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What is the worst-case time complexity of the dynamic programming solution using bitmasking for partitioning an array of size n into k subsets with equal sums?

medium📊 Complexity Q5 of Q15

Dynamic Programming: Knapsack - Partition to K Equal Sum Subsets

What is the worst-case time complexity of the dynamic programming solution using bitmasking for partitioning an array of size n into k subsets with equal sums?

AO(2^n * n * k)

BO(k * n^2)

CO(n * 2^n)

DO(n^k)

Step-by-Step Solution

Solution:

Step 1: Analyze DP with bitmask
The DP uses a bitmask of size 2^n to represent subsets and iterates over elements and subsets.
Step 2: Combine factors
For each of the 2^n subsets, the algorithm checks up to n elements and k subsets, leading to O(2^n * n * k).
Final Answer:
Option A -> Option A
Quick Check:
Bitmask DP complexity grows exponentially with n [OK]

Quick Trick: Bitmask DP complexity is exponential in n [OK]

Common Mistakes:

MISTAKES

Ignoring the 2^n factor from bitmasking
Confusing polynomial with exponential complexity
Overlooking the factor k in complexity

Trap Explanation:

PITFALL

Ignoring exponential bitmask factor leads to underestimating complexity

Interviewer Note:

CONTEXT

Tests knowledge of time complexity for bitmask DP solutions

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