Given n rectangular buildings in a 2-dimensional city, computes the skyline of these buildings, eliminating hidden lines. The main task is to view buildings from aside and remove all sections that are not visible.
All buildings share a common bottom and every building is represented by a triplet (left, ht, right)
- left: is x coordinated on the left side (or wall)
- right: is x coordinate of the right side.
- ht: is the height of the building.
A skyline is a collection of rectangular strips. A rectangular strip is represented as a pair (left, ht) where left is x coordinate of the left side of the strip and ht is the height of the strip.
Examples:
Input: buildings[][] = { {1, 11, 5}, {2, 6, 7}, {3, 13, 9}, {12, 7, 16}, {14, 3, 25}, {19, 18, 22}, {23, 13, 29}, {24, 4, 28} }
Output: { {1, 11}, {3, 13}, {9, 0}, {12, 7}, {16, 3}, {19, 18}, {22, 3}, {23, 13}, {29, 0} }
Explanation:
The skyline is formed based on the key-points (representing by “green” dots)
eliminating hidden walls of the buildings.
Input: buildings[ ][ ] = { {1, 11, 5} }
Output: { {1, 11}, {5, 0} }
The Skyline Problem Using MultiSet:
Approach:
- From the given triplets for each building, retrieve the left wall location, height and right wall location value.
- Store the left wall with its negative value of height and the right wall with its actual height as a array of pairs. This is done in order to distinguish between left and right walls of the same building.
- Sort the walls in ascending order.
- Traverse the array walls, if a left wall is found, store the height of the left wall in the multiset M. Otherwise, if a right wall is encountered, remove its corresponding height from the multiset.
- Check if the top value has changed or not. If it has changed, then update the top value and store the current wall’s abscissa(x-coordinate) value and the updated top value in a array as skyline.
- Print the value pairs stored in the skyline array.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;
// Function to create skylinevector<pair<int, int> >
createSkyline(vector<vector<int> >& buildings)
{ // Get the number of buildings
int N = buildings.size();
// To store the left and right
// wall position of the buildings
vector<pair<int, int> > wall;
// Triplet of building structure
// parameters
int left, height, right;
for (int i = 0; i < N; i++) {
// Get left point of building
left = buildings[i][0];
// Get height of building
height = buildings[i][1];
// Get right point of building
right = buildings[i][2];
// Store left point and height
// of the left wall
// Negative value means left wall
// will be inserted to multiset first
// for the same abscissa(x) as right wall
wall.push_back({ left, -height });
// Store right point and height
// of the right wall
wall.push_back(
make_pair(right, height));
}
// Sort the walls in ascending order
sort(wall.begin(), wall.end());
// To store skyline: output
vector<pair<int, int> > skyline;
// Initialize a multiset to
// keep left wall heights sorted
multiset<int> leftWallHeight = { 0 };
// Current max height among
// leftWallHeights
int top = 0;
// Traverse through the sorted walls
for (auto w : wall) {
// If left wall is found
if (w.second < 0) {
// Insert the height
leftWallHeight.insert(-w.second);
}
// If right wall is found
else {
// Remove the height
leftWallHeight.erase(
leftWallHeight.find(w.second));
}
// Mark a skyline point if top changes
// .rbegin(): reverse iterator
if (*leftWallHeight.rbegin() != top) {
top = *leftWallHeight.rbegin();
skyline.push_back(
make_pair(w.first, top));
}
}
// Return skyline to printSkyline
return skyline;
}// Function to print the output skylinevoid printSkyline(
vector<vector<int> >& buildings)
{ // Function call for creating skyline
vector<pair<int, int> > skyline
= createSkyline(buildings);
cout << "Skyline for given"
<< " buildings:\n{";
for (auto it : skyline) {
cout << "{" << it.first << ", "
<< it.second << "} ";
}
cout << "}";
}// Driver Codeint main()
{ vector<vector<int> > buildings;
// Given left and right location
// and height of the wall
buildings = { { 1, 11, 5 }, { 2, 6, 7 },
{ 3, 13, 9 }, { 12, 7, 16 },
{ 14, 3, 25 }, { 19, 18, 22 },
{ 23, 13, 29 }, { 24, 4, 28 } };
// Function Call
printSkyline(buildings);
return 0;
} |
Java
import java.util.*;
public class Skyline {
public static List<int[]> createSkyline(int[][] buildings) {
List<int[]> wall = new ArrayList<>();
int N = buildings.length;
int left, height, right;
for (int i = 0; i < N; i++) {
left = buildings[i][0];
height = buildings[i][1];
right = buildings[i][2];
wall.add(new int[]{left, -height});
wall.add(new int[]{right, height});
}
wall.sort((a, b) -> a[0] != b[0] ? a[0] - b[0] : a[1] - b[1]);
List<int[]> skyline = new ArrayList<>();
TreeSet<Integer> leftWallHeight = new TreeSet<>(Collections.singleton(0));
