mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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177 lines
21 KiB
JSON
177 lines
21 KiB
JSON
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"title": "Best Position for a Service Centre",
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"content": "<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>\n\n<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>\n\n<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>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/06/25/q4_edited.jpg\" />\n<p>Answers within <code>10<sup>-5</sup></code> of the actual value will be accepted.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/06/25/q4_e1.jpg\" style=\"width: 377px; height: 362px;\" />\n<pre>\n<strong>Input:</strong> positions = [[0,1],[1,0],[1,2],[2,1]]\n<strong>Output:</strong> 4.00000\n<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.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/06/25/q4_e3.jpg\" style=\"width: 419px; height: 419px;\" />\n<pre>\n<strong>Input:</strong> positions = [[1,1],[3,3]]\n<strong>Output:</strong> 2.82843\n<strong>Explanation:</strong> The minimum possible sum of distances = sqrt(2) + sqrt(2) = 2.82843\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= positions.length <= 50</code></li>\n\t<li><code>positions[i].length == 2</code></li>\n\t<li><code>0 <= x<sub>i</sub>, y<sub>i</sub> <= 100</code></li>\n</ul>\n",
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"translatedTitle": "服务中心的最佳位置",
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"translatedContent": "<p>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 <strong>到所有客户的欧几里得距离的总和最小</strong> 。</p>\n\n<p>给你一个数组 <code>positions</code> ，其中 <code>positions[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> 表示第 <code>i</code> 个客户在二维地图上的位置，返回到所有客户的 <strong>欧几里得距离的最小总和 。</strong></p>\n\n<p>换句话说，请你为服务中心选址，该位置的坐标 <code>[x<sub>centre</sub>, y<sub>centre</sub>]</code> 需要使下面的公式取到最小值：</p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/07/12/q4_edited.jpg\" /></p>\n\n<p>与真实值误差在 <code>10<sup>-5</sup></code>之内的答案将被视作正确答案。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/07/12/q4_e1.jpg\" /></p>\n\n<pre>\n<strong>输入：</strong>positions = [[0,1],[1,0],[1,2],[2,1]]\n<strong>输出：</strong>4.00000\n<strong>解释：</strong>如图所示，你可以选 [x<sub>centre</sub>, y<sub>centre</sub>] = [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</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/07/12/q4_e3.jpg\" /></p>\n\n<pre>\n<strong>输入：</strong>positions = [[1,1],[3,3]]\n<strong>输出：</strong>2.82843\n<strong>解释：</strong>欧几里得距离可能的最小总和为 sqrt(2) + sqrt(2) = 2.82843\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= positions.length <= 50</code></li>\n\t<li><code>positions[i].length == 2</code></li>\n\t<li><code>0 <= x<sub>i</sub>, y<sub>i</sub> <= 100</code></li>\n</ul>\n",
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"The problem can be reworded as, giving a set of points on a 2d-plane, return the geometric median.",
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"Loop over each triplet of points (positions[i], positions[j], positions[k]) where i < j < k, get the centre of the circle which goes throw the 3 points, check if all other points lie in this circle."
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