Find Median from Data Stream

Permutations

Merge K Sorted Lists

Return the median after incrementally inserting every stream value.

Insert the integers in `nums` one at a time and return the final median as a floating-point number.

## Example
```json
Input: {"nums":[1,2]}
Output: 1.5
```

## Constraints
- 1 <= nums.length <= 50000
- -100000 <= nums[i] <= 100000

## Follow-up
How would a `MedianFinder` class expose repeated `addNum` and `findMedian` calls?

The key pattern is: Two heaps balance the lower and upper halves. Identify the state and invariant before coding.

Recognize the Pattern

Advance one state transition at a time. Mark or update state before exploring dependent work.

Build the Algorithm

Test empty or minimal input, skewed shapes, duplicates where allowed, and impossible outcomes.