<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 findVal(vector<int> &p1, vector<int> &p2, vector<int> &p3){
        int x1 = p1[0];
        int x2 = p2[0];
        int x3 = p3[0];

        int y1 = p1[1];
        int y2 = p2[1];
        int y3 = p3[1];

        return (y3-y2)*(x2-x1) - (y2-y1)*(x3-x2);
    }

    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        vector<vector<int>> lower, upper;
        sort(trees.begin(), trees.end());
        int i=0, n=trees.size();
        for(auto &point:trees){
            int l = lower.size();
            int u = upper.size();
            
            // check for lower convex
            while(l>=2 && findVal(lower[l-2], lower[l-1], point)<0){
                l--;
                lower.pop_back();
            }

            // check for upper convex
            while(u>=2 && findVal(upper[u-2], upper[u-1], point)>0){
                u--;
                upper.pop_back();
            }
            upper.push_back(point);
            lower.push_back(point);
        }

        set<vector<int>> st;
        for(auto & u:upper) st.insert(u);
        for(auto & l:lower) st.insert(l);

        vector<vector<int>> result;
        for(auto &point:st){
            result.push_back(point);
        }
        return result;
    }
};
27500