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Yes, variations of this problem appear in interviews at companies like Google, Amazon, and Meta. It tests understanding of Manhattan distance, medians, and grid-based problem optimization.
The optimal approach uses the median of the row and column positions of all people on the grid. Because Manhattan distance is minimized at the median, selecting the median row and column gives the minimal total travel distance.
Simple arrays or lists are typically used to store the row and column indices of homes. After collecting them, sorting or using two pointers helps efficiently compute the median-based distance.
For Manhattan distance, the total absolute distance is minimized when the meeting coordinate is the median of all coordinates. This property allows the problem to be solved independently for rows and columns.
