[Swift]LeetCode218. 天际线问题 | The Skyline Problem

发布时间：2020-12-14 05:08:13 所属栏目：百科来源：网络整理

导读：A city‘s skyline is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Now suppose you are?given the locations and height of all the buildings?as shown on a cityscape photo (Figure A)

A city‘s skyline is the outer contour of the silhouette formed by all the buildings in that city when viewed from a distance. Now suppose you are?given the locations and height of all the buildings?as shown on a cityscape photo (Figure A),write a program to?output the skylineformed by these buildings collectively (Figure B).

The geometric information of each building is represented by a triplet of integers?[Li,Ri,Hi],where?Li?and?Ri?are the x coordinates of the left and right edge of the ith building,respectively,and?Hi?is its height. It is guaranteed that?0 ≤ Li,Ri ≤ INT_MAX,?0 < Hi ≤ INT_MAX,and?Ri - Li > 0. You may assume all buildings are perfect rectangles grounded on an absolutely flat surface at height 0.

For instance,the dimensions of all buildings in Figure A are recorded as:?[ [2 9 10],[3 7 15],[5 12 12],[15 20 10],[19 24 8] ]?.

The output is a list of "key points" (red dots in Figure B) in the format of?[ [x1,y1],[x2,y2],[x3,y3],... ]?that uniquely defines a skyline.?A key point is the left endpoint of a horizontal line segment. Note that the last key point,where the rightmost building ends,is merely used to mark the termination of the skyline,and always has zero height. Also,the ground in between any two adjacent buildings should be considered part of the skyline contour.

For instance,the skyline in Figure B should be represented as:[ [2 10],[3 15],[7 12],[12 0],[15 10],[20 8],[24,0] ].

Notes:

The number of buildings in any input list is guaranteed to be in the range?[0,10000].
The input list is already sorted in ascending order by the left x position?Li.
The output list must be sorted by the x position.
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],[12 7],...]

城市的天际线是从远处观看该城市中所有建筑物形成的轮廓的外部轮廓。现在，假设您获得了城市风光照片（图A）上显示的所有建筑物的位置和高度，请编写一个程序以输出由这些建筑物形成的天际线（图B）。

每个建筑物的几何信息用三元组?[Li，Ri，Hi]?表示，其中?Li?和?Ri分别是第 i 座建筑物左右边缘的 x 坐标，Hi?是其高度。可以保证?0 ≤ Li,?0 < Hi ≤ INT_MAX?和?Ri - Li > 0。您可以假设所有建筑物都是在绝对平坦且高度为 0 的表面上的完美矩形。

 
例如，图A中所有建筑物的尺寸记录为：[ [2 9 10],[19 24 8] ]?。 
输出是以?[ [x1,... ]?格式的“关键点”（图B中的红点）的列表，它们唯一地定义了天际线。关键点是水平线段的左端点。请注意，最右侧建筑物的最后一个关键点仅用于标记天际线的终点，并始终为零高度。此外，任何两个相邻建筑物之间的地面都应被视为天际线轮廓的一部分。 
例如，图B中的天际线应该表示为：[ [2 10],0] ]。 
说明: 

任何输入列表中的建筑物数量保证在?[0,10000]?范围内。 
 输入列表已经按升序排列在左边的 x 位置?Li?。 
 输出列表必须按 x 位排序。 
 输出天际线中不得有连续的相同高度的水平线。例如?[...[2 3],[12 7]...]?是不正确的答案；三条高度为 5 的线应该在最终输出中合并为一个：[...[2 3],...]
 


