Optimize switching puzzle solution

Q: Optimize switching puzzle solution

This is a Coding & Algorithms interview question from Optiver for Data Scientist roles. View the full question and solution on PracHub.

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Question

Consider a switching puzzle on an m×n grid of lights where toggling a cell flips its state and that of its orthogonal neighbors (Lights Out variant). Given an initial configuration and a target configuration, compute a sequence of toggles with the minimum number of moves or report that no solution exists. Explain how to model this as a linear system over GF ( 2), choose a variable ordering, perform Gaussian elimination with back-substitution to get one or all solutions, and handle multiple-solution minimization (e.g., via basis enumeration or BFS on the null space). Analyze time complexity and memory trade-offs for m,n ≤ 10.

Optimize switching puzzle solution

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