# Skyline Line Sweep

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],...]

```
import sortedcontainers
class Solution:
def getSkyline(self, buildings: List[List[int]]) -> List[List[int]]:
events = []
for i in buildings:
events.append((0, i[0], i[2]))
events.append((1, i[1], i[2]))
events = sorted(events, key = lambda x:(x[1], x[0], -x[2] if x[0] == 0 else x[2]))
# print(events)
result = []
current_hegihts = sortedcontainers.SortedList([0])
for e in events:
event_type, index, height = e
# print(e, current_hegihts)
if event_type == 0: # start
if height > current_hegihts[-1]:
result.append([index, height])
current_hegihts.add(height)
else:
current_hegihts.remove(height)
# print(current_hegihts)
if height > current_hegihts[-1]:
result.append([index, current_hegihts[-1]])
return result
```

There are also solutions using heaps/priority queues

```
class Solution(object):
def getSkyline(self, buildings):
"""
:type buildings: List[List[int]]
:rtype: List[List[int]]
"""
buildings.sort(key=lambda x:[x[0],-x[2]]) #Sort elements according to x-axis (ascending) and height(descending)
new_b=[]
max_r=-float('inf')
min_l=float('inf')
for i in buildings:
new_b.append([-i[2],i[0],i[1]]) #Create new array for priority queue with [-1*height, left,right], as we are creating max heap
max_r=max(max_r,i[1])
min_l=min(min_l,i[0])
ans=[[0,0,max_r+1]] #for default when the buildings at a specific point is over
f_ans=[]
heapq.heapify(ans)
while min_l<=max_r:
while new_b and min_l>=new_b[0][1]:
temp=new_b.pop(0)
heapq.heappush(ans,temp)
while ans and ans[0][2]<=min_l:
heapq.heappop(ans)
if not f_ans or f_ans[-1][1]!=(-ans[0][0]):
f_ans.append([min_l,-ans[0][0]])
if new_b:
min_l=min(ans[0][2],new_b[0][1]) #To update the min_l according to the next element and the element itself
else:
min_l=ans[0][2]
return f_ans
```

## Related Problems

Given an array of integers nums containing n + 1 integers where each integer is in the range [1, n] inclusive.

There is only **one repeated number** in nums, return *this repeated number*.

You must solve the problem **without** modifying the array nums and uses only constant extra space.

The Hamming Distance between two integers is the number of positions at which the corresponding bits are different.

Given two integers x and y, return *the ***Hamming distance*** between them*.

Given an integer array nums, move all 0's to the end of it while maintaining the relative order of the non-zero elements.

**Note** that you must do this in-place without making a copy of the array.

Given a roman numeral, convert it to an integer. ie given string of "LVIII" return 58