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 Object
1515 - Best Position for a Service Centre.<p>Hard</p> <p>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 <strong>the sum of the euclidean distances to all customers is minimum</strong>.</p> <p>Given an array <code>positions</code> where <code>positions[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> is the position of the <code>ith</code> customer on the map, return <em>the minimum sum of the euclidean distances</em> to all customers.</p> <p>In other words, you need to choose the position of the service center <code>[x<sub>centre</sub>, y<sub>centre</sub>]</code> such that the following formula is minimized:</p> <p><img src="https://assets.leetcode.com/uploads/2020/06/25/q4_edited.jpg" alt="" /></p> <p>Answers within <code>10<sup>-5</sup></code> of the actual value will be accepted.</p> <p><strong>Example 1:</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/06/25/q4_e1.jpg" alt="" /></p> <p><strong>Input:</strong> positions = [[0,1],[1,0],[1,2],[2,1]]</p> <p><strong>Output:</strong> 4.00000</p> <p><strong>Explanation:</strong> As shown, you can see that choosing [x<sub>centre</sub>, y<sub>centre</sub>] = [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.</p> <p><strong>Example 2:</strong></p> <p><img src="https://assets.leetcode.com/uploads/2020/06/25/q4_e3.jpg" alt="" /></p> <p><strong>Input:</strong> positions = [[1,1],[3,3]]</p> <p><strong>Output:</strong> 2.82843</p> <p><strong>Explanation:</strong> The minimum possible sum of distances = sqrt(2) + sqrt(2) = 2.82843</p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= positions.length <= 50</code></li> <li><code>positions[i].length == 2</code></li> <li><code>0 <= x<sub>i</sub>, y<sub>i</sub> <= 100</code></li> </ul>

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • getMinDistSum

      public double getMinDistSum(int[][] positions)