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

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➤微信公众号：山青咏芝（shanqingyongzhi）
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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], [4 5], [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, Ri ≤ INT_MAX, 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], [3 7 15], [5 12 12], [15 20 10], [19 24 8] ] 。

输出是以 [ [x1,y1], [x2, y2], [x3, y3], ... ] 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], [3 15], [7 12], [12 0], [15 10], [20 8], [24, 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], [4 5], [7 5], [11 5], [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], [4 5], [12 7], ...]

---

264ms

class Solution {
    func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
        var queue = [[Int]]()
        for building in buildings {
            let begin = [building[0],building[2]]
            let end = [building[1], -building[2]]
            queue.append(begin)
            queue.append(end)
        }
        
        queue.sort { (nums1, nums2) -> Bool in
            if nums1[0] == nums2[0] {
                return nums1[1] > nums2[1]
            }
            
            return nums1[0] < nums2[0]
        }
        
        
        var res = [[Int]]()
        var heights = Heap(array: [Int](), sort: >)
        var removes = Heap(array: [Int](), sort: >)
        var pHeight = 0
        for line in queue {
            let h = line[1]
            
            if h > 0 {
                if h > pHeight {
                    res.append([line[0],h])
                }
                heights.insert(h)
                pHeight = heights.peek()!
            }else {
                removes.insert(-h)
                while !heights.isEmpty && !removes.isEmpty && heights.peek()! == removes.peek()! {
                    heights.remove()
                    removes.remove()
                }
                pHeight = heights.peek() ?? 0
                if -h > pHeight {
                    res.append([line[0],pHeight])
                }
            }
        }
        return res
    }
    
    public struct Heap<T> {
        var nodes = [T]()
        
        private var orderCriteria:(T,T) -> Bool
        
        public init(sort:@escaping (T,T) -> Bool) {
            self.orderCriteria = sort
        }
        
        public init(array:[T],sort:@escaping(T, T) -> Bool) {
            self.orderCriteria = sort
            configureHeap(from:array)
        }
        
        private mutating func configureHeap(from array:[T])  {
            nodes = array
            for i in stride(from: (nodes.count - 1) / 2, through: 0, by: -1) {
                shiftDown(i)
            }
        }
        
        public var isEmpty:Bool {
            return nodes.isEmpty
        }
        
        public var count : Int {
            return nodes.count
        }
        
        @inline(__always) internal func parentIndex(ofIndex i : Int) -> Int {
            return (i - 1) / 2
        }
        
        @inline(__always) internal func leftChildIndex(ofIndex i : Int) -> Int {
            return 2 * i + 1
        }
        
        @inline(__always) internal func rightChildIndex(ofIndex i : Int) -> Int {
            return 2 * i + 2
        }
        
        public func peek() -> T? {
            return nodes.first
        }
        
        public mutating func insert(_ value: T) {
            nodes.append(value)
            shiftUp(nodes.count - 1)
        }
        
        public mutating func insert<S:Sequence>(_ sequence: S) where S.Iterator.Element == T {
            for value in sequence {
                insert(value)
            }
        }
                
        @discardableResult public mutating func remove() -> T? {
            guard !isEmpty else {return nil}
            if nodes.count == 1 {
                return nodes.removeFirst()
            }else {
                let value = nodes[0]
                nodes[0] = nodes.removeLast()
                shiftDown(0)
                return value
            }
        }
        

        @discardableResult public mutating func remove(at index: Int) -> T? {
            guard index < count else {return nil}
            
            let size = nodes.count - 1
            if index != count {
                nodes.swapAt(index, size)
                shiftDown(form: index, until: size)
                shiftUp(index)
            }
            
            return nodes.removeLast()
            
