 # Find Median from Data Stream

#1

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)
findMedian() -> 1.5
findMedian() -> 2
```

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?

#2

Use two priority queues to keep the min and max numbers and use the top of each of these queues to calculate the median.

``````class MedianFinder {
private PriorityQueue<Integer> small = new PriorityQueue<>(Collections.reverseOrder());
private PriorityQueue<Integer> large = new PriorityQueue<>();
private boolean even = true;

public double findMedian() {
System.out.println(small);
System.out.println(large);
if (even)
return (small.peek() + large.peek()) / 2.0;
else
return small.peek();
}

public void addNum(int num) {
if (even) {
large.offer(num);
small.offer(large.poll());
} else {
small.offer(num);
large.offer(small.poll());
}
even = !even;

}
};

``````