Median_of_Two_Sorted_Arrays.java

# Intuition
<!-- Describe your first thoughts on how to solve this problem. -->

# Approach
<!-- Describe your approach to solving the problem. -->

# Complexity
- Time complexity:
<!-- Add your time complexity here, e.g. $$O(n)$$ -->

- Space complexity:
<!-- Add your space complexity here, e.g. $$O(n)$$ -->

# Code
```
class Solution:
    def findMedianSortedArrays(self, nums1: List[int], nums2: List[int]) -> float:
        if len(nums1) > len(nums2):
            return self.findMedianSortedArrays(nums2, nums1)  # Ensure nums1 is the shorter array
        
        x, y = len(nums1), len(nums2)
        low, high = 0, x
        
        while low <= high:
            partitionX = (low + high) // 2
            partitionY = (x + y + 1) // 2 - partitionX
            
            maxX = float('-inf') if partitionX == 0 else nums1[partitionX - 1]
            maxY = float('-inf') if partitionY == 0 else nums2[partitionY - 1]
            
            minX = float('inf') if partitionX == x else nums1[partitionX]
            minY = float('inf') if partitionY == y else nums2[partitionY]
            
            if maxX <= minY and maxY <= minX:
                if (x + y) % 2 == 0:
                    return (max(maxX, maxY) + min(minX, minY)) / 2
                else:
                    return max(maxX, maxY)
            elif maxX > minY:
                high = partitionX - 1
            else:
                low = partitionX + 1
        
        raise ValueError("Input arrays are not sorted.")

```