# Clarify an Optimal Commute Grid Problem The preserved report identifies an “optimal commute grid” exercise through a link, says breadth-first search was used, and mentions follow-up test cases. The exact linked statement is not present in the sealed source. Explain which rules must be recovered before implementation and how you would select and validate a graph-search algorithm once the state, transitions, and optimization objective are known. ### Constraints & Assumptions - Do not replace the missing contract with an ordinary binary blocked-grid problem. - The meanings of grid cells, legal movement, start and destination, and “optimal” are not preserved. - Breadth-first search is correct only after the confirmed state graph and edge costs justify it. - Any transportation modes, time or cost fields, tie rules, and unreachable result must come from the actual interviewer contract, not inference from the link title. ### Clarifying Questions to Ask - What information does each cell contain, and which cells or transitions are legal? - Is the objective fewest moves, least time, least cost, or an ordered combination? - Does the traveler have a mode or other state beyond row and column? - What exact value should be returned for ties, the starting cell, and an unreachable destination? ```hint Define the graph before naming the search Write one state and every legal outgoing transition, including its cost. Only then decide whether BFS, 0-1 BFS, or Dijkstra's algorithm matches the contract. ``` ### What a Strong Answer Covers - A source-faithful refusal to invent the missing linked problem statement - Explicit state, transition, objective, boundary, and output questions - A justified choice among BFS and weighted shortest-path algorithms - Visited-state and predecessor handling appropriate to the confirmed state - Edge-focused tests and time and space complexity in terms of graph size ### Follow-up Questions 1. What change to the edge costs would make ordinary BFS incorrect? 2. Which test distinguishes position-only state from position-plus-mode state? 3. How would you verify that two equally optimal commutes are handled according to the stated output contract?