        }
        
        internal mutating func shiftUp(_ index : Int) {
            var childIndex = index
            let child = nodes[childIndex]
            var parentIndex = self.parentIndex(ofIndex: childIndex)
            
            while childIndex > 0 && orderCriteria(child, nodes[parentIndex]) {
                nodes[childIndex] = nodes[parentIndex]
                childIndex = parentIndex
                parentIndex = self.parentIndex(ofIndex: childIndex)
            }
            nodes[childIndex] = child
        }
        
        internal mutating func shiftDown(form index: Int, until endIndex: Int)  {
            let leftChildIndex = self.leftChildIndex(ofIndex: index)
            let rightChildIndex = leftChildIndex + 1
            var first = index
            if leftChildIndex < endIndex && orderCriteria(nodes[leftChildIndex], nodes[first]) {
                first = leftChildIndex
            }
            
            if rightChildIndex < endIndex && orderCriteria(nodes[rightChildIndex], nodes[first]) {
                first = rightChildIndex
            }
            if first == index {return}
            nodes.swapAt(index, first)
            shiftDown(form: first, until: endIndex)
        }
        
        internal mutating func shiftDown(_ index:Int) {
            
            shiftDown(form: index, until: nodes.count)
        }
        
    }
}

---

676ms

class Solution {
  func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
    var points: [Int] = []
    for building in buildings {
      points.append(building[0])
      points.append(building[1])
    }
    points.sort()

    var segs = [Int](repeating: 0, count: points.count)

    var pos = 0
    for building in buildings {
      // find start point
      while points[pos] < building[0] { pos += 1 }
      // go to end
      var i = pos

      while points[i] < building[1] {
        if segs[i] < building[2] {
          segs[i] = building[2]
        }
        i += 1
      }
    }

    var result: [[Int]] = []
    var currHeight = 0
    for (index, h) in segs.enumerated() {
      if currHeight != h {
        result.append([points[index], h])
        currHeight = h
      }
    }

    return result
  }
}

---

1660ms

class Solution {
  public struct PriorityQueue<T: Comparable> {

    fileprivate var heap = [T]()
    private let ordered: (T, T) -> Bool

    public init(ascending: Bool = false, startingValues: [T] = []) {
      self.init(order: ascending ? { $0 > $1 } : { $0 < $1 }, startingValues: startingValues)
    }

    /// Creates a new PriorityQueue with the given ordering.
    ///
    /// - parameter order: A function that specifies whether its first argument should
    ///                    come after the second argument in the PriorityQueue.
    /// - parameter startingValues: An array of elements to initialize the PriorityQueue with.
    public init(order: @escaping (T, T) -> Bool, startingValues: [T] = []) {
      ordered = order

      // Based on "Heap construction" from Sedgewick p 323
      heap = startingValues
      var i = heap.count/2 - 1
      while i >= 0 {
        sink(i)
        i -= 1
      }
    }

    /// How many elements the Priority Queue stores
    public var count: Int { return heap.count }

    /// true if and only if the Priority Queue is empty
    public var isEmpty: Bool { return heap.isEmpty }

    /// Add a new element onto the Priority Queue. O(lg n)
    ///
    /// - parameter element: The element to be inserted into the Priority Queue.
    public mutating func push(_ element: T) {
      heap.append(element)
      swim(heap.count - 1)
    }

    /// Remove and return the element with the highest priority (or lowest if ascending). O(lg n)
    ///
    /// - returns: The element with the highest priority in the Priority Queue, or nil if the PriorityQueue is empty.
    public mutating func pop() -> T? {

      if heap.isEmpty { return nil }
      if heap.count == 1 { return heap.removeFirst() }  // added for Swift 2 compatibility
      // so as not to call swap() with two instances of the same location
      heap.swapAt(0, heap.count - 1)
      let temp = heap.removeLast()
      sink(0)

      return temp
    }


    /// Removes the first occurence of a particular item. Finds it by value comparison using ==. O(n)
    /// Silently exits if no occurrence found.
    ///
    /// - parameter item: The item to remove the first occurrence of.
    public mutating func remove(_ item: T) {
      if let index = heap.index(of: item) {
        heap.swapAt(index, heap.count - 1)
        heap.removeLast()
        if index < heap.count { // if we removed the last item, nothing to swim
          swim(index)
          sink(index)
        }
      }
    }

    /// Removes all occurences of a particular item. Finds it by value comparison using ==. O(n)
    /// Silently exits if no occurrence found.
    ///
    /// - parameter item: The item to remove.
    public mutating func removeAll(_ item: T) {
      var lastCount = heap.count
      remove(item)
      while (heap.count < lastCount) {
        lastCount = heap.count
        remove(item)
      }
    }

