The distance field is a red herring for part 1 and I almost overthought it.
Clarify that the problem reduces to selecting the minimum cost from each row independently, since distance is ignored and there are no cross-row constraints. Then, for each row, find the minimum production cost and sum them up. Discuss time and space complexity, and mention edge cases like empty rows or negative costs.
Pro tip: Mention that this is a greedy approach that works because the choices are independent; if there were constraints like a budget or dependencies, dynamic programming would be needed. Also, note that the input is jagged, so handle rows of varying lengths.
Restate the problem: pick exactly one factory from each row, ignore distance, minimize total production cost. Confirm that there are no constraints linking choices across rows.
Recognize that the total minimum cost is the sum of the minimum cost in each row, because the rows are independent. This is a greedy choice.
Iterate through each row, find the minimum production cost in that row, and add it to a running total. Return the total.
Time complexity is O(N) where N is the total number of elements, as each element is visited once. Space complexity is O(1) extra space.
Consider empty input, rows with no elements, or negative costs. If any row is empty, the problem is invalid; otherwise, negative costs are fine and the algorithm still works.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.