<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 
{
public:
    
    using tree = vector<int>;
    //Thanks to Bhalerao-2002
    vector<tree> outerTrees(vector<tree>& trees) 
    {
        auto cross = [](tree& B, tree& A, tree& T) -> int
        {
            return (T[1]-B[1])*(B[0]-A[0]) - (B[1]-A[1])*(T[0]-B[0]);
        };
        
        sort(trees.begin(), trees.end());
        //Sorting whole tree
        deque<tree> F;
        
        for (tree T : trees)
        {
            while (F.size() >= 2 and cross(F[F.size()-1],F[F.size()-2],T) < 0)
                F.pop_back();
            F.push_back(T);

            while (F.size() >= 2 and cross(F[0],F[1],T) > 0)
                F.pop_front();
            F.push_front(T);
        }
        
        set<tree> unique(F.begin(), F.end());
        return vector<tree>(unique.begin(), unique.end());
    }
};
30900