264ms 
 
   1 class Solution {
  2     func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
  3         var queue = [[Int]]()
  4         for building in buildings {
  5             let begin = [building[0],building[2]]
  6             let end = [building[1],-building[2]]
  7             queue.append(begin)
  8             queue.append(end)
  9         }
 10         
 11         queue.sort { (nums1,nums2) -> Bool in
 12             if nums1[0] == nums2[0] {
 13                 return nums1[1] > nums2[1]
 14             }
 15             
 16             return nums1[0] < nums2[0]
 17         }
 18         
 19         
 20         var res = [[Int]]()
 21         var heights = Heap(array: [Int](),sort: >)
 22         var removes = Heap(array: [Int](),sort: >)
 23         var pHeight = 0
 24         for line in queue {
 25             let h = line[1]
 26             
 27             if h > 0 {
 28                 if h > pHeight {
 29                     res.append([line[0],h])
 30                 }
 31                 heights.insert(h)
 32                 pHeight = heights.peek()!
 33             }else {
 34                 removes.insert(-h)
 35                 while !heights.isEmpty && !removes.isEmpty && heights.peek()! == removes.peek()! {
 36                     heights.remove()
 37                     removes.remove()
 38                 }
 39                 pHeight = heights.peek() ?? 0
 40                 if -h > pHeight {
 41                     res.append([line[0],pHeight])
 42                 }
 43             }
 44         }
 45         return res
 46     }
 47     
 48     public struct Heap<T> {
 49         var nodes = [T]()
 50         
 51         private var orderCriteria:(T,T) -> Bool
 52         
 53         public init(sort:@escaping (T,T) -> Bool) {
 54             self.orderCriteria = sort
 55         }
 56         
 57         public init(array:[T],sort:@escaping(T,T) -> Bool) {
 58             self.orderCriteria = sort
 59             configureHeap(from:array)
 60         }
 61         
 62         private mutating func configureHeap(from array:[T])  {
 63             nodes = array
 64             for i in stride(from: (nodes.count - 1) / 2,through: 0,by: -1) {
 65                 shiftDown(i)
 66             }
 67         }
 68         
 69         public var isEmpty:Bool {
 70             return nodes.isEmpty
 71         }
 72         
 73         public var count : Int {
 74             return nodes.count
 75         }
 76         
 77         @inline(__always) internal func parentIndex(ofIndex i : Int) -> Int {
 78             return (i - 1) / 2
 79         }
 80         
 81         @inline(__always) internal func leftChildIndex(ofIndex i : Int) -> Int {
 82             return 2 * i + 1
 83         }
 84         
 85         @inline(__always) internal func rightChildIndex(ofIndex i : Int) -> Int {
 86             return 2 * i + 2
 87         }
 88         
 89         public func peek() -> T? {
 90             return nodes.first
 91         }
 92         
 93         public mutating func insert(_ value: T) {
 94             nodes.append(value)
 95             shiftUp(nodes.count - 1)
 96         }
 97         
 98         public mutating func insert<S:Sequence>(_ sequence: S) where S.Iterator.Element == T {
 99             for value in sequence {
100                 insert(value)
101             }
102         }
103                 
104         @discardableResult public mutating func remove() -> T? {
105             guard !isEmpty else {return nil}
106             if nodes.count == 1 {
107                 return nodes.removeFirst()
108             }else {
109                 let value = nodes[0]
110                 nodes[0] = nodes.removeLast()
111                 shiftDown(0)
112                 return value
113             }
114         }
115         
116 
117         @discardableResult public mutating func remove(at index: Int) -> T? {
118             guard index < count else {return nil}
119             
120             let size = nodes.count - 1
121             if index != count {
122                 nodes.swapAt(index,size)
123                 shiftDown(form: index,until: size)
124                 shiftUp(index)
125             }
126             
127             return nodes.removeLast()
128             
129         }
130         
131         internal mutating func shiftUp(_ index : Int) {
132             var childIndex = index
133             let child = nodes[childIndex]
134             var parentIndex = self.parentIndex(ofIndex: childIndex)
135             
136             while childIndex > 0 && orderCriteria(child,nodes[parentIndex]) {
137                 nodes[childIndex] = nodes[parentIndex]
138                 childIndex = parentIndex
139                 parentIndex = self.parentIndex(ofIndex: childIndex)
140             }
141             nodes[childIndex] = child
142         }
143         
144         internal mutating func shiftDown(form index: Int,until endIndex: Int)  {
145             let leftChildIndex = self.leftChildIndex(ofIndex: index)
146             let rightChildIndex = leftChildIndex + 1
147             var first = index
148             if leftChildIndex < endIndex && orderCriteria(nodes[leftChildIndex],nodes[first]) {
149                 first = leftChildIndex
150             }
151             
152             if rightChildIndex < endIndex && orderCriteria(nodes[rightChildIndex],nodes[first]) {
153                 first = rightChildIndex
154             }
155             if first == index {return}
156             nodes.swapAt(index,first)
157             shiftDown(form: first,until: endIndex)
158         }
159         
160         internal mutating func shiftDown(_ index:Int) {
161             
162             shiftDown(form: index,until: nodes.count)
163         }
164         
165     }
166 } 
 

