<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>

#define pii pair<int,int>

class Solution {
public:
    int getSlopeVal(pii p1, pii p2, pii p3){
        int x1=p1.first;
        int x2=p2.first;
        int x3=p3.first;
        int y1=p1.second;
        int y2=p2.second;
        int y3=p3.second;
        return (y3-y2)*(x2-x1) - (y2-y1)*(x3-x2);
    }
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        sort(trees.begin(), trees.end());
        deque<pii>lower,upper;
        for(auto pvec: trees){
            pii p = {pvec[0], pvec[1]};
            while(lower.size()>=2 && getSlopeVal(lower[lower.size()-2], lower[lower.size()-1], p)<0){
                lower.pop_back();
            }
            while(upper.size()>=2 && getSlopeVal(upper[upper.size()-2], upper[upper.size()-1], p)>0){
                upper.pop_back();
            }
            lower.push_back(p);
            upper.push_back(p);
        }

        set<pii>s;
        for(auto p: upper){
            s.insert(p);
        }
        for(auto p: lower){
            s.insert(p);
        }
        vector<vector<int>>res;
        for(auto p: s){
            res.push_back(vector<int>{p.first, p.second});
        }
        return res;
    }
};

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