You’re given two sorted integer arrays, nums1 and nums2, of size $m$ and $n$, respectively. Your task is to return the median of the two sorted arrays.

The overall run time complexity should be $O(\log (m, n))$.

Constraints:

• nums1.length $= m$

• nums2.length $= n$

• $0 \leq m \leq 1000$

• $0 \leq n \leq 1000$

• $1 \leq m + n \leq 2000$

• $-10^5 \leq$ nums1[i], nums2[i] $\leq 10^5$

To solve this problem, we’ll use a binary search approach starting with the smaller array to find a partition such that the left and right partitions of the merged array are sorted correctly, which helps in finding the median directly. This approach is necessary because directly merging the arrays and then finding the median would result in a time complexity of $O(m+n)$, which does not meet the requirements of the problem statement. Instead, we use a modified binary search approach to efficiently locate the median by taking advantage of the sorted nature of the arrays.

The algorithm starts by setting the initial partition point in the smaller array as the middle, using the first step of binary search: