Which approach guarantees an optimal solution with O(n) time and O(1) space complexity?
easy🔍 Pattern Recognition Q11 of Q15
Greedy Algorithms - Wiggle Subsequence
You are given a sequence of integers and need to find the length of the longest subsequence where the differences between successive elements strictly alternate between positive and negative. Which approach guarantees an optimal solution with O(n) time and O(1) space complexity?
ADynamic Programming with a 2D table tracking subsequence lengths for each index and difference sign
BBrute force recursion exploring all subsequences and checking alternating differences
CGreedy approach tracking the direction of the last difference and counting peaks and valleys
DSliding window approach maintaining a contiguous alternating difference substring
Step-by-Step Solution
Solution:
Step 1: Understand problem constraints
The problem requires the longest subsequence with alternating positive and negative differences, not necessarily contiguous.
Step 2: Identify optimal approach
Dynamic programming is possible but less efficient; brute force is exponential; sliding window fails because subsequence need not be contiguous. The greedy approach tracking last difference direction and counting peaks and valleys achieves O(n) time and O(1) space optimally.
Final Answer:
Option C -> Option C
Quick Check:
Greedy with direction tracking matches problem requirements [OK]
Quick Trick:Longest alternating difference subsequence -> greedy direction tracking
Common Mistakes:
MISTAKES
Confusing subsequence with substring
Assuming DP is always needed
Trying brute force without pruning
Trap Explanation:
PITFALL
DP looks plausible but is more complex and slower; sliding window fails on non-contiguous subsequences.
Interviewer Note:
CONTEXT
Tests if candidate can recognize the greedy pattern beyond brute force or DP.
Master "Wiggle Subsequence" in Greedy Algorithms
3 interactive learning modes - each teaches the same concept differently
