Subsets & Combinations - Largest Divisible Subset
What is the worst-case time complexity of the optimized dynamic programming solution for the Largest Divisible Subset problem, where n is the number of elements in the input array?
What is the worst-case time complexity of the optimized dynamic programming solution for the Largest Divisible Subset problem, where n is the number of elements in the input array?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify main operations
Sorting takes O(n log n). The DP uses two nested loops: outer loop over n elements, inner loop up to i elements.Step 2: Analyze nested loops
Each pair (i,j) is checked once, resulting in O(n^2) divisibility checks. Early break may speed up in practice but worst case remains O(n^2).Final Answer:
Option A -> Option AQuick Check:
DP nested loops dominate complexity [OK]
Quick Trick: DP nested loops -> O(n^2) worst case [OK]
Common Mistakes:
MISTAKES- Confusing sorting time as dominant (O(n log n))
- Assuming triple nested loops due to subset checks
- Thinking brute force complexity applies to DP
Trap Explanation:
PITFALL- Sorting is O(n log n) but DP nested loops cause O(n^2) complexity, which is often underestimated.
Interviewer Note:
CONTEXT- Checks if candidate understands complexity beyond sorting and naive brute force.
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