[Solved] Consider two approaches to solve the Matchsticks to Square problem:... When is approach (2) clearly better than (1)? | Subsets & Combinations

Subsets & Combinations - Matchsticks to Square

Consider two approaches to solve the Matchsticks to Square problem: (1) Backtracking with sorting and early pruning, and (2) Backtracking with bitmask and memoization. When is approach (2) clearly better than (1)?

AWhen matchsticks are sorted ascending

BWhen matchsticks have many duplicates and pruning is ineffective

CWhen the number of matchsticks is very small (n < 10)

DWhen n is large and repeated states occur frequently

Step-by-Step Solution

Solution:

Step 1: Compare pruning vs memoization
Sorting and pruning reduce search space but do not avoid recomputing same states.
Step 2: Memoization advantage
Bitmask memoization caches results of states, preventing repeated work, especially beneficial when n is large and states repeat.
Final Answer:
Option D -> Option D
Quick Check:
Memoization excels with large n and repeated states [OK]

Quick Trick: Memoization avoids recomputation, better for large n [OK]

Common Mistakes:

MISTAKES

Assuming pruning always beats memoization
Ignoring repeated state benefits

Trap Explanation:

PITFALL

Candidates confuse pruning effectiveness with memoization benefits on large inputs.

Interviewer Note:

CONTEXT

Tests understanding of trade-offs between pruning and memoization.

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When is approach (2) clearly better than (1)?

Step 1: Compare pruning vs memoization

Step 2: Memoization advantage

Final Answer:

Quick Check:

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