LeetCode – Find Median from Data Stream (Java)

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.

Analysis

First of all, it seems that the best time complexity we can get for this problem is O(log(n)) of add() and O(1) of getMedian(). This data structure seems highly likely to be a tree.

We can use heap to solve this problem. In Java, the PriorityQueue class is a priority heap. We can use two heaps to store the lower half and the higher half of the data stream. The size of the two heaps differs at most 1.

find-median-from-stream

Java Solution

class MedianFinder {
    PriorityQueue<Integer> maxHeap;//lower half
    PriorityQueue<Integer> minHeap;//higher half
 
    public MedianFinder(){
        maxHeap = new PriorityQueue<Integer>(Collections.reverseOrder());
        minHeap = new PriorityQueue<Integer>();
    }
 
    // Adds a number into the data structure.
    public void addNum(int num) {
        maxHeap.offer(num);
        minHeap.offer(maxHeap.poll());
 
        if(maxHeap.size() < minHeap.size()){
            maxHeap.offer(minHeap.poll());
        }
    }
 
    // Returns the median of current data stream
    public double findMedian() {
        if(maxHeap.size()==minHeap.size()){
            return (double)(maxHeap.peek()+(minHeap.peek()))/2;
        }else{
            return maxHeap.peek();
        }
    }
}
Category >> Algorithms  
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