# LC295 - Find Median from Data Stream

## Problem

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

**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

## Solution

Time complexity is about $$O(\log n)$$, and $$O(n)$$ extra space is used.

```python
def __init__(self):
	self.small = []
	self.large = []

def addNum(self, num: int) -> None:

	# python doesn't have maxheap, most ops are log(n)
	heapq.heappush(self.small, -1 * num)
	if (self.small and self.large and (-1 * self.small[0]) > self.large[0]):
		val = -1 * heapq.heappop(self.small)
		heapq.heappush(self.large, val)
		
	if len(self.small) > len(self.large) + 1:
		val = -1 * heapq.heappop(self.small)
		heapq.heappush(self.large, val)
	
	if len(self.large) > len(self.small) + 1:
		val = heapq.heappop(self.large)
		heapq.heappush(self.small, -1 * val)

  

def findMedian(self) -> float:
	# Odd numb of elements
	if len(self.small) > len(self.large):	
		return -1 * self.small[0]

	elif len(self.large) > len(self.small):
		return self.large[0]

	return (-1 * self.small[0] + self.large[0])/2
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://www.vjssn.dev/practice/24-06-17/lc295-find-median-from-data-stream.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.