    /// Get a look at the current highest priority item, without removing it. O(1)
    ///
    /// - returns: The element with the highest priority in the PriorityQueue, or nil if the PriorityQueue is empty.
    public func peek() -> T? {
      return heap.first
    }

    /// Eliminate all of the elements from the Priority Queue.
    public mutating func clear() {
      heap.removeAll(keepingCapacity: false)
    }

    // Based on example from Sedgewick p 316
    private mutating func sink(_ index: Int) {
      var index = index
      while 2 * index + 1 < heap.count {

        var j = 2 * index + 1

        if j < (heap.count - 1) && ordered(heap[j], heap[j + 1]) { j += 1 }
        if !ordered(heap[index], heap[j]) { break }

        heap.swapAt(index, j)
        index = j
      }
    }

    // Based on example from Sedgewick p 316
    private mutating func swim(_ index: Int) {
      var index = index
      while index > 0 && ordered(heap[(index - 1) / 2], heap[index]) {
        heap.swapAt((index - 1) / 2, index)
        index = (index - 1) / 2
      }
    }
  }

  func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
    var heights: [(pos: Int, h: Int)] = []
    for building in buildings {
      heights.append((building[0], -building[2]))
      heights.append((building[1], building[2]))
    }
    heights.sort { (a, b) in
      if (a.pos == b.pos) {
        return a.h < b.h
      } else {
        return a.pos < b.pos
      }
    }

    var heap = PriorityQueue<Int>()
    var result: [[Int]] = []
    var prev = 0

    heap.push(0)
    for h in heights {
      if (h.h < 0) {
        heap.push(-h.h)
      } else {
        heap.remove(h.h)
      }
      if let curr = heap.peek(), prev != curr {
        result.append([h.pos, curr])
        prev = curr
      }
    }

    return result
  }
}

---

1712ms

class PriorityQueue<T> {
    private var heap: [T] = [T]()
    private let ordered: (T, T) -> Bool

    init(order: @escaping (T, T) -> Bool) {
        self.ordered = order
    }

    var isEmpty: Bool {
        return heap.isEmpty
    }
    var count: Int {
        return heap.count
    }

    func push(_ element: T) {
        heap.append(element)
        swim(heap.count - 1)
    }

    func pop() -> T? {
        if self.isEmpty {
            return nil
        }

        if self.heap.count == 1 {
            return heap.remove(at: 0)
        }

        heap.swapAt(0, heap.count - 1)
        let temp = heap.removeLast()
        sink(0)
        return temp
    }

    func peek() -> T? {
        if self.isEmpty {
            return nil
        }

        return self.heap[0]
    }

    private func sink(_ index: Int) {
        var index = index
        while 2 * index + 1 < heap.count {
            let leftChildIndex = 2 * index + 1

            var first = index
            if leftChildIndex < heap.count && ordered(heap[leftChildIndex], heap[first]) {
                first = leftChildIndex
            }

            let rightChildIndex = leftChildIndex + 1
            if rightChildIndex < heap.count && ordered(heap[rightChildIndex], heap[first]) {
                first = rightChildIndex
            }

            if index == first {
                break
            }

            heap.swapAt(index, first)
            index = first
        }
    }

    private func swim(_ index: Int) {
        var index = index
        while index > 0 && ordered(heap[index], heap[(index - 1) / 2]) {
            heap.swapAt((index - 1) / 2, index)
            index = (index - 1) / 2
        }
    }
}

extension PriorityQueue where T: Comparable {
    func remove(_ element: T) {
        if let index = heap.index(of: element) {
            heap.swapAt(index, heap.count - 1)
            heap.removeLast()
            if index < heap.count {
                swim(index)
                sink(index)
            }
        }
    }
}

class Solution {
    class Point {
        var pos: Int
        var height: Int
        var isStart: Bool

        init(_ pos: Int, _ height: Int, _ isStart: Bool) {
            self.pos = pos
            self.height = height
            self.isStart = isStart
        }
    }

