76. Find Median from Data Stream

Topic :

priority queue

Difficulty :

hard

Problem Link :

problem statement

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

For example, for arr = [2,3,4], the median is 3.
For example, for arr = [2,3], the median is (2 + 3) / 2 = 2.5.

Implement the MedianFinder class:

MedianFinder() initializes the MedianFinder object.
void addNum(int num) adds the integer num from the data stream to the data structure.
double findMedian() returns the median of all elements so far. Answers within 10-5 of the actual answer will be accepted.

Example 1:

Input
["MedianFinder", "addNum", "addNum", "findMedian", "addNum", "findMedian"]
[[], [1], [2], [], [3], []]
Output
[null, null, null, 1.5, null, 2.0]

Explanation
MedianFinder medianFinder = new MedianFinder();
medianFinder.addNum(1);    // arr = [1]
medianFinder.addNum(2);    // arr = [1, 2]
medianFinder.findMedian(); // return 1.5 (i.e., (1 + 2) / 2)
medianFinder.addNum(3);    // arr[1, 2, 3]
medianFinder.findMedian(); // return 2.0

Constraints:

-105 <= num <= 105
There will be at least one element in the data structure before calling findMedian.
At most 5 * 104 calls will be made to addNum and findMedian.

solution

import java.io.*;
import java.util.*;
 class Median_from_Data_Stream
{
    class MedianFinder {
    
     PriorityQueue <Integer> maxHeap=new PriorityQueue<>(Collections.reverseOrder());// stores the smaller numbers 
     PriorityQueue <Integer> minHeap=new PriorityQueue<>(); // stores the larger numbers    
    public MedianFinder() {
        
      }
    
     void addNum(int num) {
       if(maxHeap.isEmpty() ||num<=maxHeap.peek())
          maxHeap.add(num);
        else
            minHeap.add(num);
    
    
       if(maxHeap.size() > minHeap.size()+1){
        minHeap.add(maxHeap.poll());
        }
      
    
       else if(minHeap.size()>maxHeap.size())
        maxHeap.add(minHeap.poll());
    } 
     double findMedian() {
        
        int x= maxHeap.peek();
        
        int y=!minHeap.isEmpty() ? minHeap.peek(): 0;
        
        if(maxHeap.size()==minHeap.size()) // there are even no.of elements
        return (x+y)/2.0;
        
        return x;
    }
  }
    void main ()
  { MedianFinder medianFinder = new MedianFinder();
    medianFinder.addNum(1);    // arr = [1]
    medianFinder.addNum(2);    // arr = [1, 2]
    System.out.println(medianFinder.findMedian()); // return 1.5 (i.e., (1 + 2) / 2)
    medianFinder.addNum(3);    // arr[1, 2, 3]
    System.out.println(medianFinder.findMedian()); // return 2.0
   
    }
}