676ms 
 
  1 class Solution {
 2   func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
 3     var points: [Int] = []
 4     for building in buildings {
 5       points.append(building[0])
 6       points.append(building[1])
 7     }
 8     points.sort()
 9 
10     var segs = [Int](repeating: 0,count: points.count)
11 
12     var pos = 0
13     for building in buildings {
14       // find start point
15       while points[pos] < building[0] { pos += 1 }
16       // go to end
17       var i = pos
18 
19       while points[i] < building[1] {
20         if segs[i] < building[2] {
21           segs[i] = building[2]
22         }
23         i += 1
24       }
25     }
26 
27     var result: [[Int]] = []
28     var currHeight = 0
29     for (index,h) in segs.enumerated() {
30       if currHeight != h {
31         result.append([points[index],h])
32         currHeight = h
33       }
34     }
35 
36     return result
37   }
38 } 
 

1660ms 
 
   1 class Solution {
  2   public struct PriorityQueue<T: Comparable> {
  3 
  4     fileprivate var heap = [T]()
  5     private let ordered: (T,T) -> Bool
  6 
  7     public init(ascending: Bool = false,startingValues: [T] = []) {
  8       self.init(order: ascending ? { $0 > $1 } : { $0 < $1 },startingValues: startingValues)
  9     }
 10 
 11     /// Creates a new PriorityQueue with the given ordering.
 12     ///
 13     /// - parameter order: A function that specifies whether its first argument should
 14     ///                    come after the second argument in the PriorityQueue.
 15     /// - parameter startingValues: An array of elements to initialize the PriorityQueue with.
 16     public init(order: @escaping (T,T) -> Bool,startingValues: [T] = []) {
 17       ordered = order
 18 
 19       // Based on "Heap construction" from Sedgewick p 323
 20       heap = startingValues
 21       var i = heap.count/2 - 1
 22       while i >= 0 {
 23         sink(i)
 24         i -= 1
 25       }
 26     }
 27 
 28     /// How many elements the Priority Queue stores
 29     public var count: Int { return heap.count }
 30 
 31     /// true if and only if the Priority Queue is empty
 32     public var isEmpty: Bool { return heap.isEmpty }
 33 
 34     /// Add a new element onto the Priority Queue. O(lg n)
 35     ///
 36     /// - parameter element: The element to be inserted into the Priority Queue.
 37     public mutating func push(_ element: T) {
 38       heap.append(element)
 39       swim(heap.count - 1)
 40     }
 41 
 42     /// Remove and return the element with the highest priority (or lowest if ascending). O(lg n)
 43     ///
 44     /// - returns: The element with the highest priority in the Priority Queue,or nil if the PriorityQueue is empty.
 45     public mutating func pop() -> T? {
 46 
 47       if heap.isEmpty { return nil }
 48       if heap.count == 1 { return heap.removeFirst() }  // added for Swift 2 compatibility
 49       // so as not to call swap() with two instances of the same location
 50       heap.swapAt(0,heap.count - 1)
 51       let temp = heap.removeLast()
 52       sink(0)
 53 
 54       return temp
 55     }
 56 
 57 
 58     /// Removes the first occurence of a particular item. Finds it by value comparison using ==. O(n)
 59     /// Silently exits if no occurrence found.
 60     ///
 61     /// - parameter item: The item to remove the first occurrence of.
 62     public mutating func remove(_ item: T) {
 63       if let index = heap.index(of: item) {
 64         heap.swapAt(index,heap.count - 1)
 65         heap.removeLast()
 66         if index < heap.count { // if we removed the last item,nothing to swim
 67           swim(index)
 68           sink(index)
 69         }
 70       }
 71     }
 72 
 73     /// Removes all occurences of a particular item. Finds it by value comparison using ==. O(n)
 74     /// Silently exits if no occurrence found.
 75     ///
 76     /// - parameter item: The item to remove.
 77     public mutating func removeAll(_ item: T) {
 78       var lastCount = heap.count
 79       remove(item)
 80       while (heap.count < lastCount) {
 81         lastCount = heap.count
 82         remove(item)
 83       }
 84     }
 85 
 86     /// Get a look at the current highest priority item,without removing it. O(1)
 87     ///
 88     /// - returns: The element with the highest priority in the PriorityQueue,or nil if the PriorityQueue is empty.
 89     public func peek() -> T? {
 90       return heap.first
 91     }
 92 
 93     /// Eliminate all of the elements from the Priority Queue.
 94     public mutating func clear() {
 95       heap.removeAll(keepingCapacity: false)
 96     }
 97 
 98     // Based on example from Sedgewick p 316
 99     private mutating func sink(_ index: Int) {
100       var index = index
101       while 2 * index + 1 < heap.count {
102 
103         var j = 2 * index + 1
104 
105         if j < (heap.count - 1) && ordered(heap[j],heap[j + 1]) { j += 1 }
106         if !ordered(heap[index],heap[j]) { break }
107 
108         heap.swapAt(index,j)
109         index = j
110       }
111     }
112 
113     // Based on example from Sedgewick p 316
114     private mutating func swim(_ index: Int) {
115       var index = index
116       while index > 0 && ordered(heap[(index - 1) / 2],heap[index]) {
117         heap.swapAt((index - 1) / 2,index)
118         index = (index - 1) / 2
119       }
120     }
121   }
122 
123   func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
124     var heights: [(pos: Int,h: Int)] = []
125     for building in buildings {
126       heights.append((building[0],-building[2]))
127       heights.append((building[1],building[2]))
128     }
129     heights.sort { (a,b) in
130       if (a.pos == b.pos) {
131         return a.h < b.h
132       } else {
133         return a.pos < b.pos
134       }
135     }
136 
137     var heap = PriorityQueue<Int>()
138     var result: [[Int]] = []
139     var prev = 0
140 
141     heap.push(0)
142     for h in heights {
143       if (h.h < 0) {
144         heap.push(-h.h)
145       } else {
146         heap.remove(h.h)
147       }
148       if let curr = heap.peek(),prev != curr {
149         result.append([h.pos,curr])
150         prev = curr
151       }
152     }
153 
154     return result
155   }
156 } 
 

