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17.20. Continuous Median

Description

Numbers are randomly generated and passed to a method. Write a program to find and maintain the median value as new values are generated.

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

Solutions

Solution 1

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class MedianFinder:
    def __init__(self):
        """
        initialize your data structure here.
        """
        self.h1 = []
        self.h2 = []

    def addNum(self, num: int) -> None:
        heappush(self.h1, num)
        heappush(self.h2, -heappop(self.h1))
        if len(self.h2) - len(self.h1) > 1:
            heappush(self.h1, -heappop(self.h2))

    def findMedian(self) -> float:
        if len(self.h2) > len(self.h1):
            return -self.h2[0]
        return (self.h1[0] - self.h2[0]) / 2


# Your MedianFinder object will be instantiated and called as such:
# obj = MedianFinder()
# obj.addNum(num)
# param_2 = obj.findMedian()

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class MedianFinder {
    private PriorityQueue<Integer> q1 = new PriorityQueue<>();
    private PriorityQueue<Integer> q2 = new PriorityQueue<>(Collections.reverseOrder());

    /** initialize your data structure here. */
    public MedianFinder() {
    }

    public void addNum(int num) {
        q1.offer(num);
        q2.offer(q1.poll());
        if (q2.size() - q1.size() > 1) {
            q1.offer(q2.poll());
        }
    }

    public double findMedian() {
        if (q2.size() > q1.size()) {
            return q2.peek();
        }
        return (q1.peek() + q2.peek()) * 1.0 / 2;
    }
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * MedianFinder obj = new MedianFinder();
 * obj.addNum(num);
 * double param_2 = obj.findMedian();
 */

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class MedianFinder {
public:
    /** initialize your data structure here. */
    MedianFinder() {
    }

    void addNum(int num) {
        q1.push(num);
        q2.push(q1.top());
        q1.pop();
        if (q2.size() - q1.size() > 1) {
            q1.push(q2.top());
            q2.pop();
        }
    }

    double findMedian() {
        if (q2.size() > q1.size()) {
            return q2.top();
        }
        return (double) (q1.top() + q2.top()) / 2;
    }

private:
    priority_queue<int, vector<int>, greater<int>> q1;
    priority_queue<int> q2;
};

/**
 * Your MedianFinder object will be instantiated and called as such:
 * MedianFinder* obj = new MedianFinder();
 * obj->addNum(num);
 * double param_2 = obj->findMedian();
 */

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type MedianFinder struct {
    q1 hp
    q2 hp
}

/** initialize your data structure here. */
func Constructor() MedianFinder {
    return MedianFinder{hp{}, hp{}}
}

func (this *MedianFinder) AddNum(num int) {
    heap.Push(&this.q1, num)
    heap.Push(&this.q2, -heap.Pop(&this.q1).(int))
    if this.q2.Len()-this.q1.Len() > 1 {
        heap.Push(&this.q1, -heap.Pop(&this.q2).(int))
    }
}

func (this *MedianFinder) FindMedian() float64 {
    if this.q2.Len() > this.q1.Len() {
        return -float64(this.q2.IntSlice[0])
    }
    return float64(this.q1.IntSlice[0]-this.q2.IntSlice[0]) / 2.0
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * obj := Constructor();
 * obj.AddNum(num);
 * param_2 := obj.FindMedian();
 */

type hp struct{ sort.IntSlice }

func (h hp) Less(i, j int) bool { return h.IntSlice[i] < h.IntSlice[j] }
func (h *hp) Push(v any)        { h.IntSlice = append(h.IntSlice, v.(int)) }
func (h *hp) Pop() any {
    a := h.IntSlice
    v := a[len(a)-1]
    h.IntSlice = a[:len(a)-1]
    return v
}

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class MedianFinder {
    private var minHeap = Heap<Int>(sort: <)
    private var maxHeap = Heap<Int>(sort: >)

    init() {
    }

    func addNum(_ num: Int) {
        maxHeap.insert(num)
        minHeap.insert(maxHeap.remove()!)

        if maxHeap.count < minHeap.count {
            maxHeap.insert(minHeap.remove()!)
        }
    }

    func findMedian() -> Double {
        if maxHeap.count > minHeap.count {
            return Double(maxHeap.peek()!)
        }
        return (Double(maxHeap.peek()!) + Double(minHeap.peek()!)) / 2.0
    }
}

struct Heap<T> {
    var elements: [T]
    let sort: (T, T) -> Bool

    init(sort: @escaping (T, T) -> Bool, elements: [T] = []) {
        self.sort = sort
        self.elements = elements
        if !elements.isEmpty {
            for i in stride(from: elements.count / 2 - 1, through: 0, by: -1) {
                siftDown(from: i)
            }
        }
    }

    var isEmpty: Bool {
        return elements.isEmpty
    }

    var count: Int {
        return elements.count
    }

    func peek() -> T? {
        return elements.first
    }

    mutating func insert(_ value: T) {
        elements.append(value)
        siftUp(from: elements.count - 1)
    }

    mutating func remove() -> T? {
        guard !elements.isEmpty else { return nil }
        elements.swapAt(0, elements.count - 1)
        let removedValue = elements.removeLast()
        siftDown(from: 0)
        return removedValue
    }

    private mutating func siftUp(from index: Int) {
        var child = index
        var parent = parentIndex(ofChildAt: child)
        while child > 0 && sort(elements[child], elements[parent]) {
            elements.swapAt(child, parent)
            child = parent
            parent = parentIndex(ofChildAt: child)
        }
    }

    private mutating func siftDown(from index: Int) {
        var parent = index
        while true {
            let left = leftChildIndex(ofParentAt: parent)
            let right = rightChildIndex(ofParentAt: parent)
            var candidate = parent
            if left < count && sort(elements[left], elements[candidate]) {
                candidate = left
            }
            if right < count && sort(elements[right], elements[candidate]) {
                candidate = right
            }
            if candidate == parent {
                return
            }
            elements.swapAt(parent, candidate)
            parent = candidate
        }
    }

    private func parentIndex(ofChildAt index: Int) -> Int {
        return (index - 1) / 2
    }

    private func leftChildIndex(ofParentAt index: Int) -> Int {
        return 2 * index + 1
    }

    private func rightChildIndex(ofParentAt index: Int) -> Int {
        return 2 * index + 2
    }
}

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