involved

DO(n^2) because it compares each element with all previous elements

Step-by-Step Solution

Solution:

Step 1: Analyze algorithm operations
The greedy algorithm iterates through the list once, computing differences and updating counters in O(1) time per element.
Step 2: Address common misconceptions
Some candidates confuse it with brute force or DP approaches, thinking it compares pairs or explores subsequences exponentially, leading to O(n^2) or O(2^n) assumptions.
Final Answer:
Option A -> Option A
Quick Check:
Single pass with constant work per element -> O(n) [OK]

Quick Trick: Single pass with constant updates -> O(n)

Common Mistakes:

MISTAKES

Confusing with brute force exponential time
Assuming nested loops for comparisons
Thinking sorting is involved

Trap Explanation:

PITFALL

O(n^2) looks plausible if one imagines pairwise comparisons; O(2^n) if thinking brute force.

Interviewer Note:

CONTEXT

Checks if candidate understands why greedy is efficient and not exponential or quadratic.

Master "Wiggle Subsequence" in Greedy Algorithms

3 interactive learning modes - each teaches the same concept differently

Try It Solution Trace

Want More Practice?

15+ quiz questions · All difficulty levels · Free

Free Signup - Practice All Questions

More Greedy Algorithms Quizzes