Subsets & Combinations - Count of Subsets With Sum K
Suppose now the problem changes: you can use each element unlimited times to form subsets summing to K. Which approach is best suited to solve this variant?
Suppose now the problem changes: you can use each element unlimited times to form subsets summing to K. Which approach is best suited to solve this variant?
hard🎤 Interviewer Follow-up Q10 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand variant
Unlimited usage means classic unbounded subset sum problem.Step 2: Identify correct DP iteration
For unbounded subsets, DP must iterate forward over sums to allow multiple uses.Step 3: Evaluate options
Space-optimized DP iterating forward over sums (forward iteration DP) is correct approach; greedy fails for counting subsets.Final Answer:
Option C → Option CQuick Check:
Unbounded subset sum → forward iteration DP [OK]
Quick Trick: Unbounded subsets → forward iteration in DP [OK]
Common Mistakes:
MISTAKES- Using backward iteration DP or greedy for unbounded subsets
Trap Explanation:
PITFALL- Candidates often reuse bounded subset DP code incorrectly for unbounded variant.
Interviewer Note:
CONTEXT- Tests ability to adapt DP approach to problem variants with unlimited element usage.
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