<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 orientation(vector<int> &origin, vector<int> &a, vector<int> &b) {
  double v = origin[0] * (a[1] - b[1]) + a[0] * (b[1] - origin[1]) +
             b[0] * (origin[1] - a[1]);
  if (v < 0)
    return -1;
  else if (v > 0)
    return 1;
  else
    return 0;
}


vector<vector<int>> outerTrees(vector<vector<int>> &trees) {
  vector<vector<int>> points;
  vector<int> start = trees[0];
  for (int i = 0; i < trees.size(); i++) {
    if (trees[i][1] < start[1] ||
        (trees[i][1] == start[1] && trees[i][0] < start[0])) {
      start = {trees[i][0], trees[i][1]};
    }
  }

  sort(trees.begin(), trees.end(), [&start, this](vector<int> &a, vector<int> &b) {
    int orient = orientation(start, a, b);
    if (orient == 0)
      return hypotl(a[0] - start[0], a[1] - start[1]) <
             hypotl(b[0] - start[0], b[1] - start[1]);
    return orient < 0;
  });
  int track = trees.size() - 1;
  while (track >= 0 &&
         orientation(start, trees[track], trees[trees.size() - 1]) == 0) {
    track--;
  }

  reverse(trees.begin() + track + 1, trees.end());

  for (int i = 0; i < trees.size(); i++) {
    while (points.size() > 1 &&
           orientation(points[points.size() - 2], points[points.size() - 1],
                       trees[i]) > 0) {
      points.pop_back();
    }
    points.push_back({trees[i][0], trees[i][1]});
  }
  return points;
}


};
25000