Erect the Fence
<p>You are given an array <code>trees</code> where <code>trees[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> represents the location of a tree in the garden.</p>

<p>Fence the entire garden using the minimum length of rope, as it is expensive. The garden is well-fenced only if <strong>all the trees are enclosed</strong>.</p>

<p>Return <em>the coordinates of trees that are exactly located on the fence perimeter</em>. You may return the answer in <strong>any order</strong>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0500-0599/0587.Erect%20the%20Fence/images/erect2-plane.jpg" style="width: 400px; height: 393px;" />
<pre>
<strong>Input:</strong> trees = [[1,1],[2,2],[2,0],[2,4],[3,3],[4,2]]
<strong>Output:</strong> [[1,1],[2,0],[4,2],[3,3],[2,4]]
<strong>Explanation:</strong> All the trees will be on the perimeter of the fence except the tree at [2, 2], which will be inside the fence.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0500-0599/0587.Erect%20the%20Fence/images/erect1-plane.jpg" style="width: 400px; height: 393px;" />
<pre>
<strong>Input:</strong> trees = [[1,2],[2,2],[4,2]]
<strong>Output:</strong> [[4,2],[2,2],[1,2]]
<strong>Explanation:</strong> The fence forms a line that passes through all the trees.
</pre>

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

<ul>
	<li><code>1 &lt;= trees.length &lt;= 3000</code></li>
	<li><code>trees[i].length == 2</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 100</code></li>
	<li>All the given positions are <strong>unique</strong>.</li>
</ul>
Geometry; Array; Math
class Solution {
public:
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        int n = trees.size();
        if (n < 4) return trees;
        sort(trees.begin(), trees.end());
        vector<int> vis(n);
        vector<int> stk(n + 10);
        int cnt = 1;
        for (int i = 1; i < n; ++i) {
            while (cnt > 1 && cross(trees[stk[cnt - 1]], trees[stk[cnt - 2]], trees[i]) < 0) vis[stk[--cnt]] = false;
            vis[i] = true;
            stk[cnt++] = i;
        }
        int m = cnt;
        for (int i = n - 1; i >= 0; --i) {
            if (vis[i]) continue;
            while (cnt > m && cross(trees[stk[cnt - 1]], trees[stk[cnt - 2]], trees[i]) < 0) --cnt;
            stk[cnt++] = i;
        }
        vector<vector<int>> ans;
        for (int i = 0; i < cnt - 1; ++i) ans.push_back(trees[stk[i]]);
        return ans;
    }

    int cross(vector<int>& a, vector<int>& b, vector<int>& c) {
        return (b[0] - a[0]) * (c[1] - b[1]) - (b[1] - a[1]) * (c[0] - b[0]);
    }
};