1712ms 
 
   1 class PriorityQueue<T> {
  2     private var heap: [T] = [T]()
  3     private let ordered: (T,T) -> Bool
  4 
  5     init(order: @escaping (T,T) -> Bool) {
  6         self.ordered = order
  7     }
  8 
  9     var isEmpty: Bool {
 10         return heap.isEmpty
 11     }
 12     var count: Int {
 13         return heap.count
 14     }
 15 
 16     func push(_ element: T) {
 17         heap.append(element)
 18         swim(heap.count - 1)
 19     }
 20 
 21     func pop() -> T? {
 22         if self.isEmpty {
 23             return nil
 24         }
 25 
 26         if self.heap.count == 1 {
 27             return heap.remove(at: 0)
 28         }
 29 
 30         heap.swapAt(0,heap.count - 1)
 31         let temp = heap.removeLast()
 32         sink(0)
 33         return temp
 34     }
 35 
 36     func peek() -> T? {
 37         if self.isEmpty {
 38             return nil
 39         }
 40 
 41         return self.heap[0]
 42     }
 43 
 44     private func sink(_ index: Int) {
 45         var index = index
 46         while 2 * index + 1 < heap.count {
 47             let leftChildIndex = 2 * index + 1
 48 
 49             var first = index
 50             if leftChildIndex < heap.count && ordered(heap[leftChildIndex],heap[first]) {
 51                 first = leftChildIndex
 52             }
 53 
 54             let rightChildIndex = leftChildIndex + 1
 55             if rightChildIndex < heap.count && ordered(heap[rightChildIndex],heap[first]) {
 56                 first = rightChildIndex
 57             }
 58 
 59             if index == first {
 60                 break
 61             }
 62 
 63             heap.swapAt(index,first)
 64             index = first
 65         }
 66     }
 67 
 68     private func swim(_ index: Int) {
 69         var index = index
 70         while index > 0 && ordered(heap[index],heap[(index - 1) / 2]) {
 71             heap.swapAt((index - 1) / 2,index)
 72             index = (index - 1) / 2
 73         }
 74     }
 75 }
 76 
 77 extension PriorityQueue where T: Comparable {
 78     func remove(_ element: T) {
 79         if let index = heap.index(of: element) {
 80             heap.swapAt(index,heap.count - 1)
 81             heap.removeLast()
 82             if index < heap.count {
 83                 swim(index)
 84                 sink(index)
 85             }
 86         }
 87     }
 88 }
 89 
 90 class Solution {
 91     class Point {
 92         var pos: Int
 93         var height: Int
 94         var isStart: Bool
 95 
 96         init(_ pos: Int,_ height: Int,_ isStart: Bool) {
 97             self.pos = pos
 98             self.height = height
 99             self.isStart = isStart
100         }
101     }
102 
103     func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
104         guard buildings.count > 0 && buildings[0].count > 0 else {
105             return []
106         }
107 
108         var positions = Array(repeating: Point(0,0,false),count: buildings.count * 2)
109         for idx in 0 ..< buildings.count {
110             let start = Point(buildings[idx][0],buildings[idx][2],true)
111             positions[idx * 2] = start
112 
113             let end = Point(buildings[idx][1],false)
114             positions[idx * 2 + 1] = end
115         }
116 
117         positions.sort { pt1,pt2 in
118             if pt1.pos != pt2.pos {
119                 return pt1.pos < pt2.pos
120             }
121 
122             if pt1.isStart && pt2.isStart {
123                 return pt1.height > pt2.height
124             }
125 
126             if !pt1.isStart && !pt2.isStart {
127                 return pt1.height < pt2.height
128             }
129 
130             return pt1.isStart
131          }
132 
133         let queue = PriorityQueue<Int>(order: >)
134         queue.push(0)
135 
136         var result: [[Int]] = []
137         var preMaxVal = 0
138         for point in positions {
139             if point.isStart {
140                 queue.push(point.height)
141                 let curMaxVal = queue.peek()!
142                 if curMaxVal > preMaxVal {
143                     result.append([point.pos,point.height])
144                     preMaxVal = curMaxVal
145                 }
146             } else {
147                 queue.remove(point.height)
148                 let curMaxVal = queue.peek()!
149                 if curMaxVal < preMaxVal {
150                     result.append([point.pos,curMaxVal])
151                     preMaxVal = curMaxVal
152                 }
153             }
154         }
155 
156         return result
157     }
158 } 
 

