<p>A city&#39;s <strong>skyline</strong> is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Given the locations and heights of all the buildings, return <em>the <strong>skyline</strong> formed by these buildings collectively</em>.</p>

<p>The geometric information of each building is given in the array <code>buildings</code> where <code>buildings[i] = [left<sub>i</sub>, right<sub>i</sub>, height<sub>i</sub>]</code>:</p>

<ul>
	<li><code>left<sub>i</sub></code> is the x coordinate of the left edge of the <code>i<sup>th</sup></code> building.</li>
	<li><code>right<sub>i</sub></code> is the x coordinate of the right edge of the <code>i<sup>th</sup></code> building.</li>
	<li><code>height<sub>i</sub></code> is the height of the <code>i<sup>th</sup></code> building.</li>
</ul>

<p>You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height <code>0</code>.</p>

<p>The <strong>skyline</strong> should be represented as a list of &quot;key points&quot; <strong>sorted by their x-coordinate</strong> in the form <code>[[x<sub>1</sub>,y<sub>1</sub>],[x<sub>2</sub>,y<sub>2</sub>],...]</code>. Each key point is the left endpoint of some horizontal segment in the skyline except the last point in the list, which always has a y-coordinate <code>0</code> and is used to mark the skyline&#39;s termination where the rightmost building ends. Any ground between the leftmost and rightmost buildings should be part of the skyline&#39;s contour.</p>

<p><b>Note:</b> There must be no consecutive horizontal lines of equal height in the output skyline. For instance, <code>[...,[2 3],[4 5],[7 5],[11 5],[12 7],...]</code> is not acceptable; the three lines of height 5 should be merged into one in the final output as such: <code>[...,[2 3],[4 5],[12 7],...]</code></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/12/01/merged.jpg" style="width: 800px; height: 331px;" />
<pre>
<strong>Input:</strong> buildings = [[2,9,10],[3,7,15],[5,12,12],[15,20,10],[19,24,8]]
<strong>Output:</strong> [[2,10],[3,15],[7,12],[12,0],[15,10],[20,8],[24,0]]
<strong>Explanation:</strong>
Figure A shows the buildings of the input.
Figure B shows the skyline formed by those buildings. The red points in figure B represent the key points in the output list.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> buildings = [[0,2,3],[2,5,3]]
<strong>Output:</strong> [[0,3],[5,0]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= buildings.length &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= left<sub>i</sub> &lt; right<sub>i</sub> &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>1 &lt;= height<sub>i</sub> &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>buildings</code> is sorted by <code>left<sub>i</sub></code> in&nbsp;non-decreasing order.</li>
</ul>

class Solution {
private:
    void printvec(vector<vector<int>>& vec) {
        cout << '[';
        for (auto& v: vec) {
            cout << '(' << v[0] << ',' << v[1] << "),";
        }
        cout << ']' << endl;
    }

    vector<vector<int>> helper(vector<vector<int>>& buildings, int i, int j) {

        vector<vector<int>> ans{};
        int mid = (j - i) / 2 + i;

        // std::cout << '[' << i << ", " << mid << ", " << j << ']' << endl;

        if (i+1 == j && i < buildings.size()) {
            ans.push_back(vector{buildings[i][0], buildings[i][2]});
            ans.push_back(vector{buildings[i][1], 0});
            return ans;
        }

        vector<vector<int>> left = helper(buildings, i, mid);
        vector<vector<int>> right = helper(buildings, mid, j);

        // std::cout << '[' << i << ", " << mid << "] + [" << mid << ", " << j << ']' << endl;
        // printvec(left);
        // printvec(right);

        int s{}, t{};
        while (s < left.size() && t < right.size()) {

            // cout << "S: " << s << ", T: " << t << endl;
            // cout << "I-LFT: "; printvec(left);
            // cout << "I-RGT: "; printvec(right);
            // cout << "I-ANS: "; printvec(ans);

            if (left[s][0] != right[t][0]) {
                // segments are offset from each other

                if (left[s][0] < right[t][0]) {
                    if (ans.empty() || ans.back()[1] != left[s][1]) {
                        ans.push_back(left[s]);
                    }
                    if (s == left.size()-1 || left[s+1][0] <= right[t][0]) {
                        ++s; // segment fits
                    } else {
                        left[s][0] = right[t][0]; // crop to remainder
                    }
                }
                else {
                    if (ans.empty() || ans.back()[1] != right[t][1]) {
                        ans.push_back(right[t]);
                    }
                    if (t == right.size()-1 || right[t+1][0] <= left[s][0]) {
                        ++t; // segment fits
                    } else {
                        right[t][0] = left[s][0]; // crop to remainder
                    }
                }

            } else {
                // segments line up, check heights

                if (s == left.size()-1 && t == right.size()-1) {
                    ans.push_back(left[s]);
                    ++s;
                    ++t;
                }
                else if (left[s][1] >= right[t][1]) {
                    if (ans.empty() || ans.back()[1] != left[s][1]) {
                        ans.push_back(left[s]);
                    }
                    if (t == right.size()-1 ||
                        (s != left.size()-1 && left[s+1][0] < right[t+1][0]))
                    {
                        right[t][0] = left[s+1][0]; // crop to remainder
                    } else {
                        ++t; // hidden completely
                    }
                }
                else {
                    if (ans.empty() || ans.back()[1] != right[t][1]) {
                        ans.push_back(right[t]);
                    }
                    if (s == left.size()-1 ||
                        (t != right.size()-1 && right[t+1][0] < left[s+1][0]))
                    {
                        left[s][0] = right[t+1][0]; // crop to remainder
                    } else {
                        ++s; // hidden completely
                    }
                }
            }

            // cout << "O-LFT: "; printvec(left);
            // cout << "O-RGT: "; printvec(right);
            // cout << "O-ANS: "; printvec(ans);
        }

        while (s < left.size()) {
            if (ans.empty() || ans.back()[1] != left[s][1]) {
                ans.push_back(left[s]);
            }
            ++s;
        }

        while (t < right.size()) {
            if (ans.empty() || ans.back()[1] != right[t][1]) {
                ans.push_back(right[t]);
            }
            ++t;
        }

        // printvec(ans);

        return ans;
    }

public:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        return helper(buildings, 0, buildings.size());
    }
};
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