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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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"The problem can be reworded as, giving a set of points on a 2d-plane, return the geometric median.",
"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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