刷題295. Find Median from Data Stream

一、題目說明

題目295. Find Median from Data Stream，數據流的中位數（數據爲奇數個，則爲中間的；否則爲中間2個數的平均數）。

二、我的解答

用一個數組實現，但是超時。改用插入排序如下：

class MedianFinder {
    vector<int> store;

public:
    void addNum(int num)
    {
        if (store.empty())
            store.push_back(num);
        else
            store.insert(lower_bound(store.begin(), store.end(), num), num);    
    }
    double findMedian()
    {
        int n = store.size();
        return n & 1 ? store[n / 2] : (store[n / 2 - 1] + store[n / 2]) * 0.5;
    }
};

Runtime: 304 ms, faster than 9.04% of C++ online submissions for Find Median from Data Stream.
Memory Usage: 42.7 MB, less than 60.87% of C++ online submissions for Find Median from Data Stream.

三、優化措施

用2個優先級隊列實現：

class MedianFinder {
    priority_queue<int> max;//大根堆
    priority_queue<int, vector<int>, greater<int>> min;
public:
    //數據優先放入大頂堆中，然後將大頂堆堆頂元素放入小頂堆中
    //如果大頂堆元素數量小於小頂堆元素數量，則從小頂堆中彈出一個元素放入大頂堆中
    //如果數據總量爲奇數，則中位數爲大頂堆堆頂元素，否則爲大頂堆和小頂堆元素和除以2。
    MedianFinder() {
        
    }
    
    void addNum(int num) {
        max.push(num);
        min.push(max.top());
        max.pop();
        if (max.size() < min.size()) {
            max.push(min.top());
            min.pop();
        }        
    }
    
    double findMedian() {
        int size = max.size() + min.size();
        return size % 2 == 1 ? max.top() : (max.top() + min.top()) / 2.0;
    }
};

性能如下：

Runtime: 172 ms, faster than 47.48% of C++ online submissions for Find Median from Data Stream.
Memory Usage: 42.4 MB, less than 100.00% of C++ online submissions for Find Median from Data Stream.