[Swift]LeetCode295. 数据流的中位数 | Find Median from Data Stream

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Median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value. So the median is the mean of the two middle value.

For example,

[2,3,4], the median is 3

[2,3], the median is (2 + 3) / 2 = 2.5

Design a data structure that supports the following two operations:

• void addNum(int num) - Add a integer number from the data stream to the data structure.
• double findMedian() - Return the median of all elements so far.

Example:

addNum(1)
addNum(2)
findMedian() -> 1.5
addNum(3) 
findMedian() -> 2

Follow up:

1. If all integer numbers from the stream are between 0 and 100, how would you optimize it?
2. If 99% of all integer numbers from the stream are between 0 and 100, how would you optimize it?

---

中位数是有序列表中间的数。如果列表长度是偶数，中位数则是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：

addNum(1)
addNum(2)
findMedian() -> 1.5
addNum(3) 
findMedian() -> 2

进阶:

1. 如果数据流中所有整数都在 0 到 100 范围内，你将如何优化你的算法？
2. 如果数据流中 99% 的整数都在 0 到 100 范围内，你将如何优化你的算法？

---

736ms

class MedianFinder {
    var nums : [Int]
    
    /** initialize your data structure here. */
    init() {
        nums = [Int]()
    }
    
    func addNum(_ num: Int) {
        if nums.isEmpty {
            nums.append(num)
            return
        }
        
        var left = 0
        var right = nums.count - 1
        while left <= right {
            let mid = (left + right) / 2
            if nums[mid] < num {
                left = mid + 1
            }else if nums[mid] == num {
                left = mid
                break
            }else {
                right = mid - 1
            }
        }
        
        nums.insert(num, at: left)        
    }
    
    func findMedian() -> Double {
        if nums.isEmpty {
            return 0
        }
        
        if nums.count % 2 == 1 {
            return Double(nums[nums.count / 2])
        }else {
            let r1 = nums[nums.count / 2]
            let r2 = nums[nums.count / 2 - 1]
            return Double(r1 + r2) / 2
        }
    }
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * let obj = MedianFinder()
 * obj.addNum(num)
 * let ret_2: Double = obj.findMedian()
 */

---

1208ms

class MedianFinder {
    //Holds the small part of the stream but track the largest one
    let maxQueue: PriorityQueue<Int>
    //Holds the larger part of the stream but track the smallest one
    let minQueue: PriorityQueue<Int>
    /** initialize your data structure here. */
    init() {
        maxQueue = PriorityQueue<Int>(priorityFunction:{ $0 > $1 })
        minQueue = PriorityQueue<Int>(priorityFunction:{ $0 < $1 })
    }
    
    func addNum(_ num: Int) {
        maxQueue.enqueue(num)
        if let num = maxQueue.dequeue() {
            minQueue.enqueue(num)
            if maxQueue.count < minQueue.count {
                if let minNum = minQueue.dequeue() {
                    maxQueue.enqueue(minNum)
                }
            }
        }
    }
    
    func findMedian() -> Double {
        if maxQueue.count == minQueue.count {
            return (Double(maxQueue.peek()!) + Double(minQueue.peek()!)) / 2
        } else {
            return Double(maxQueue.peek()!)
        }
    }
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * let obj = MedianFinder()
 * obj.addNum(num)
 * let ret_2: Double = obj.findMedian()
 */
 

public class PriorityQueue<Element> {
    var elements: [Element]
    var priorityFunction: (Element, Element) -> Bool
    var count: Int { return elements.count }
    
    init(priorityFunction:@escaping (Element, Element) -> Bool) {
        self.elements = [Element]()
        self.priorityFunction = priorityFunction
    }
    
    func isHigherPriority(at index:Int,than secondIndex:Int) -> Bool {
        return self.priorityFunction(elements[index], elements[secondIndex])
    }
    
    func enqueue(_ element:Element) {
        elements.append(element)
        siftUp(index: elements.count - 1)
    }
    
    func dequeue() -> Element? {
        if elements.count == 0 {
            return nil
        }
        
        elements.swapAt(0, elements.count - 1)
        let element = elements.removeLast()
        siftDown(index: 0)
        return element
    }
    
    func peek() -> Element? {
        return elements.first
    }
    
    func siftUp(index:Int) {
        if index == 0 {
            return
        }
        
        let parent = parentIndex(for: index)
        if isHigherPriority(at: index, than: parent) {
            elements.swapAt(index, parent)
            siftUp(index: parent)
        }
    }
    
    func siftDown(index:Int) {
        var highIndex = index
        let leftIndex = leftChildIndex(for: index)
        let rightIndex = rightChildIndex(for: index)
        if leftIndex < count && isHigherPriority(at: leftIndex, than: index) {
            highIndex = leftIndex
        }
        if rightIndex < count && isHigherPriority(at: rightIndex, than: highIndex) {
            highIndex = rightIndex
        }
        if highIndex == index {
            return
        } else {
            elements.swapAt(highIndex, index)
            siftDown(index: highIndex)
        }
    }
    
    func parentIndex(for index:Int) -> Int {
        return (index - 1)/2
    }
    
    func leftChildIndex(for index:Int) -> Int {
        return index * 2 + 1
    }
    
    func rightChildIndex(for index:Int) -> Int {
        return index * 2 + 2
    }
}