Data Stream Median

Numbers keep coming, return the median of numbers at every time a new number added.

Clarification

What‘s the definition of Median?
- Median is the number that in the middle of a sorted array. If there are n numbers in a sorted array A, the median is A[(n - 1) / 2]. For example, ifA=[1,2,3], median is 2. If A=[1,19], median is 1.

Example

For numbers coming list: [1, 2, 3, 4, 5], return [1, 1, 2, 2, 3].

For numbers coming list: [4, 5, 1, 3, 2, 6, 0], return[4, 4, 4, 3, 3, 3, 3].

For numbers coming list: [2, 20, 100], return [2, 2, 20].

分析：
使用两个heap，一个min heap(root的值最小) and max heap (root的值最大)。保持两个heap的size差别最大为1，并且,min heap永远不会不max heap的size大。

 1 public class Solution {
 2     /**
 3      * @param nums: A list of integers.
 4      * @return: the median of numbers
 5      */
 6     public int[] medianII(int[] nums) {
 7         if (nums == null || nums.length == 0)
 8             return null;
 9
10         int[] med = new int[nums.length];
11
12         PriorityQueue<Integer> minHeap = new PriorityQueue<Integer>();
13         PriorityQueue<Integer> maxHeap = new PriorityQueue<Integer>(11, new Comparator<Integer>() {
14             public int compare(Integer x, Integer y) {
15                 return y - x;
16             }
17         });
18
19         med[0] = nums[0];
20         maxHeap.offer(nums[0]);
21
22         for (int i = 1; i < nums.length; i++) {
23             if (nums[i] < maxHeap.peek()) {
24                 maxHeap.offer(nums[i]);
25             } else {
26                 minHeap.offer(nums[i]);
27             }
28
29             if (maxHeap.size() > minHeap.size() + 1) {
30                 minHeap.offer(maxHeap.poll());
31             } else if (maxHeap.size() < minHeap.size()) {
32                 maxHeap.offer(minHeap.poll());
33             }
34             med[i] = maxHeap.peek();
35         }
36         return med;
37     }
38 }