[Solved] Given the following memo dictionary state from the bitmask backtrackin... memo = { (0b001, 1, 0): True, (0b011, 2, 0): False, (0b111, 0, 3): True } Which of these inputs is consistent with this memo? | Subsets & Combinations

Subsets & Combinations - Matchsticks to Square

Given the following memo dictionary state from the bitmask backtracking solution for n=3 matchsticks, which input list of matchsticks could have produced it? Memo keys are tuples (used_mask, curr_sum, sides_formed) with boolean values. memo = { (0b001, 1, 0): True, (0b011, 2, 0): False, (0b111, 0, 3): True } Which of these inputs is consistent with this memo?

A[1, 1, 2]

B[1, 2, 3]

C[2, 2, 2]

D[1, 1, 1]

Step-by-Step Solution

Solution:

Step 1: Interpret memo states
State (0b001, 1, 0): used first stick (index 0) with length 1, partial sum 1, 0 sides formed -> True.
Step 2: Check which input matches sums
Input [1,1,2] can produce partial sums 1 and 2 with used sticks matching memo keys, and all sticks used (0b111) with 3 sides formed.
Final Answer:
Option A -> Option A
Quick Check:
Memo states consistent with [1,1,2] sums and usage [OK]

Quick Trick: Match memo states to partial sums and used sticks [OK]

Common Mistakes:

MISTAKES

Ignoring bitmask meaning
Mismatching sums with inputs

Trap Explanation:

PITFALL

Candidates often fail to reason backward from memo states to input values.

Interviewer Note:

CONTEXT

Tests deep understanding of bitmask state representation and memoization.

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More Subsets & Combinations Quizzes

memo = { (0b001, 1, 0): True, (0b011, 2, 0): False, (0b111, 0, 3): True } Which of these inputs is consistent with this memo?

Step 1: Interpret memo states

Step 2: Check which input matches sums

Final Answer:

Quick Check:

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