Is Best Meeting Point easy or hard?

Best Meeting Point is classified as Hard on LeetCode because the key insight about medians is not obvious at first. Once you recognize that Manhattan distance separates into independent row and column components, the implementation becomes relatively straightforward.

Best Meeting Point Python/Java solution

Python and Java solutions typically collect row and column indices into lists, compute the median element, and sum absolute distances to that median. The logic is identical across languages: iterate through the grid, build coordinate arrays, determine medians, and compute total Manhattan distance.

How to solve Best Meeting Point in O(n)?

Treat row and column distances independently. Traverse the grid to collect all row indices and column indices of homes. Because traversal order keeps them sorted, the median element of each list is the optimal coordinate. Summing absolute differences from all rows to the row median and all columns to the column median gives the minimal total distance in O(mn) time.

What is the best approach for Best Meeting Point?

The optimal approach uses the median of home coordinates. Collect all row indices and column indices of homes, then choose the median row and median column as the meeting point. The median minimizes the sum of absolute differences, which directly minimizes Manhattan distance. This yields an O(mn) or O(mn log mn) solution depending on whether sorting is needed.

Is Best Meeting Point asked at Google/Amazon/Meta?

Best Meeting Point has appeared in interviews at companies that emphasize algorithmic grid problems, including Google and Meta-style interview rounds. It tests understanding of Manhattan distance, median properties, and grid traversal optimization.

What data structure is used in Best Meeting Point?

The solution primarily uses arrays or lists to store row and column indices of homes. After collecting coordinates, the algorithm relies on median selection and simple absolute difference calculations rather than complex data structures.

What is the time complexity of Best Meeting Point?

The optimal implementation runs in O(mn) time where m and n are grid dimensions. By collecting row indices in row order and column indices in column order, both arrays are naturally sorted and the median can be accessed directly. A simpler implementation that sorts the coordinate arrays runs in O(mn log mn).

Description Hints 1 Solution Video 37:46

296. Best Meeting Point

Hard61.1% acceptance9 companiesPremium elsewhere, free here

Given an m x n binary grid grid where each 1 marks the home of one friend, return the minimal total travel distance.

The total travel distance is the sum of the distances between the houses of the friends and the meeting point.

The distance is calculated using Manhattan Distance, where distance(p1, p2) = |p2.x - p1.x| + |p2.y - p1.y|.

Example 1:

Input: grid = [[1,0,0,0,1],[0,0,0,0,0],[0,0,1,0,0]]
Output: 6
Explanation: Given three friends living at (0,0), (0,4), and (2,2).
The point (0,2) is an ideal meeting point, as the total travel distance of 2 + 2 + 2 = 6 is minimal.
So return 6.

Example 2: