Which modification to the backtracking approach correctly handles this?
hard🎤 Interviewer Follow-up Q15 of Q15
Subsets & Combinations - Subsets
Suppose you want to generate all subsets of nums but now elements can be reused unlimited times in each subset (i.e., multisets). Which modification to the backtracking approach correctly handles this?
AAt each recursion step, recurse twice: once including current element and staying at same index to allow reuse, once excluding and moving to next index
BAt each recursion step, recurse with <code>index + 1</code> only, excluding current element to avoid duplicates
CUse bit manipulation as before, but allow bits to be set multiple times to represent reuse
DSort the array and use two pointers to generate subsets with repeated elements
Step-by-Step Solution
Step 1: Understand reuse requirement
Allowing unlimited reuse means after including an element, we can include it again without advancing index.
Step 2: Modify recursion accordingly
Recurse twice: include current element and recurse with same index, or exclude and recurse with next index.
Step 3: Why other options fail
At each recursion step, recurse with index + 1 only, excluding current element to avoid duplicates excludes reuse by always advancing index; Use bit manipulation as before, but allow bits to be set multiple times to represent reuse is invalid as bitmask can't represent multiple counts; Sort the array and use two pointers to generate subsets with repeated elements is unrelated.
Final Answer:
Option A -> Option A
Quick Check:
Staying at same index after include enables repeated elements [OK]
Quick Trick:Reuse means recurse with same index after include [OK]
Common Mistakes:
MISTAKES
Advancing index after include prevents reuse
Trying bitmask for multisets
Trap Explanation:
PITFALL
Naive include/exclude advancing index breaks reuse logic, tempting candidates.
Interviewer Note:
CONTEXT
Tests if candidate can adapt backtracking to multiset variants.
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