<p>Alice is throwing <code>n</code> darts on a very large wall. You are given an array <code>darts</code> where <code>darts[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> is the position of the <code>i<sup>th</sup></code> dart that Alice threw on the wall.</p>

<p>Bob knows the positions of the <code>n</code> darts on the wall. He wants to place a dartboard of radius <code>r</code> on the wall so that the maximum number of darts that Alice throws lie&nbsp;on the dartboard.</p>

<p>Given the integer <code>r</code>, return <em>the maximum number of darts that can lie on the dartboard</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/29/sample_1_1806.png" style="width: 248px; height: 211px;" />
<pre>
<strong>Input:</strong> darts = [[-2,0],[2,0],[0,2],[0,-2]], r = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> Circle dartboard with center in (0,0) and radius = 2 contain all points.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/04/29/sample_2_1806.png" style="width: 306px; height: 244px;" />
<pre>
<strong>Input:</strong> darts = [[-3,0],[3,0],[2,6],[5,4],[0,9],[7,8]], r = 5
<strong>Output:</strong> 5
<strong>Explanation:</strong> Circle dartboard with center in (0,4) and radius = 5 contain all points except the point (7,8).
</pre>

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

<ul>
	<li><code>1 &lt;= darts.length &lt;= 100</code></li>
	<li><code>darts[i].length == 2</code></li>
	<li><code>-10<sup>4</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>4</sup></code></li>
	<li>All the <code>darts</code>&nbsp;are unique</li>
	<li><code>1 &lt;= r &lt;= 5000</code></li>
</ul>

class Solution {
public:
    int numPoints(vector<vector<int>>& points, int r) {
        int res = 1;
        
        for (int i = 0; i < points.size() - 1; i++) {
            for (int j = i + 1; j < points.size(); j++) {
                int x1 = points[i][0], y1 = points[i][1];
                int x2 = points[j][0], y2 = points[j][1];
                double d = (pow(x1 - x2, 2) + pow(y1 - y2, 2)) / 4.0;
                
                if (d > r * r) {
                    continue;
                }
                
                double x0 = (x1 + x2) / 2.0 + (y2 - y1) * pow((r * r - d), 0.5) / pow((d * 4), 0.5);
                double y0 = (y1 + y2) / 2.0 - (x2 - x1) * pow((r * r - d), 0.5) / pow((d * 4), 0.5);
                
                int cnt = 0;
                
                for (vector<int>& point : points) {
                    double x = point[0];
                    double y = point[1];
                    if (pow((x - x0), 2) + pow((y - y0), 2) <= (double)(r * r) + 0.00001) {
                        cnt++;
                    }
                }
                
                res = max(res, cnt);
                
                x0 = (x1 + x2) / 2.0 - (y2 - y1) * pow((r * r - d), 0.5);
                y0 = (y1 + y2) / 2.0 + (x2 - x1) * pow((r * r - d), 0.5);
                
                cnt = 0;
                
                for (vector<int>& point : points) {
                    double x = point[0];
                    double y = point[1];
                    if (pow((x - x0), 2) + pow((y - y0), 2) <= (double)(r * r) + 0.00001) {
                        cnt++;
                    }
                }
                
                res = max(res, cnt);
            }
        }
        
        return res;
    }
};
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