<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:
    
    bool isClockwiseTurn(vector<int> &a, vector<int> &b, vector<int> &c) {
        int xa = a[0], xb = b[0], xc = c[0];
        int ya = a[1], yb = b[1], yc = c[1];
        bool isConvex = (((yc - yb) * (xb - xa)) - ((yb - ya) * (xc - xb))) >= 0;
        return isConvex;
    }
    
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        vector<vector<int>> convexHull;
        int n = trees.size();
       
        auto cmp = [&](vector<int> &a, vector<int> &b) {
            if(a[0] < b[0]) {
                return true;
            } else if (a[0] == b[0] && a[1] < b[1]) {
                return true;
            }
            return false;
        };
        
        sort(trees.begin(), trees.end(), cmp);
        
        for(int i = 0; i < n; i++) {
            while(convexHull.size() > 1 && !isClockwiseTurn(convexHull[convexHull.size() - 2], convexHull[convexHull.size() - 1], trees[i])) {
                convexHull.pop_back();
            }
            convexHull.push_back(trees[i]);
        }
        
        for(int i = n - 1; i >= 0; i--) {
            while(convexHull.size() > 1 && !isClockwiseTurn(convexHull[convexHull.size() - 2], convexHull[convexHull.size() - 1], trees[i])) {
                convexHull.pop_back();
            }
            convexHull.push_back(trees[i]);
        }
        convexHull.pop_back(); 
        sort(convexHull.begin(), convexHull.end(), cmp);
        convexHull.erase(unique(convexHull.begin(), convexHull.end()), convexHull.end());
        return convexHull;
    }
};
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