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I think the ideal position will try to best satisfy the condition that:
- Zoro September 29, 20131) number of points to its left equals number of points to its right
2) number of points to its up equals number of points to its down side
The reasoning behind this is in a one-dimension problem, any point in between 2 points gives shortest sum of distances. Extending it to two-dimension has similar behavior.
So to solve this problem, just sort the x's and y's of the points, and pick the middle-indexed x and y will do. If the total number of points is even, then pick an x in between the middle two x's and a y in between the middle two x's.