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[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:
10-5 of the actual value will be accepted.
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.
Input: positions = [[1,1],[3,3]] Output: 2.82843 Explanation: The minimum possible sum of distances = sqrt(2) + sqrt(2) = 2.82843
1 <= positions.length <= 50
positions[i].length == 2
0 <= xi, yi <= 100