[LeetCode] Best Meeting Point

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For the 1d case, the best meeting point is just the median point.

Problem Description:

Since the distance is computed using the Manhattan Distance, we can decompose this 2-d problem into two 1-d problems and combine (add) their solutions. In fact, the best meeting point is just the point that comprised by the two best meeting points in each dimension.

A group of two or more 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|.

This post shares a nice Python code. However, translating it into C++ makes it so ugly...

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.