Median of Two Sorted Arrays

Given two sorted arrays nums1 and nums2 of size m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).

Examples

Example 1:

Input: nums1 = [1,3], nums2 = [2]
Output: 2.00000
Explanation: merged array = [1,2,3] and median is 2.

Example 2:

Input: nums1 = [1,2], nums2 = [3,4]
Output: 2.50000
Explanation: merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5.

Constraints

nums1.length == m
nums2.length == n
0 <= m <= 1000
0 <= n <= 1000
1 <= m + n <= 2000
-10^6 <= nums1[i], nums2[i] <= 10^6

Function Signature

function findMedianSortedArrays(nums1, nums2) {
  // Your code here
}

Test Cases

• Base cases: nums1 = [1], nums2 = [2] → 1.5, nums1 = [], nums2 = [1] → 1.0
• Simple cases: nums1 = [1,3], nums2 = [2] → 2.0, nums1 = [1,2], nums2 = [3,4] → 2.5
• Edge cases: nums1 = [], nums2 = [] → 0.0, nums1 = [1], nums2 = [] → 1.0
• Complex cases: nums1 = [1,2,3,4,5], nums2 = [6,7,8,9,10] → 5.5
• Mixed cases: nums1 = [1,3,5,7], nums2 = [2,4,6,8] → 4.5

Notes

• Both input arrays are sorted in ascending order
• Need to find the median without merging the arrays
• Median is the middle value (odd length) or average of two middle values (even length)
• Optimal solution uses binary search with O(log(min(m,n))) time complexity
• Handle edge cases where arrays might be empty or have different sizes