<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>
<img alt="" src="https://assets.leetcode.com/uploads/2020/06/25/q4_edited.jpg" />
<p>Answers within <code>10<sup>-5</sup></code> of the actual value will be accepted.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/06/25/q4_e1.jpg" style="width: 377px; height: 362px;" />
<pre>
<strong>Input:</strong> positions = [[0,1],[1,0],[1,2],[2,1]]
<strong>Output:</strong> 4.00000
<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.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/06/25/q4_e3.jpg" style="width: 419px; height: 419px;" />
<pre>
<strong>Input:</strong> positions = [[1,1],[3,3]]
<strong>Output:</strong> 2.82843
<strong>Explanation:</strong> The minimum possible sum of distances = sqrt(2) + sqrt(2) = 2.82843
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= positions.length &lt;= 50</code></li>
	<li><code>positions[i].length == 2</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 100</code></li>
</ul>

class Solution {
public:
    double getMinDistSum(vector<vector<int>>& positions) {
        double xc=0,yc=0;
        int n = positions.size();
        for(auto pos:positions)
        {
            xc+=pos[0];
            yc+=pos[1];
        }
        xc/=n;yc/=n;
        for(auto pos:positions)
        {
            if(xc==pos[0] && yc==pos[1])
            {
                double ans=0;
                for(auto pos2:positions)
                {
                    ans+=sqrt(pow((pos2[0]-xc),2)+pow((pos2[1]-yc),2));
                }
                return ans;
            }
        }
        double ans=0;
        double err=100;
        while(err>1e-7)
        {
        // int flag=1;
        // for(int i=1;i<n;i++)
        // {
        //     vector<int> pos=positions[i],prev=positions[i-1];
        //     if(sqrt(pow((pos[0]-xc),2)+pow((pos[1]-yc),2))!=sqrt(pow((prev[0]-xc),2)+pow((prev[1]-yc),2)))
        //     {
        //         flag=0;
        //         break;
        //     }
        // }
        // if(flag)break;
        double weight=0,y_temp=0,x_temp=0;
        for(auto pos:positions)
        {
            y_temp+=pos[1]/sqrt(pow((pos[0]-xc),2)+pow((pos[1]-yc),2));
            x_temp+=pos[0]/sqrt(pow((pos[0]-xc),2)+pow((pos[1]-yc),2));
            weight+=1/sqrt(pow((pos[0]-xc),2)+pow((pos[1]-yc),2));
        }
        x_temp/=weight;
        y_temp/=weight;
        err=sqrt((xc-x_temp)*(xc-x_temp)+(yc-y_temp)*(yc-y_temp));
        xc=x_temp;
        yc=y_temp;
        }
        for(auto pos:positions)
        {
            ans+=sqrt(pow((pos[0]-xc),2)+pow((pos[1]-yc),2));
        }
        return ans;
    }
};
14500