Dynamic Programming: Knapsack - Equal Partition (Partition Equal Subset Sum)
What is the time complexity of the space-optimized bottom-up DP solution for the Equal Partition problem with n elements and total sum S?
What is the time complexity of the space-optimized bottom-up DP solution for the Equal Partition problem with n elements and total sum S?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand DP loops
Outer loop runs n times, inner loop runs up to target = S/2, so roughly O(S).Step 2: Calculate total complexity
Multiplying loops: O(n * S) time complexity.Final Answer:
Option C -> Option CQuick Check:
DP over n items and sum S -> O(n*S) [OK]
Quick Trick: DP time depends on n and sum S [OK]
Common Mistakes:
MISTAKES- Thinking time is O(n) only
- Confusing with O(n^2) due to nested loops
Trap Explanation:
PITFALL- Candidates often ignore that inner loop depends on sum, not just n.
Interviewer Note:
CONTEXT- Tests understanding of DP time complexity with sum dimension
Master "Equal Partition (Partition Equal Subset Sum)" in Dynamic Programming: Knapsack
Want More Practice?
15+ quiz questions · All difficulty levels · Free
Free Signup - Practice All QuestionsMore Dynamic Programming: Knapsack Quizzes