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Consider two approaches to count subsets with sum K: (1) Memoization (top-down DP) and (2) Iterative bottom-up tabulation. When is memoization preferable over tabulation?

hard⚖️ Approach Comparison Q8 of Q15

Subsets & Combinations - Count of Subsets With Sum K

Consider two approaches to count subsets with sum K: (1) Memoization (top-down DP) and (2) Iterative bottom-up tabulation. When is memoization preferable over tabulation?

AWhen the input array is very large and K is small

BWhen the problem has many unreachable states and pruning reduces computations

CWhen all subsets must be enumerated explicitly

DWhen space optimization is critical and tabulation uses less memory

Step-by-Step Solution

Solution:

Step 1: Compare memoization and tabulation
Memoization explores only reachable states, tabulation computes all states.
Step 2: Identify when memoization is better
If many states are unreachable, memoization prunes computations, saving time.
Final Answer:
Option B → Option B
Quick Check:
Memoization prunes unreachable states → better when many unreachable [OK]

Quick Trick: Memoization prunes unreachable states, tabulation computes all [OK]

Common Mistakes:

MISTAKES

Assuming tabulation always better or uses less memory

Trap Explanation:

PITFALL

Candidates often think tabulation is always better without considering pruning benefits.

Interviewer Note:

CONTEXT

Tests understanding of trade-offs between memoization and tabulation.

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