<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) {
        vector<pair<double, double>> angles;
        int ans = 1;
        for(auto p1: darts) {
            angles.clear();
            for(auto p2: darts) {
                if(p1[0] == p2[0] && p1[1] == p2[1]) continue;
                double d = sqrt(pow(p2[0] - p1[0], 2) + pow(p2[1] - p1[1], 2));
                if(d > 2 * r) continue;
                double angle = atan2((p2[1] - p1[1]), (p2[0] - p1[0]));
                double delta = acos(d / (2.0 * r));
                angles.push_back(pair<double, double>(angle-delta, -1));
                angles.push_back(pair<double, double>(angle+delta, 1));
                // cout << angle << " " << delta << "  " << d << endl;
            }
            // cout << "---" << endl;
            sort(angles.begin(), angles.end(), [](const pair<double, double> &l, const pair<double, double> &r) {
                if(l.first == r.first) return l.second < r.second;
                return l.first < r.first;
            });
            int current = 1;
            for(auto a: angles) {
                if(a.second == -1) current++;
                ans = max(ans, current);
                if(a.second == 1) current--;
            }
        }
        return ans;
    }
};
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