What is the time complexity of the DP with bitmask tabulation approach for partitioning an array of size n into k equal sum subsets, where the algorithm iterates over all subsets and elements?

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Dynamic Programming: Knapsack - Partition to K Equal Sum Subsets

What is the time complexity of the DP with bitmask tabulation approach for partitioning an array of size n into k equal sum subsets, where the algorithm iterates over all subsets and elements?

AO(k^n) because it tries all assignments of elements to k buckets

BO(n * 2^n) because it iterates over all subsets and elements

CO(n * target) where target is the subset sum

DO(2^n * n^2) due to nested loops over subsets and elements

Step-by-Step Solution

Step 1: Identify loops in the algorithm
The outer loop iterates over all subsets (2^n), inner loop over n elements.
Step 2: Calculate total complexity
Combining loops gives O(n * 2^n). The target sum does not affect iteration count directly.
Final Answer:
Option A -> Option A
Quick Check:
DP bitmask iterates all subsets and elements [OK]

Quick Trick: Bitmask DP complexity is n times 2^n subsets [OK]

Common Mistakes:

MISTAKES

Confusing brute force backtracking complexity with DP complexity
Assuming complexity depends on target sum

Trap Explanation:

PITFALL

Brute force complexity O(k^n) looks plausible but DP reduces it to O(n*2^n).

Interviewer Note:

CONTEXT

Checks if candidate understands difference between brute force and DP complexities.

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More Dynamic Programming: Knapsack Quizzes

What is the time complexity of the DP with bitmask tabulation approach for partitioning an array of size n into k equal sum subsets, where the algorithm iterates over all subsets and elements?

Step 1: Identify loops in the algorithm

Step 2: Calculate total complexity

Final Answer:

Quick Check:

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