Data Stream Median

最新推荐文章于 2021-08-27 01:10:20 发布

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本文介绍了一种使用最大堆和最小堆的数据结构方法来实时计算一组连续输入整数的中位数。通过维持两个堆之间的平衡，可以在每次添加新元素后高效地获取当前集合的中位数。

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

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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, if A=[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].

使用大小堆的方式进行处理

public class Solution {
    /*
     * @param nums: A list of integers
     * @return: the median of numbers
     */
    public int[] medianII(int[] nums) {
        // write your code here
        if (nums == null || nums.length == 0) {
            return new int[]{};
        }
        Comparator<Integer> cmp = new Comparator<Integer>() {
            public int compare(Integer a, Integer b) {
                return b - a;
            }
        };
        Queue<Integer> minHeap = new PriorityQueue<>();
        Queue<Integer> maxHeap = new PriorityQueue<>(1, cmp);
        int[] res = new int[nums.length];
        res[0] = nums[0];
        maxHeap.offer(nums[0]);
        for (int i = 1; i < nums.length; i++) {
            int val = maxHeap.peek();
            if (nums[i] < val) {
                maxHeap.offer(nums[i]);
            } else {
                minHeap.offer(nums[i]);
            }
            if (maxHeap.size() > minHeap.size() + 1) {
                minHeap.offer(maxHeap.poll());
            } else if (minHeap.size() > maxHeap.size()) {
                maxHeap.offer(minHeap.poll());
            }
            res[i] = maxHeap.peek();
        }
        return res;
    }
}