<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://assets.leetcode.com/uploads/2021/04/24/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://assets.leetcode.com/uploads/2021/04/24/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>

class Solution {
    int cross(vector<int>&o,vector<int>&a,vector<int>&b){
        return (b[1]-o[1])*(a[0]-o[0])-(a[1]-o[1])*(b[0]-o[0]);
    }
    
    static bool equal(vector<int>&a,vector<int>&b){
        return a[0]==b[0] && a[1]==b[1];
    }

public:
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        int n = trees.size();

        auto cmp = [&](const vector<int>& a,const vector<int> &b){
            return a[0]<b[0] || (a[0]==b[0]) && a[1]<b[1];
        };
        sort(trees.begin(),trees.end(),cmp);
        
        vector<vector<int>>L(n),U(n),H;

        int p = 0;
         
        
        for(int i=0;i<n;i++){
            while(p>=2 && cross(L[p-2],L[p-1],trees[i])<0) p--;
            L[p++]=trees[i];
        }
        L.resize(p);
        p=0;
        
        
        for(int i=n-1;i>=0;i--){
            while(p>=2 && cross(U[p-2],U[p-1],trees[i])<0) p--;
            U[p++]=trees[i];
        }
        U.resize(p);
        
        
        for(auto it:L)H.push_back(it);
        for(auto it:U)H.push_back(it);
        
        sort(H.begin(),H.end(),cmp);
        H.erase(unique(H.begin(),H.end(),equal),H.end());
        return H;
    }
};

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