[hard]295. Find Median from Data Stream

数据流中位数算法

最新推荐文章于 2025-12-02 18:04:47 发布

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本文介绍了一种高效的数据结构，用于处理数据流中的中位数查找问题。该数据结构支持添加整数并能返回当前所有元素的中位数。通过维护两个堆，确保即使在大量数据输入的情况下也能快速响应。

295. Find Median from Data Stream

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.

Examples:

[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.

For example:

add(1)
add(2)
findMedian() -> 1.5
add(3) 
findMedian() -> 2

Credits:
Special thanks to @Louis1992 for adding this problem and creating all test cases.

Solution:

It's a super classic problem, maintain two heaps. view codes to see my tricks.

class MedianFinder {
private:
    priority_queue <int> tail_half;
    priority_queue <int, vector <int>, greater<int> > head_half;
public:

    // Adds a number into the data structure.
    void addNum(int num) {
        tail_half.push(num);
        head_half.push(tail_half.top());
        tail_half.pop();

        if (head_half.size() > tail_half.size()) {
            tail_half.push(head_half.top());
            head_half.pop();
        }
    }

    // Returns the median of current data stream
    double findMedian() {
        size_t size = head_half.size() + tail_half.size();
        if (size & 1)
            return tail_half.top();
        return (head_half.top() + tail_half.top()) / 2.0;
    }
};