    func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
        guard buildings.count > 0 && buildings[0].count > 0 else {
            return []
        }

        var positions = Array(repeating: Point(0, 0, false), count: buildings.count * 2)
        for idx in 0 ..< buildings.count {
            let start = Point(buildings[idx][0], buildings[idx][2], true)
            positions[idx * 2] = start

            let end = Point(buildings[idx][1], buildings[idx][2], false)
            positions[idx * 2 + 1] = end
        }

        positions.sort { pt1, pt2 in
            if pt1.pos != pt2.pos {
                return pt1.pos < pt2.pos
            }

            if pt1.isStart && pt2.isStart {
                return pt1.height > pt2.height
            }

            if !pt1.isStart && !pt2.isStart {
                return pt1.height < pt2.height
            }

            return pt1.isStart
         }

        let queue = PriorityQueue<Int>(order: >)
        queue.push(0)

        var result: [[Int]] = []
        var preMaxVal = 0
        for point in positions {
            if point.isStart {
                queue.push(point.height)
                let curMaxVal = queue.peek()!
                if curMaxVal > preMaxVal {
                    result.append([point.pos, point.height])
                    preMaxVal = curMaxVal
                }
            } else {
                queue.remove(point.height)
                let curMaxVal = queue.peek()!
                if curMaxVal < preMaxVal {
                    result.append([point.pos, curMaxVal])
                    preMaxVal = curMaxVal
                }
            }
        }

        return result
    }
}

---

1916ms

class Solution {
    func getSkyline(_ buildings: [[Int]]) -> [[Int]] {
        if buildings.count == 0 {
            return []   
        }
        if buildings.count == 1 {
            let b = buildings[0]
            let x1 = b[0]; let x2 = b[1]; let y = b[2]
            return [[x1, y], [x2, 0]]
        }
        var bsplit: [(Int, Int, Bool)] = []
        for b in buildings {
            let x1 = b[0]; let x2 = b[1]; let y = b[2]
            bsplit.append((x1, y, false))
            bsplit.append((x2, y, true))            
        }
        // TODO replace h with priority queue
        var h: [(Int, Int)] = []    
        let s1: ((Int, Int), (Int, Int)) -> Bool = {
            $0.1 > $1.1 
            || ($0.1 == $1.1 && $0.0 > $0.1)            
        }
        let so: ((Int, Int, Bool), (Int, Int, Bool)) -> Bool = {
            $0.0 < $1.0 
            || ($0.0 == $1.0 && $0.2 == false && $1.2 == true)
            || ($0.0 == $1.0 && $0.1 > $1.1)            
        }
        let buildingsSorted = bsplit.sorted(by: so)
//        print("buildingsSorted (buildingsSorted)")
        var ans: [[Int]] = []
        for i in 0..<buildingsSorted.count {
            let b = buildingsSorted[i]
            let bx = b.0; let by = b.1; let close = b.2 == true
//            print("b (b) h (h)")
            if h.count == 0 {
                h.append((bx, by))
                ans.append([bx, by])
                continue
            }
            if close {
                if let index = h.firstIndex(where: {$0.1 == by}) {
                    h.remove(at: index)
                    if h.count == 0 { ans.append([bx, 0]) }
                    if let l = h.first {
                        if l.1 < by { ans.append([bx, l.1]) }
                    }
                }
                continue
            }
    //        print("b (b) h (h)")
            if let l = h.first {
                if l.1 < by { ans.append([bx, by]) }
//                print("l.1 (l.1) by (by) x3 ans (ans)")
            }
            if let index = h.firstIndex(where: { $0.1 < by }) {
                h.insert((bx, by), at:index)                
            } else {
                h.append((bx, by))            
            }
            /*
            h.append((bx, by))
            h.sort(by: s1) // need to optimize???
            */
//            print("hx (h)")
        }
//        print("ans (ans)")
        var i = 1
        while i < ans.count {
//            print("i (i) ans (ans)")
            if ans[i][0] == ans[i-1][0] {
                ans.remove(at: i - 1)
                continue
            }
            i += 1
        }
        return ans
    }
}