[Solved] Suppose the problem is modified so that elements can be chosen multiple times (unlimited... Which approach correctly adapts to count the number of max bitwise-OR subsets under this new constraint? | Subsets & Combinations

Subsets & Combinations - Count Number of Max Bitwise-OR Subsets

Suppose the problem is modified so that elements can be chosen multiple times (unlimited reuse) to form subsets. Which approach correctly adapts to count the number of max bitwise-OR subsets under this new constraint?

AUse dynamic programming over OR values with state compression to count combinations

BUse backtracking with memoization to handle repeated elements and prune search

CUse the same bitmask enumeration approach since subsets remain finite

DSort elements and greedily pick those with highest bits until max OR is reached

Step-by-Step Solution

Step 1: Recognize infinite subsets due to unlimited reuse
Bitmask enumeration is infeasible as subsets are infinite with reuse allowed.
Step 2: Use DP over OR states to count combinations efficiently
DP with state compression tracks counts of subsets achieving each OR value, handling reuse.
Step 3: Understand greedy or naive backtracking fail due to infinite or redundant subsets
Greedy misses combinations; naive backtracking is exponential and inefficient.
Final Answer:
Option A -> Option A
Quick Check:
DP over OR states handles reuse -> correct and efficient [OK]

Quick Trick: Reuse means infinite subsets -> DP over OR states needed [OK]

Common Mistakes:

MISTAKES

Trying bitmask enumeration despite infinite subsets
Using greedy approach ignoring subset counts

Trap Explanation:

PITFALL

Naive reuse handling looks similar but breaks due to infinite subsets, requiring DP.

Interviewer Note:

CONTEXT

Tests candidate's ability to adapt solutions to problem variants with reuse and infinite subsets.

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More Subsets & Combinations Quizzes

Which approach correctly adapts to count the number of max bitwise-OR subsets under this new constraint?

Step 1: Recognize infinite subsets due to unlimited reuse

Step 2: Use DP over OR states to count combinations efficiently

Step 3: Understand greedy or naive backtracking fail due to infinite or redundant subsets

Final Answer:

Quick Check:

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