What is the space complexity of the DP with bitmask tabulation approach for partitioning an array of size n into k equal sum subsets?

medium🪤 Complexity Trap Q6 of Q15

Dynamic Programming: Knapsack - Partition to K Equal Sum Subsets

What is the space complexity of the DP with bitmask tabulation approach for partitioning an array of size n into k equal sum subsets?

AO(n * k)

BO(2^n)

CO(n * 2^n)

DO(k * 2^n)

Step-by-Step Solution

Solution:

Step 1: Analyze DP storage
DP array stores one value per subset mask, total 2^n entries.
Step 2: Consider auxiliary space
Each dp entry stores a small integer (sum modulo target), so total space is O(2^n). No extra arrays proportional to n or k.
Final Answer:
Option B -> Option B
Quick Check:
DP table size dominates space -> O(2^n) [OK]

Quick Trick: DP table size = 2^n entries -> O(2^n) space [OK]

Common Mistakes:

MISTAKES

Trap Explanation:

PITFALL

Candidates confuse recursive memoization stack space with tabulation space or multiply by k.

Interviewer Note:

CONTEXT

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