<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 concave(vector<int>& a, vector<int>& b, vector<int>& c){
        return (c[1]-b[1])*(b[0]-a[0])-(b[1]-a[1])*(c[0]-b[0]);
    }
public:
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        sort(trees.begin(), trees.end());
        vector<vector<int>> ans;
        vector<vector<int>> upper, lower;
        for(auto& it: trees){
            int l = lower.size(), u = upper.size();
            while(l>1 && concave(lower[l-2], lower[l-1], it)>0){
                --l;
                lower.pop_back();
            }
            while(u>1 && concave(upper[u-2], upper[u-1], it)<0){
                --u;
                upper.pop_back();
            }
            upper.push_back(it);
            lower.push_back(it);
        }
        set<vector<int>> st;
        for(auto& it: upper){
            st.insert(it);
        }
        for(auto& it: lower){
            st.insert(it);
        }
        for(auto& it: st){
            ans.push_back(it);
        }
        return ans;
    }
};
27300