295. Find Median from Data Stream

Problem Statement

The median is the middle value in an ordered integer list. If the size of the list is even, there is no middle value, and the median is the mean of the two middle values.

For example, for arr = [2,3,4], the median is 3.
For example, for arr = [2,3], the median is (2 + 3) / 2 = 2.5.

Implement the MedianFinder class:

MedianFinder() initializes the MedianFinder object.
void addNum(int num) adds the integer num from the data stream to the data structure.
double findMedian() returns the median of all elements so far. Answers within 10-5 of the actual answer will be accepted.

Example 1:

Input
["MedianFinder", "addNum", "addNum", "findMedian", "addNum", "findMedian"]
[[], [1], [2], [], [3], []]
Output
[null, null, null, 1.5, null, 2.0]

Explanation
MedianFinder medianFinder = new MedianFinder();
medianFinder.addNum(1);    // arr = [1]
medianFinder.addNum(2);    // arr = [1, 2]
medianFinder.findMedian(); // return 1.5 (i.e., (1 + 2) / 2)
medianFinder.addNum(3);    // arr[1, 2, 3]
medianFinder.findMedian(); // return 2.0

Constraints:

-105 <= num <= 105
There will be at least one element in the data structure before calling findMedian.
At most 5 * 104 calls will be made to addNum and findMedian.

Intuition

MAintain two heaps and Balance them, For more refer Sliding Window Median

Video Links

Approach 1:

C++

class MedianFinder {
public:  
    priority_queue<int> max_heap;
    priority_queue<int, vector<int>, greater<int>> min_heap;

    void addNum(int num) {
        if(max_heap.empty() or num <= max_heap.top())
            max_heap.push(num);
        
        else 
            min_heap.push(num);

        if(max_heap.size()+1 < min_heap.size()){
            max_heap.push(min_heap.top());
            min_heap.pop();
        }
        else if(min_heap.size()+1 < max_heap.size()){
            min_heap.push(max_heap.top());
            max_heap.pop();
        }
    }
    
    double findMedian() {
        if(max_heap.size() == min_heap.size())
            return ((double)min_heap.top() + (double)max_heap.top()) / 2.0;

        else if(max_heap.size() > min_heap.size())
            return (double)max_heap.top();

        return (double)min_heap.top();

    }
};

Approach 2:

Self code

C++

class MedianFinder {
public:
    priority_queue<int> max_heap;
    priority_queue<int, vector<int>, greater<int>> min_heap;
    void balance(){
        int a=max_heap.size(), b=min_heap.size();
        if(a==b or a==1+b or b==1+a)
            return ;

        else if(b>a and b!=1+a){
            int temp = min_heap.top();
            min_heap.pop();
            max_heap.push(temp);
        }
        else if(a>b and a!= 1+b){
            int temp = max_heap.top();
            max_heap.pop();
            min_heap.push(temp);
        }
    }

    void addNum(int num) {
        if(max_heap.size() == 0 or min_heap.size() == 0)
            max_heap.push(num);
        else if(num < max_heap.top()){
            max_heap.push(num);
        }
        else
            min_heap.push(num);

        

        balance();
    }
    
    double findMedian() {
        int a=max_heap.size(), b=min_heap.size();
        // return 0;
        if(a == b)
            return (max_heap.top() + min_heap.top() )/ 2.0;
        else if(a > b)
            return max_heap.top();
        return min_heap.top();
    }
};

Approach 3:

C++

Approach 4:

C++