Which algorithmic approach is most suitable to guarantee an optimal solution for this problem?
easy🔍 Pattern Recognition Q11 of Q15
Subsets & Combinations - Matchsticks to Square
You are given a set of sticks with various lengths. The goal is to determine if these sticks can be arranged to form a perfect square, using all sticks exactly once. Which algorithmic approach is most suitable to guarantee an optimal solution for this problem?
ABacktracking with bitmasking and memoization to explore all subsets efficiently while pruning invalid paths.
BGreedy algorithm that always picks the longest stick first and tries to form sides sequentially.
CDynamic programming based on subset sums without pruning or memoization.
DSimple brute force recursion that tries all possible assignments of sticks to sides without optimization.
Step-by-Step Solution
Solution:
Step 1: Understand problem constraints
The problem requires using all sticks exactly once to form four equal sides, which is a partitioning problem with strict constraints.
Step 2: Identify suitable algorithm
Greedy approaches fail because local choices don't guarantee global feasibility. Simple brute force is correct but inefficient. DP without pruning is too slow. Backtracking with bitmask and memoization efficiently explores subsets and prunes invalid paths, guaranteeing optimality.
Final Answer:
Option A -> Option A
Quick Check:
Bitmask + memoization prunes repeated states [OK]
Quick Trick:Bitmask + memoization prunes repeated states [OK]
Common Mistakes:
MISTAKES
Assuming greedy always works for partitioning
Confusing DP without pruning as efficient
Ignoring memoization benefits
Trap Explanation:
PITFALL
Greedy looks simpler and faster but fails on many inputs; DP without pruning is correct but inefficient, making backtracking with bitmask + memoization the best choice.
Interviewer Note:
CONTEXT
Tests if candidate can recognize the need for state compression and pruning in subset partitioning.
Master "Matchsticks to Square" in Subsets & Combinations
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