<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();
        int maximum_darts = 1;
        for (int i = 0; i < n; i++) {
            vector<pair<double, char>> angles;
            for (int j = 0; j < n; j++) {
                double dist = hypot(darts[j][0] - darts[i][0], darts[j][1] - darts[i][1]);
                if (i == j || dist > 2 * r) {
                    continue;
                }
                double alfa = atan2(darts[j][1] - darts[i][1], darts[j][0] - darts[i][0]);
                double delta = acos(dist / (2 * r));
                angles.push_back({alfa - delta, false});
                angles.push_back({alfa + delta, true});
            }
            sort(angles.begin(), angles.end());
            int current_darts = 1;
            for (const auto& [angle, is_exit] : angles) {
                current_darts += (is_exit ? -1 : 1);
                maximum_darts = max(maximum_darts, current_darts);
            }
        }
        return maximum_darts;
    }
};
17600