Find median of two sorted arrays

You are given two sorted arrays of integers nums1 and nums2 in non-decreasing order.

Let the lengths be m = nums1.length and n = nums2.length. Either array may be empty, but not both at the same time.

If you were to conceptually merge them into a single sorted array merged of length m + n, the median is defined as:

• If m + n is odd: the element at index (m + n) / 2 (0-based) in merged .
• If m + n is even: the average of the two middle elements at indices (m + n) / 2 - 1 and (m + n) / 2 in merged .

Task

Implement a function that returns the median of the two sorted arrays without actually merging them.

• Function signature (conceptual):
  • Input: nums1: integer[] , nums2: integer[]
  • Output: median: float (or double)

Constraints (you may assume)

• 0 ≤ m, n ≤ 10^5
• m + n ≥ 1
• Each array is individually sorted in non-decreasing order.
• Integer values fit in a 32-bit signed integer range.
• Target time complexity: O(log(m + n)) .
• Extra space complexity: O(1) beyond input storage.