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Given the memo dictionary state after partial execution of backtracking with bitmask memoization: {0b0000111: True, 0b0001011: False, 0b0011111: True} Which of the following input arrays and k values could produce this memo state?

hard🔄 Reverse Engineer Q9 of Q15
Subsets & Combinations - Partition to K Equal Sum Subsets
Given the memo dictionary state after partial execution of backtracking with bitmask memoization: {0b0000111: True, 0b0001011: False, 0b0011111: True} Which of the following input arrays and k values could produce this memo state?
Anums = [1,1,1,1,1], k = 5
Bnums = [1,2,3,4,5], k = 3
Cnums = [2,2,2,2,2], k = 2
Dnums = [3,3,3,3,3], k = 1
Step-by-Step Solution
Solution:

  1. Step 1: Analyze bitmask meaning

    Bitmask 0b0000111 means first three elements used; 0b0001011 means elements 0,1,3 used; 0b0011111 means first five elements used.

  2. Step 2: Match input and k

    Equal elements with k=2 fits memo states showing partial subsets; nums with identical elements and k=2 is plausible.

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    Bitmask states correspond to subsets in equal elements array [OK]
Quick Trick: Bitmask states reflect subsets used in equal elements array [OK]
Common Mistakes:
MISTAKES
  • Ignoring bitmask meaning
  • Picking inputs with unequal sums
Trap Explanation:
PITFALL
  • Candidates often mismatch bitmask states with input arrays, missing subset usage patterns.
Interviewer Note:
CONTEXT
  • Tests deep understanding of bitmask states and input-output relation.
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