{ "data": { "question": { "questionId": "1638", "questionFrontendId": "1515", "categoryTitle": "Algorithms", "boundTopicId": 325190, "title": "Best Position for a Service Centre", "titleSlug": "best-position-for-a-service-centre", "content": "

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.

\n\n

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.

\n\n

In other words, you need to choose the position of the service center [xcentre, ycentre] such that the following formula is minimized:

\n\"\"\n

Answers within 10-5 of the actual value will be accepted.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: positions = [[0,1],[1,0],[1,2],[2,1]]\nOutput: 4.00000\nExplanation: 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.\n
\n\n

Example 2:

\n\"\"\n
\nInput: positions = [[1,1],[3,3]]\nOutput: 2.82843\nExplanation: The minimum possible sum of distances = sqrt(2) + sqrt(2) = 2.82843\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "服务中心的最佳位置", "translatedContent": "

一家快递公司希望在新城市建立新的服务中心。公司统计了该城市所有客户在二维地图上的坐标，并希望能够以此为依据为新的服务中心选址：使服务中心 到所有客户的欧几里得距离的总和最小 。

\n\n

给你一个数组 positions ，其中 positions[i] = [xi, yi] 表示第 i 个客户在二维地图上的位置，返回到所有客户的 欧几里得距离的最小总和 。

\n\n

换句话说，请你为服务中心选址，该位置的坐标 [xcentre, ycentre] 需要使下面的公式取到最小值：

\n\n

\"\"

\n\n

与真实值误差在 10-5之内的答案将被视作正确答案。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：positions = [[0,1],[1,0],[1,2],[2,1]]\n输出：4.00000\n解释：如图所示，你可以选 [xcentre, ycentre] = [1, 1] 作为新中心的位置，这样一来到每个客户的距离就都是 1，所有距离之和为 4 ，这也是可以找到的最小值。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：positions = [[1,1],[3,3]]\n输出：2.82843\n解释：欧几里得距离可能的最小总和为 sqrt(2) + sqrt(2) = 2.82843\n
\n\n

 

\n\n

提示：

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