Sunday, August 7, 2016

Best Meeting Point

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|.
For example, given three people living at (0,0)(0,4), and (2,2):
1 - 0 - 0 - 0 - 1
|   |   |   |   |
0 - 0 - 0 - 0 - 0
|   |   |   |   |
0 - 0 - 1 - 0 - 0
The point (0,2) is an ideal meeting point, as the total travel distance of 2+2+2=6 is minimal. So return 6.
Strategy:
best meeting point of one-dimension is at the middle point. for 2D is the same. find the mid-x and mid-y, it is the meeting place.
http://happycoding2010.blogspot.in/2015/11/leetcode-296-best-meeting-point.html
http://www.programcreek.com/2014/07/leetcode-best-meeting-point-java/

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