1916ms 
 
  1 class Solution {
 2     func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
 3         if buildings.count == 0 {
 4             return []   
 5         }
 6         if buildings.count == 1 {
 7             let b = buildings[0]
 8             let x1 = b[0]; let x2 = b[1]; let y = b[2]
 9             return [[x1,y],0]]
10         }
11         var bsplit: [(Int,Int,Bool)] = []
12         for b in buildings {
13             let x1 = b[0]; let x2 = b[1]; let y = b[2]
14             bsplit.append((x1,y,false))
15             bsplit.append((x2,true))            
16         }
17         // TODO replace h with priority queue
18         var h: [(Int,Int)] = []    
19         let s1: ((Int,Int),(Int,Int)) -> Bool = {
20             $0.1 > $1.1 
21             || ($0.1 == $1.1 && $0.0 > $0.1)            
22         }
23         let so: ((Int,Bool),Bool)) -> Bool = {
24             $0.0 < $1.0 
25             || ($0.0 == $1.0 && $0.2 == false && $1.2 == true)
26             || ($0.0 == $1.0 && $0.1 > $1.1)            
27         }
28         let buildingsSorted = bsplit.sorted(by: so)
29 //        print("buildingsSorted (buildingsSorted)")
30         var ans: [[Int]] = []
31         for i in 0..<buildingsSorted.count {
32             let b = buildingsSorted[i]
33             let bx = b.0; let by = b.1; let close = b.2 == true
34 //            print("b (b) h (h)")
35             if h.count == 0 {
36                 h.append((bx,by))
37                 ans.append([bx,by])
38                 continue
39             }
40             if close {
41                 if let index = h.firstIndex(where: {$0.1 == by}) {
42                     h.remove(at: index)
43                     if h.count == 0 { ans.append([bx,0]) }
44                     if let l = h.first {
45                         if l.1 < by { ans.append([bx,l.1]) }
46                     }
47                 }
48                 continue
49             }
50     //        print("b (b) h (h)")
51             if let l = h.first {
52                 if l.1 < by { ans.append([bx,by]) }
53 //                print("l.1 (l.1) by (by) x3 ans (ans)")
54             }
55             if let index = h.firstIndex(where: { $0.1 < by }) {
56                 h.insert((bx,by),at:index)                
57             } else {
58                 h.append((bx,by))            
59             }
60             /*
61             h.append((bx,by))
62             h.sort(by: s1) // need to optimize???
63             */
64 //            print("hx (h)")
65         }
66 //        print("ans (ans)")
67         var i = 1
68         while i < ans.count {
69 //            print("i (i) ans (ans)")
70             if ans[i][0] == ans[i-1][0] {
71                 ans.remove(at: i - 1)
72                 continue
73             }
74             i += 1
75         }
76         return ans
77     }
78 }


            
        	


                        （编辑：李大同）
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