[Solved] Suppose the problem is modified so that each element in the array can be used... Which of the following modifications to the DP with bitmask tabulation approach correctly adapts to this change? | Dynamic Programming: Knapsack

Dynamic Programming: Knapsack - Partition to K Equal Sum Subsets

Suppose the problem is modified so that each element in the array can be used multiple times (unlimited reuse) to form k equal sum subsets. Which of the following modifications to the DP with bitmask tabulation approach correctly adapts to this change?

AUse backtracking with memoization on subsets but do not use bitmasking since reuse breaks subset uniqueness

BKeep the same bitmask DP but allow setting dp[next_mask] multiple times without restriction

CReplace bitmask DP with a classic unbounded knapsack DP that tracks sums without bitmasking

DModify the bitmask DP to reset dp states after each full subset sum is reached to allow reuse

Step-by-Step Solution

Step 1: Understand reuse impact
Allowing unlimited reuse breaks the uniqueness assumption of subsets represented by bitmasks.
Step 2: Identify suitable DP approach
Classic unbounded knapsack DP tracks sums without bitmasking, correctly handling reuse.
Step 3: Evaluate other options
Bitmask DP relies on unique element usage; modifying it without removing bitmasking leads to incorrect states.
Final Answer:
Option C -> Option C
Quick Check:
Unbounded knapsack DP handles reuse correctly [OK]

Quick Trick: Bitmask DP assumes unique usage; reuse needs unbounded knapsack DP [OK]

Common Mistakes:

MISTAKES

Trying to reuse bitmask DP without removing uniqueness assumption
Ignoring that reuse breaks subset partitioning logic

Trap Explanation:

PITFALL

Bitmask DP looks reusable but fails when elements can be reused multiple times.

Interviewer Note:

CONTEXT

Tests if candidate understands assumptions behind bitmask DP and can adapt to problem variants.

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More Dynamic Programming: Knapsack Quizzes

Which of the following modifications to the DP with bitmask tabulation approach correctly adapts to this change?

Step 1: Understand reuse impact

Step 2: Identify suitable DP approach

Step 3: Evaluate other options

Final Answer:

Quick Check:

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