int top = 0;
for (int[] w : wall) {
if (w[1] < 0) {
leftWallHeight.add(-w[1]);
} else {
leftWallHeight.remove(w[1]);
}
int curTop = leftWallHeight.last();
if (curTop != top) {
top = curTop;
skyline.add(new int[]{w[0], top});
}
}
return skyline;
}
public static void printSkyline(int[][] buildings) {
List<int[]> skyline = createSkyline(buildings);
System.out.println("Skyline for given buildings:");
System.out.print("{");
for (int[] it : skyline) {
System.out.print("{" + it[0] + ", " + it[1] + "} ");
}
System.out.println("}");
}
public static void main(String[] args) {
int[][] buildings = {{1, 11, 5}, {2, 6, 7}, {3, 13, 9}, {12, 7, 16},
{14, 3, 25}, {19, 18, 22}, {23, 13, 29}, {24, 4, 28}};
printSkyline(buildings);
}
} |
Python3
# pyton equivalent codefrom functools import cmp_to_key
def func(a, b):
if(a[0] != b[0]):
return a[0] - b[0]
else:
return a[1] - b[1]
def createSkyline(buildings):
wall = []
N = len(buildings)
left = 0
height = 0
right = 0
for i in range(N):
left = buildings[i][0]
height = buildings[i][1]
right = buildings[i][2]
wall.append([left, -height])
wall.append([right, height])
letter_cmp_key = cmp_to_key(func)
wall.sort(key = letter_cmp_key)
# wall.sort(func)
skyline = []
leftWallHeight = set()
leftWallHeight.add(0)
top = 0
for w in wall:
if w[1] < 0:
leftWallHeight.add(-w[1])
else:
leftWallHeight.remove(w[1])
curTop = max(leftWallHeight)
if curTop != top:
top = curTop;
skyline.append([w[0], top])
return skyline
def printSkyline(buildings):
skyline = createSkyline(buildings)
print('Skyline for given buildings:')
temp = '{'
for it in skyline:
temp = temp + "{" + str(it[0]) + "," + str(it[1]) + "} "
print(temp + '}')
buildings = [[1, 11, 5], [2, 6, 7], [3, 13, 9], [12, 7, 16],
[14, 3, 25], [19, 18, 22], [23, 13, 29], [24, 4, 28]]
printSkyline(buildings)# The code is contributed by Nidhi goel. |
C#
// C# program for the above approachusing System;
using System.Collections.Generic;
using System.Linq;
class Program
{ static int func(int[] a, int[] b)
{
if (a[0] != b[0])
{
return a[0] - b[0];
}
else
{
return a[1] - b[1];
}
}
static List<int[]> createSkyline(List<int[]> buildings)
{
List<int[]> wall = new List<int[]>();
int N = buildings.Count;
int left = 0;
int height = 0;
int right = 0;
for (int i = 0; i < N; i++)
{
left = buildings[i][0];
height = buildings[i][1];
right = buildings[i][2];
wall.Add(new int[] { left, -height });
wall.Add(new int[] { right, height });
}
Comparison<int[]> letter_cmp_key = new Comparison<int[]>(func);
wall.Sort(letter_cmp_key);
List<int[]> skyline = new List<int[]>();
SortedSet<int> leftWallHeight = new SortedSet<int>();
leftWallHeight.Add(0);
int top = 0;
foreach (int[] w in wall)
{
if (w[1] < 0)
{
leftWallHeight.Add(-w[1]);
}
else
{
leftWallHeight.Remove(w[1]);
}
int curTop = leftWallHeight.Max;
if (curTop != top)
{
top = curTop;
skyline.Add(new int[] { w[0], top });
}
}
return skyline;
}
static void printSkyline(List<int[]> buildings)
{
List<int[]> skyline = createSkyline(buildings);
Console.WriteLine("Skyline for given buildings:");
string temp = "{";
foreach (int[] it in skyline)
{
temp = temp + "{" + it[0] + "," + it[1] + "} ";
}
Console.WriteLine(temp + "}");
}
static void Main(string[] args)
{
List<int[]> buildings = new List<int[]> {
new int[] {1, 11, 5},
new int[] {2, 6, 7},
new int[] {3, 13, 9},
new int[] {12, 7, 16},
new int[] {14, 3, 25},
new int[] {19, 18, 22},
new int[] {23, 13, 29},
new int[] {24, 4, 28}
};
printSkyline(buildings);
}
}// The code is contributed by shivamsharma215. |
Javascript
// Javascript equivalent codeconst createSkyline = (buildings) => { let wall = [];
let N = buildings.length;
let left, height, right;
for (let i = 0; i < N; i++) {
left = buildings[i][0];
height = buildings[i][1];
right = buildings[i][2];
wall.push([left, -height]);
wall.push([right, height]);
}
wall.sort((a, b) => {
if (a[0] !== b[0]) {
return a[0] - b[0];
} else {
return a[1] - b[1];
}
});
let skyline = [];
let leftWallHeight = new Set([0]);
let top = 0;
for (let w of wall) {
if (w[1] < 0) {
leftWallHeight.add(-w[1]);
} else {
leftWallHeight.delete(w[1]);
}
let curTop = Math.max(...leftWallHeight);
if (curTop !== top) {
top = curTop;
skyline.push([w[0], top]);
}
}
return skyline;
}const printSkyline = (buildings) => { let skyline = createSkyline(buildings);
console.log('Skyline for given buildings:');
temp = '{';
for (let it of skyline) {
temp = temp +`{${it[0]}, ${it[1]}} `;
}
console.log(temp + '}');
}let buildings = [[1, 11, 5], [2, 6, 7], [3, 13, 9], [12, 7, 16],[14, 3, 25], [19, 18, 22], [23, 13, 29], [24, 4, 28]];printSkyline(buildings); |
Output
Skyline for given buildings:
{{1, 11} {3, 13} {9, 0} {12, 7} {16, 3} {19, 18} {22, 3} {23, 13} {29, 0} }
Time Complexity: O(N logN)
Auxilary Space:O(N)
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