[leetcode] Best Meeting Point


Best Meeting Point

A group of people wants to meet and minimize the total travel distance. You are given a 2D grid of values 0 or 1, where each 1 marks the home of someone in the group. The distance is calculated using Manhattan Distance, where distance(p1, p2) = |p2.x - p1.x| + |p2.y - p1.y|.

For example, given three people 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.

Dynamic programming.

Brute force solution is trivial. O(n^4).

This solution optimize it to O(n^2)

Decompose the 2D manhattan distance into two 1D manhattan distance, since the two dimension is individual.

 

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