<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 result = 0;
        for (int i = 0; i < points.size(); ++i) {
            result = max(result, countPoints(points, r, i));
        }
        return result;
    }

private:
    int countPoints(const vector<vector<int>>& points, int r, int i) {
        vector<pair<double, bool>> angles;
        for (int j = 0; j < points.size(); ++j) {
            if (j == i) {
                continue;
            }
            int dx = points[i][0] - points[j][0];
            int dy = points[i][1] - points[j][1];
            const auto d = sqrt(dx * dx + dy * dy);
            if (d > 2 * r) {
                continue;
            }
            const auto delta = acos(d / (2 * r));
            const auto angle = atan2(dy, dx);
            angles.emplace_back(angle - delta, false);
            angles.emplace_back(angle + delta, true);
        }
        sort(begin(angles), end(angles));
        int result = 1, count = 1;
        for (const auto& [_, is_closed] : angles) {  // angle sweep
            if (!is_closed) {
                ++count;
            } else {
                --count;
            }
            result = max(result, count);
        }
        return result;
    }
};
18400