# 295. Find Median from Data Stream

## Problem Statement

<br>

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.

&#x20;

**Example 1:**

<pre><code><strong>Input
</strong>["MedianFinder", "addNum", "addNum", "findMedian", "addNum", "findMedian"]
[[], [1], [2], [], [3], []]
<strong>Output
</strong>[null, null, null, 1.5, null, 2.0]

<strong>Explanation
</strong>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
</code></pre>

&#x20;

**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
```

### Links

<https://leetcode.com/problems/find-median-from-data-stream/description/>

### Video Links

### Approach 1:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
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();

    }
};
```

{% endcode %}

### Approach 2:

```
Self code
```

{% code title="C++" lineNumbers="true" %}

```cpp
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();
    }
};
```

{% endcode %}

### Approach 3:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Approach 4:

```
```

{% code title="C++" lineNumbers="true" %}

```cpp
```

{% endcode %}

### Similar Problems

###


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