755 字
4 分钟
数据流中的中位数
题目
如何得到一个数据流中的中位数?如果从数据流中读出奇数个数值,那么中位数就是所有数值排序之后位于中间的数值。如果从数据流中读出偶数个数值,那么中位数就是所有数值排序之后中间两个数的平均值。
例如,
[2,3,4] 的中位数是 3
[2,3] 的中位数是 (2 + 3) / 2 = 2.5
设计一个支持以下两种操作的数据结构:
void addNum(int num) - 从数据流中添加一个整数到数据结构中。
double findMedian() - 返回目前所有元素的中位数。
示例 1:
输入:
[“MedianFinder”,“addNum”,“addNum”,“findMedian”,“addNum”,“findMedian”]
[[],[1],[2],[],[3],[]]
输出:[null,null,null,1.50000,null,2.00000]
示例 2:
输入:
[“MedianFinder”,“addNum”,“findMedian”,“addNum”,“findMedian”]
[[],[2],[],[3],[]]
输出:[null,null,2.00000,null,2.50000]
限制:
最多会对 addNum 、 findMedian 进行 50000 次调用。
注意:本题与主站 295 题相同:https://leetcode-cn.com/problems/find-median-from-data-stream/
来源:力扣(LeetCode)
链接:https://leetcode-cn.com/problems/shu-ju-liu-zhong-de-zhong-wei-shu-lcof 著作权归领扣网络所有。商业转载请联系官方授权,非商业转载请注明出处。
大小堆
class MedianFinder {
var minStack = SwiftPriorityQueue<Int>(hasHigherPriority: { $0 > $1 }, isEqual: { $0 == $1 }) var maxStack = SwiftPriorityQueue<Int>(hasHigherPriority: { $0 < $1 }, isEqual: { $0 == $1 })
/** initialize your data structure here. */ init() {
}
func addNum(_ num: Int) { if maxStack.count > minStack.count { minStack.enqueue(num) } else if minStack.count > maxStack.count { maxStack.enqueue(num) } else { if let minMax = minStack.array().first, minMax > num { minStack.enqueue(num) } else if let maxMin = maxStack.array().first, maxMin < num { maxStack.enqueue(num) } else { maxStack.enqueue(num) } }
if let minMax = minStack.array().first, let maxMin = maxStack.array().first, minMax > maxMin { minStack.dequeue() minStack.enqueue(maxMin)
maxStack.dequeue() maxStack.enqueue(minMax) }
// print("大堆:\(maxStack)")// print("小堆:\(minStack)")// print("======") }
func findMedian() -> Double { if minStack.count == maxStack.count, let a = minStack.peek(), let b = maxStack.peek() { return Double((a + b)) / 2.0 } else if minStack.count > maxStack.count { return Double(minStack.peek() ?? 0) } else if maxStack.count > minStack.count { return Double(maxStack.peek() ?? 0) } return 0 }}
let obj = MedianFinder()obj.addNum(-1)obj.addNum(-2)obj.addNum(-3)obj.addNum(-4)obj.addNum(-5)obj.addNum(6)
let ret_2: Double = obj.findMedian()
Swift - 优先队列
import Foundation
public struct SwiftPriorityQueue<Element> { private let _hasHigherPriority: (Element, Element) -> Bool private let _isEqual: (Element, Element) -> Bool
private var _elements = [Element]()
public init(hasHigherPriority: @escaping (Element, Element) -> Bool, isEqual: @escaping (Element, Element) -> Bool) { _hasHigherPriority = hasHigherPriority _isEqual = isEqual }
public mutating func enqueue(_ element: Element) { _elements.append(element) bubbleToHigherPriority(_elements.count - 1) }
public func peek() -> Element? { return _elements.first }
public func array() -> [Element] { return _elements }
public var isEmpty: Bool { return _elements.count == 0 }
public var count: Int { return _elements.count }
public mutating func dequeue() -> Element? { guard let front = peek() else { return nil }
removeAt(0)
return front }
public mutating func remove(_ element: Element) { for i in 0 ..< _elements.count { if _isEqual(_elements[i], element) { removeAt(i) return } } }
private mutating func removeAt(_ index: Int) { let removingLast = index == _elements.count - 1 if !removingLast { _elements.swapAt(index, _elements.count - 1) }
_ = _elements.popLast()
if !removingLast { bubbleToHigherPriority(index) bubbleToLowerPriority(index) } }
private mutating func bubbleToHigherPriority(_ initialUnbalancedIndex: Int) { precondition(initialUnbalancedIndex >= 0) precondition(initialUnbalancedIndex < _elements.count)
var unbalancedIndex = initialUnbalancedIndex
while unbalancedIndex > 0 { let parentIndex = (unbalancedIndex - 1) / 2 guard _hasHigherPriority(_elements[unbalancedIndex], _elements[parentIndex]) else { break } _elements.swapAt(unbalancedIndex, parentIndex) unbalancedIndex = parentIndex } }
private mutating func bubbleToLowerPriority(_ initialUnbalancedIndex: Int) { precondition(initialUnbalancedIndex >= 0) precondition(initialUnbalancedIndex < _elements.count)
var unbalancedIndex = initialUnbalancedIndex while true { let leftChildIndex = unbalancedIndex * 2 + 1 let rightChildIndex = unbalancedIndex * 2 + 2
var highestPriorityIndex = unbalancedIndex
if leftChildIndex < _elements.count && _hasHigherPriority(_elements[leftChildIndex], _elements[highestPriorityIndex]) { highestPriorityIndex = leftChildIndex }
if rightChildIndex < _elements.count && _hasHigherPriority(_elements[rightChildIndex], _elements[highestPriorityIndex]) { highestPriorityIndex = rightChildIndex }
guard highestPriorityIndex != unbalancedIndex else { break } _elements.swapAt(highestPriorityIndex, unbalancedIndex)
unbalancedIndex = highestPriorityIndex } }}
extension SwiftPriorityQueue : CustomDebugStringConvertible { public var debugDescription: String { return _elements.debugDescription }}