<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 DAndC(0, buildings.size() - 1, buildings);
    }

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

        int mid = (left + right) / 2;
        auto leftHalf = DAndC(left, mid, buildings);
        auto rightHalf = DAndC(mid + 1, right, buildings);
        return merge(leftHalf, rightHalf);
    }

    vector<vector<int>> merge(const vector<vector<int>>& leftHalf, const vector<vector<int>>& rightHalf) const {
        vector<vector<int>> result;

        int leftIndex = 0, rightIndex = 0;
        int lastLeftHeight = 0, lastRightHeight = 0;
        int lastHeight = 0;

        while (leftIndex < leftHalf.size() && rightIndex < rightHalf.size()) {
            auto leftPos = leftHalf[leftIndex][0], leftHeight = leftHalf[leftIndex][1];
            auto rightPos = rightHalf[rightIndex][0], rightHeight = rightHalf[rightIndex][1];

            if (leftPos < rightPos) {
                int maxHeight = max(leftHeight, lastRightHeight);
                
                if (maxHeight != lastHeight) {
                    result.push_back({leftPos, max(leftHeight, lastRightHeight)});
                    lastHeight = maxHeight;
                }

                lastLeftHeight = leftHeight;
                ++leftIndex;
            } else if (leftPos > rightPos) {
                int maxHeight = max(rightHeight, lastLeftHeight);

                if (maxHeight != lastHeight) {
                    result.push_back({rightPos, max(rightHeight, lastLeftHeight)});
                    lastHeight = maxHeight;
                }

                lastRightHeight = rightHeight;
                ++rightIndex;
            } else {
                int maxHeight = max(leftHeight, rightHeight);

                if (maxHeight != lastHeight) {
                    result.push_back({leftPos, max(leftHeight, rightHeight)});
                    lastHeight = maxHeight;
                }

                lastRightHeight = rightHeight;
                lastLeftHeight = leftHeight;
                ++leftIndex, ++rightIndex;
            }
        }

        while (leftIndex < leftHalf.size())
            result.push_back(leftHalf[leftIndex++]);

        while (rightIndex < rightHalf.size())
            result.push_back(rightHalf[rightIndex++]);

        return result;
    }
};

auto init = []() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    return 'c';
}();
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