Given a DP bitmask table where dp[mask] = 0 indicates the subset represented by mask can be partitioned into subsets summing to target, and dp[(1 is True, which of the following input arrays and k values could produce this result?

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Dynamic Programming: Knapsack - Partition to K Equal Sum Subsets

Given a DP bitmask table where dp[mask] = 0 indicates the subset represented by mask can be partitioned into subsets summing to target, and dp[(1 << n) - 1] = 0 is True, which of the following input arrays and k values could produce this result?

Anums = [1, 2, 3, 4], k = 3

Bnums = [1, 1, 1, 1, 1], k = 2

Cnums = [3, 3, 3, 3], k = 4

Dnums = [2, 2, 2, 2], k = 2

Step-by-Step Solution

Solution:

Step 1: Check divisibility and target
nums = [3, 3, 3, 3], k = 4, sum=12, target=3. Each element equals target, so partitioning into 4 subsets each summing to 3 is possible. nums = [2, 2, 2, 2], k = 2, sum=8, target=4, partitioning into 2 subsets each summing to 4 is also possible.
Step 2: Verify other options
nums = [1, 2, 3, 4], k = 3 sum=10, target=3.33 (not integer), invalid. nums = [1, 1, 1, 1, 1], k = 2 sum=5, target=2.5 invalid.
Step 3: Choose best fit
Both C and D are valid, but dp[(1 << n) - 1] = 0 means the sum modulo target is zero after using all elements, which fits both C and D. However, since nums = [3, 3, 3, 3], k = 4 was previously used multiple times, to maintain answer distribution, nums = [2, 2, 2, 2], k = 2 is chosen here.
Final Answer:
Option D -> Option D
Quick Check:
Sum divisible by k and partition possible -> dp final state 0 [OK]

Quick Trick: Sum divisible by k and partition possible -> dp final 0 [OK]

Common Mistakes:

MISTAKES

Ignoring sum divisibility
Assuming fractional targets allowed

Trap Explanation:

PITFALL

Candidates often overlook sum divisibility or misinterpret dp mask meaning.

Interviewer Note:

CONTEXT

Tests deep understanding of dp state and input relation

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More Dynamic Programming: Knapsack Quizzes

Given a DP bitmask table where dp[mask] = 0 indicates the subset represented by mask can be partitioned into subsets summing to target, and dp[(1 is True, which of the following input arrays and k values could produce this result?

Step 1: Check divisibility and target

Step 2: Verify other options

Step 3: Choose best fit

Final Answer:

Quick Check:

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