package com.thealgorithms.datastructures.heaps;
import java.util.PriorityQueue;
/**
* This class maintains the median of a dynamically changing data stream using
* two heaps: a max-heap and a min-heap. The max-heap stores the smaller half
* of the numbers, and the min-heap stores the larger half.
* This data structure ensures that retrieving the median is efficient.
*
* Time Complexity:
* - Adding a number: O(log n) due to heap insertion.
* - Finding the median: O(1).
*
* Space Complexity: O(n), where n is the total number of elements added.
*
* @author Hardvan
*/
public final class MedianFinder {
MedianFinder() {
}
private PriorityQueue<Integer> minHeap = new PriorityQueue<>();
private PriorityQueue<Integer> maxHeap = new PriorityQueue<>((a, b) -> b - a);
/**
* Adds a new number to the data stream. The number is placed in the appropriate
* heap to maintain the balance between the two heaps.
*
* @param num the number to be added to the data stream
*/
public void addNum(int num) {
if (maxHeap.isEmpty() || num <= maxHeap.peek()) {
maxHeap.offer(num);
} else {
minHeap.offer(num);
}
if (maxHeap.size() > minHeap.size() + 1) {
minHeap.offer(maxHeap.poll());
} else if (minHeap.size() > maxHeap.size()) {
maxHeap.offer(minHeap.poll());
}
}
/**
* Finds the median of the numbers added so far. If the total number of elements
* is even, the median is the average of the two middle elements. If odd, the
* median is the middle element from the max-heap.
*
* @return the median of the numbers in the data stream
*/
public double findMedian() {
if (maxHeap.size() == minHeap.size()) {
return (maxHeap.peek() + minHeap.peek()) / 2.0;
}
return maxHeap.peek();
}
}