Package g1501_1600.s1515_best_position_for_a_service_centre

Class Solution

java.lang.Object
g1501_1600.s1515_best_position_for_a_service_centre.Solution
public class Solution extends java.lang.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

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    double
    getMinDistSum(int[][] positions)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • getMinDistSum

      public double getMinDistSum(int[][] positions)