<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 {
public:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        return divideAndConquer(buildings, 0, buildings.size() - 1);
    }

private:
    vector<vector<int>> divideAndConquer(vector<vector<int>>& buildings, int left, int right) {
        if (left > right) return {};
        if (left == right) {
            return {{buildings[left][0], buildings[left][2]}, {buildings[left][1], 0}};
        }

        int mid = left + (right - left) / 2;
        // cout << mid << endl;
        vector<vector<int>> leftSkyline = divideAndConquer(buildings, left, mid);
        // for(auto vec: leftSkyline) {
        //     cout << "[";
        //     for(auto vec2: vec) {
        //         cout << vec2 << ",";
        //     }
        //     cout << "],";
        // }
        // cout << endl;
        vector<vector<int>> rightSkyline = divideAndConquer(buildings, mid + 1, right);
        // for(auto vec: rightSkyline) {
        //     cout << "[";
        //     for(auto vec2: vec) {
        //         cout << vec2 << ",";
        //     }
        //     cout << "],";
        // }
        // cout << endl;
        return mergeSkylines(leftSkyline, rightSkyline);
    }

    vector<vector<int>> mergeSkylines(vector<vector<int>>& left, vector<vector<int>>& right) {
        vector<vector<int>> result;
        int h1 = 0, h2 = 0;
        int i = 0, j = 0;
        // cout << "mergeSkylines start" << endl;
        while (i < left.size() && j < right.size()) {
            int x1 = left[i][0];
            int x2 = right[j][0];
            int x;

            // cout << "x1="<< x1 << ", x2=" << x2 << endl;
            if (x1 < x2) {
                x = x1;
                h1 = left[i][1];
                // cout << "h1="<< h1 << endl;
                i++;
            } else if (x1 > x2) {
                x = x2;
                h2 = right[j][1];
                // cout << "h2="<< h2 << endl;
                j++;
            } else {
                // cout << "jeff 1, x1="<< x1 << ", i=" << i << ", j=" << j << endl;
                x = x1;
                h1 = left[i][1];
                h2 = right[j][1];
                i++;
                j++;
                // cout << "jeff 2" << endl;
            }

            int maxHeight = max(h1, h2);
            // cout << "h1="<< h1 << ", h2=" << h2 << ", maxHeight=" << maxHeight << endl;

            if (result.empty() || result.back()[1] != maxHeight) {
                // if (!result.empty())
                //     cout << "result.back()[1]=" << result.back()[1] << endl;
                result.push_back({x, maxHeight});
            }
        }

        while (i < left.size()) {
            // cout << "i < left.size()" << endl;
            result.push_back(left[i++]);
        }

        while (j < right.size()) {
            // cout << "j < right.size()" << endl;
            result.push_back(right[j++]);
        }

        // cout << "mergeSkylines end" << endl;
        return result;
    }
};

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