The Skyline Problem LeetCode Solution

Here, We see The Skyline Problem LeetCode Solution. This Leetcode problem is done in many programming languages like C++, Java, JavaScript, Python, etc. with different approaches.

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The Skyline Problem LeetCode Solution

The Skyline Problem LeetCode Solution

Problem Statement

A city’s skyline 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 the skyline formed by these buildings collectively.

The geometric information of each building is given in the array buildings where buildings[i] = [lefti, righti, heighti]:

  • lefti is the x coordinate of the left edge of the ith building.
  • righti is the x coordinate of the right edge of the ith building.
  • heighti is the height of the ith building.

You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height 0.

The skyline should be represented as a list of “key points” sorted by their x-coordinate in the form [[x1,y1],[x2,y2],...]. 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 0 and is used to mark the skyline’s termination where the rightmost building ends. Any ground between the leftmost and rightmost buildings should be part of the skyline’s contour.

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

Example 1:

merged

Input: buildings = [[2,9,10],[3,7,15],[5,12,12],[15,20,10],[19,24,8]]
Output: [[2,10],[3,15],[7,12],[12,0],[15,10],[20,8],[24,0]]
Explanation: 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.

Example 2:
Input: buildings = [[0,2,3],[2,5,3]]
Output: [[0,3],[5,0]]

The Skyline Problem LeetCode Solution C++

class Solution {
public:
    vector<vector<int>> getSkyline(vector<vector<int>>& buildings) {
        int edge_idx = 0;
        vector<pair<int, int>> edges;
        priority_queue<pair<int, int>> pq;
        vector<vector<int>> skyline;
        for (int i = 0; i < buildings.size(); ++i) {
            const auto &b = buildings[i];
            edges.emplace_back(b[0], i);
            edges.emplace_back(b[1], i);
        }
        std::sort(edges.begin(), edges.end());
        while (edge_idx < edges.size()) {
            int curr_height;
            const auto &[curr_x, _] = edges[edge_idx];
            while (edge_idx < edges.size() &&
                    curr_x == edges[edge_idx].first) {
                const auto &[_, building_idx] = edges[edge_idx];
                const auto &b = buildings[building_idx];
                if (b[0] == curr_x)
                    pq.emplace(b[2], b[1]);
                ++edge_idx;
            }
            while (!pq.empty() && pq.top().second <= curr_x)
                pq.pop();
            curr_height = pq.empty() ? 0 : pq.top().first;
            if (skyline.empty() || skyline.back()[1] != curr_height)
                skyline.push_back({curr_x, curr_height});
        }
        return skyline;
    }
};Code language: PHP (php)

The Skyline Problem LeetCode Solution Java

class TopNode {
    int x;
    int h;
    TopNode next;
    TopNode() {
    }
    TopNode(int x, int h) {
        this.x = x;
        this.h = h;
    }

    void insert(TopNode n) {
        n.next = next;
        next = n;
    }
}
class Solution {
    static final int LEFT=0, RIGHT=1, HEIGHT=2;
    public List<List<Integer>> getSkyline(int[][] buildings) {
        TopNode head = new TopNode(0,0);
        head.insert(new TopNode(Integer.MAX_VALUE, 0));
        TopNode start = head;
        for (int i = 0; i<buildings.length; i++) {
            int[] b = buildings[i];
            int bL = buildings[i][LEFT];
            int bR = buildings[i][RIGHT];
            int bH = buildings[i][HEIGHT];
            //System.out.println(Arrays.toString(buildings[i]));
            while (bL >= start.next.x) { start = start.next; } 
            //System.out.println(start.toString());
            for (TopNode t = start ; bR > t.x; t = t.next) {
                //System.out.println(head.toString());
                if (bH <= t.h) {
                    continue;
                }
                TopNode stop = t;
                while (stop.next != null && stop.next.x < bR && stop.next.h <= bH ) {
                    stop = stop.next;
                }
                if (bL <= t.x) {
                    if (bR >= stop.next.x) {
                        t.next = stop.next;
                        t.h = bH;
                    }
                    else if (t == stop) {
                        t.insert(new TopNode(bR,t.h));
                        t.h = bH;
                        break;
                    }
                    else {
                        stop.x = bR;
                        t.h = bH;
                        t.next = stop;
                        break;
                    }
                }
                else {
                    if (bR >= stop.next.x) {
                        if (t == stop) {
                            t.insert(new TopNode(bL, bH));
                        }
                        else {
                            t.next = stop;
                            stop.x = bL;
                            stop.h = bH;
                        }
                        break;
                    }
                    else if (t == stop) {
                        t.insert(new TopNode(bL,bH));
                        t.next.insert(new TopNode(bR,t.h));
                        break;
                    }
                    else {
                        t.next = stop;
                        t.insert(new TopNode(bL,bH));
                        stop.x = bR;
                        break;
                    }
                }
                t = stop;

            }
        }

        List<List<Integer>> skyline = new ArrayList<>();
        if (head.h == 0)
            head = head.next;
        while (head != null) {
            int height = head.h;
            skyline.add(List.of(head.x, height));
            while ( (head = head.next) != null && head.h == height) {}
        }
        return skyline;
    }

}Code language: PHP (php)

The Skyline Problem LeetCode Solution JavaScript

var getSkyline = function(buildings) {
    const data = [];
    for (let [x1, x2, h] of buildings) {
        data.push([x1, h], [x2, -h]);
    }
    data.sort(([x1, h1], [x2, h2]) => x1 - x2 || h2 - h1);
    const heights = [];
    
    const addHeight = (heights, h) => {
        let left = 0;
        let right = heights.length - 1;
        while (left <= right) {
            const mid = Math.floor((left + right) / 2);
            if (heights[mid] >= h) {
                right = mid - 1;
            }  else {
                left = mid + 1;
            }
        }
        heights.splice(left, 0, h);
    }
    const removeHeight = (heights, h) => {
        let left = 0;
        let right = heights.length - 1;
        while (left <= right) {
            const mid = Math.floor((left + right) / 2);
            if (heights[mid] >= h) {
                right = mid - 1;
            }  else {
                left = mid + 1;
            }
        }
        heights.splice(left, 1);
    }
    const answer = [];
    let previousHeight = 0;
    for (let [x, h] of data) {
        if (h > 0) {
            addHeight(heights, h);
        } else {
            removeHeight(heights, -h);
        }
        let currentHeight = heights[heights.length - 1] || 0;
        if (currentHeight !== previousHeight) {
            answer.push([x, currentHeight]);
            previousHeight = currentHeight;
        }
    }
    return answer;
};Code language: JavaScript (javascript)

The Skyline Problem LeetCode Solution Python

class Solution(object):
    def getSkyline(self, buildings):
        x_height_right_tuples = sorted([(L, -H, R) for L, R, H in buildings] + [(R, 0, "doesn't matter") for _, R, _ in buildings])
        result, max_heap = [[0, 0]], [(0, float('inf'))]
        for x, negative_height, R in x_height_right_tuples:
            while x >= max_heap[0][1]:
                heapq.heappop(max_heap)
            if negative_height:
                heapq.heappush(max_heap, (negative_height, R))
            curr_max_height = -max_heap[0][0]
            if result[-1][1] != curr_max_height:
                result.append([x, curr_max_height])
        return result[1:] 
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