<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 fun1(vector<vector<int>>& a,int l,int h)
    {
        int p=l-1;
        for(int i=l;i<h;i++)
        {
            if((a[i][0]<a[h][0])||(a[i][0]==a[h][0] && a[i][1]<=a[h][1]))
            {
                p++;
                swap(a[p],a[i]);
            }
        }
        p++;
swap(a[p],a[h]);
        return p;
    }
    void fun(vector<vector<int>>& a,int l,int h)
    {
        if(l<=h)
        {
            int p=fun1(a,l,h);
            fun(a,l,p-1);
            fun(a,p+1,h);
        }
    }
        bool fun(vector<int> a,vector<int> b,vector<int> c)
        {
            if((b[0]-a[0])*(c[1]-b[1])-(b[1]-a[1])*(c[0]-b[0])>=0) return true;
            return false;
        }
    void insertionSort(vector<vector<int>>& a) {
    int n = a.size();
    for (int i = 1; i < n; ++i) {
        vector<int> key = a[i];
        int j = i - 1;

        // Compare the current element with the sorted part of the array
        while (j >= 0 && (a[j][0] > key[0] || (a[j][0] == key[0] && a[j][1] > key[1]))) {
            a[j + 1] = a[j];
            j--;
        }
        a[j + 1] = key;
    }
}
int partition(vector<vector<int>>& a, int low, int high) {
    vector<int> pivot = a[high]; // Choose the last element as pivot
    int i = low - 1;

    for (int j = low; j < high; j++) {
        // If current element is smaller than or equal to pivot
        if (a[j][0] < pivot[0] || (a[j][0] == pivot[0] && a[j][1] <= pivot[1])) {
            i++; // Increment index of smaller element
            swap(a[i], a[j]);
        }
    }
    swap(a[i + 1], a[high]);
    return i + 1;
}

// QuickSort function
void quickSort(vector<vector<int>>& a, int low, int high) {
    if (low < high) {
        // pi is the partitioning index
        int pi = partition(a, low, high);

        // Recursively sort elements before and after partition
        quickSort(a, low, pi - 1);
        quickSort(a, pi + 1, high);
    }
}
    vector<vector<int>> outerTrees(vector<vector<int>>& trees) {
        if(trees.size()<=3) return trees;
        fun(trees,0,trees.size()-1);
        //sort(trees.begin(),trees.end());
        //quickSort(trees,0,trees.size()-1);
        vector<vector<int>> a;
        //print(trees);
        for(auto i:trees)
        {
            while(a.size()>1 && !fun(a[a.size()-2],a[a.size()-1],i)) a.pop_back();
            a.push_back(i);
            //print(a);
        }
        if(a.size()==trees.size()) return a;
        for(int j=trees.size()-2;j>=0;j--)
        {
            auto i=trees[j];
            while(a.size()>1 && !fun(a[a.size()-2],a[a.size()-1],i)) a.pop_back();
            a.push_back(i);
        }
        a.pop_back();
        return a;
    }
};
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