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If the problem changes so that elements can be reused unlimited times in subsets (i.e., multisets), which modification to the backtracking approach correctly generates all such subsets?

hard🎤 Interviewer Follow-up Q15 of Q15
Bit Manipulation - Subsets Using Bitmask
If the problem changes so that elements can be reused unlimited times in subsets (i.e., multisets), which modification to the backtracking approach correctly generates all such subsets?
AUse bitmask enumeration as before without any changes
BChange recursive call to backtrack(i + 1, path) to prevent reuse of elements
CSort the array and skip duplicates during recursion to avoid repeated subsets
DChange recursive call to backtrack(i, path) to allow reuse of the current element
Step-by-Step Solution
Solution:

  1. Step 1: Understand reuse means elements can appear multiple times

    Allowing reuse means after including nums[i], we can include it again in subsequent recursive calls.

  2. Step 2: Modify recursion to call backtrack(i, path) instead of backtrack(i + 1, path)

    This keeps the index at i, allowing repeated inclusion of nums[i].

  3. Step 3: Confirm other options break correctness

    Advancing index (i + 1) prevents reuse; skipping duplicates is unrelated to reuse; bitmask enumeration assumes unique inclusion per element.

  4. Final Answer:

    Option D -> Option D

  5. Quick Check:

    Recursing with same index enables unlimited reuse [OK]
Quick Trick: Reuse requires recursive call with same index [OK]
Common Mistakes:
MISTAKES
  • Forgetting to keep index same to allow reuse
  • Assuming bitmask works unchanged for reuse
Trap Explanation:
PITFALL
  • Bitmask enumeration and advancing index prevent reuse, making them plausible but incorrect here.
Interviewer Note:
CONTEXT
  • Tests candidate's ability to adapt backtracking for reuse constraints.
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