<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>>& darts, int r) {
        int n = darts.size();
        if(!n)
            return 0;
        int ret = 1;
        for(int i = 0;i<n;i++){
            for(int j = i+1;j<n;j++){
                double x, y;
                if(!CircleCenter(darts[i][0], darts[i][1], darts[j][0], darts[j][1], r, x, y))
                    continue;
                int tot = 0;
                for(const auto&cur:darts){
                    tot += inCircle(x, y, cur[0], cur[1], r);
                }
                ret = max(ret, tot);
            }
        }
        return ret;
    }
    
    
    bool inCircle(double x, double y, double x0, double y0, double r){
        return (x-x0)*(x-x0)+(y-y0)*(y-y0)-r*r <= 1e-5;
    }
    
    bool CircleCenter(double x1,double y1,double x2,double y2,double R,double &x,double &y)  
    { 
        double c1 = (x2*x2 - x1*x1 + y2*y2 - y1*y1) / (2 *(x2 - x1));  
        double c2 = (y2 - y1) / (x2 - x1);  //斜率
        double A = (c2*c2 + 1);  
        double B = (2 * x1*c2 - 2 * c1*c2 - 2 * y1);  
        double C = x1*x1 - 2 * x1*c1 + c1*c1 + y1*y1 - R*R;  
        y = (-B + sqrt(B*B - 4 * A*C)) / (2 * A);
        x = c1 - c2 * y;    
        return true;
    }
};
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