Find Median from Data Stream

Description

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

Clarification

What's the definition of Median?

• The median is not equal to median in math.
• 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]A[(n−1)/2].
• For example, if A=[1,2,3], median is 2. If A=[1,19], median is 1.

Example

Example 1

Input: [1,2,3,4,5]
Output: [1,1,2,2,3]
Explanation:
The medium of [1] and [1,2] is 1.
The medium of [1,2,3] and [1,2,3,4] is 2.
The medium of [1,2,3,4,5] is 3.

Example 2

Input: [4,5,1,3,2,6,0]
Output: [4,4,4,3,3,3,3]
Explanation:
The medium of [4], [4,5], [4,5,1] is 4.
The medium of [4,5,1,3], [4,5,1,3,2], [4,5,1,3,2,6] and [4,5,1,3,2,6,0] is 3.

Challenge

Total run time in O(nlogn).

思路：用 maxheap 保存左半部分的数，用 minheap 保存右半部分的数。
把所有的数一左一右的加入到每个部分。左边部分最大的数就一直都是 median。
这个过程中，可能会出现左边部分并不完全都 <= 右边部分的情况。这种情况发生的时候，交换左边最大和右边最小的数即可。

public class Solution {
    /**
     * @param nums: A list of integers.
     * @return: the median of numbers
     */
    private PriorityQueue<Integer> maxHeap, minHeap;
    private int numOfElements = 0;

    public int[] medianII(int[] nums) {
        // write your code here
        Comparator<Integer> revCmp = new Comparator<Integer>() {
            @Override
            public int compare(Integer left, Integer right) {
                return right.compareTo(left);
            }
        };
        int cnt = nums.length;
        maxHeap = new PriorityQueue<Integer>(cnt, revCmp);
        minHeap = new PriorityQueue<Integer>(cnt);
        int[] ans = new int[cnt];
        for (int i = 0; i < cnt; ++i) {
            addNumber(nums[i]);
            ans[i] = getMedian();
        }
        return ans;
    }
    void addNumber(int value) {
        maxHeap.add(value);
        if (numOfElements%2 == 0) {
            if (minHeap.isEmpty()) {
                numOfElements++;
                return;
            }
            else if (maxHeap.peek() > minHeap.peek()) {
                Integer maxHeapRoot = maxHeap.poll();
                Integer minHeapRoot = minHeap.poll();
                maxHeap.add(minHeapRoot);
                minHeap.add(maxHeapRoot);
            }
        }
        else {
            minHeap.add(maxHeap.poll());
        }
        numOfElements++;
    }
    int getMedian() {
        return maxHeap.peek();
    }
}