<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:
    int solve(pair<int,int> p1,pair<int,int> p2,pair<int,int> 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;
        int x=((y3-y2)*(x2-x1)-(y2-y1)*(x3-x2));
        return x;
    }
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        sort(trees.begin(),trees.end());
        deque<pair<int,int>> l,u;

        for(auto point:trees)
        {
            int x=point[0];
            int y=point[1];
            int m=l.size();
            int n=u.size();
            while(m>=2 && solve(l[m-2],l[m-1],{x,y})<0)
            {
                l.pop_back();
                m--;
            }
            while(n>=2 && solve(u[n-2],u[n-1],{x,y})>0)
            {
                u.pop_back();
                n--;
            }
            l.push_back({x,y});
            u.push_back({x,y});

        }
        set<pair<int,int>> st;
        for(auto p:l)
        st.insert(p);
        for(auto p:u)
        st.insert(p);
        vector<vector<int>> ans;
        for(auto p:st)
        {
            int x=p.first;
            int y=p.second;
            ans.push_back({x,y});
        }
        return ans;

    }
};
25500