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Given the following partial memoization cache for Combination Sum (Reuse Allowed) with candidates = [2,3,5] and target = 8: memo = { 0: [[]], 2: [[2]], 3: [[3]], 4: [[2,2]], 5: [[5]], 6: [[3,3],[2,2,2]], 7: [[2,5],[3,2,2]], 8: [[3,5],[2,3,3],[2,2,2,2]] } Which candidate was most likely chosen last to form the combination [2,3,3] for target 8?

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Subsets & Combinations - Combination Sum (Reuse Allowed)
Given the following partial memoization cache for Combination Sum (Reuse Allowed) with candidates = [2,3,5] and target = 8: memo = { 0: [[]], 2: [[2]], 3: [[3]], 4: [[2,2]], 5: [[5]], 6: [[3,3],[2,2,2]], 7: [[2,5],[3,2,2]], 8: [[3,5],[2,3,3],[2,2,2,2]] } Which candidate was most likely chosen last to form the combination [2,3,3] for target 8?
A2
B3
C5
DCannot determine from memo
Step-by-Step Solution
Solution:
  1. Step 1: Analyze combination [2,3,3]

    Sum is 8; last candidate added must be 3 to reach 8 from 5.
  2. Step 2: Check memo entries

    Target 5 has [5], so adding 3 leads to 8 with [2,3,3].
  3. Final Answer:

    Option B -> Option B
  4. Quick Check:

    Last candidate added to reach 8 in [2,3,3] is 3 [OK]
Quick Trick: Last candidate added equals difference from previous target [OK]
Common Mistakes:
MISTAKES
  • Assuming last candidate is smallest
  • Ignoring memo structure
Trap Explanation:
PITFALL
  • Candidates often confuse order or cannot reason backward from memo.
Interviewer Note:
CONTEXT
  • Tests deep understanding of memoization and solution reconstruction.
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