public class Solution
extends Object
1515 - Best Position for a Service Centre\.
Hard
A delivery company wants to build a new service center in a new city. The company knows the positions of all the customers in this city on a 2D-Map and wants to build the new center in a position such that **the sum of the euclidean distances to all customers is minimum**.
Given an array `positions` where positions[i] = [xi, yi] is the position of the `ith` customer on the map, return _the minimum sum of the euclidean distances_ to all customers.
In other words, you need to choose the position of the service center [xcentre, ycentre] such that the following formula is minimized:
Answers within 10-5 of the actual value will be accepted.
**Example 1:**
**Input:** positions = \[\[0,1],[1,0],[1,2],[2,1]]
**Output:** 4.00000
**Explanation:** As shown, you can see that choosing [xcentre, ycentre] = [1, 1] will make the distance to each customer = 1, the sum of all distances is 4 which is the minimum possible we can achieve.
**Example 2:**
**Input:** positions = \[\[1,1],[3,3]]
**Output:** 2.82843
**Explanation:** The minimum possible sum of distances = sqrt(2) + sqrt(2) = 2.82843
**Constraints:**
* `1 <= positions.length <= 50`
* `positions[i].length == 2`
* 0 <= xi, yi <= 100