Median of Two Sorted Arrays

Hard

Description

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

Input:nums1 = [1,3], nums2 = [2]
Output:2.0
Explanation:

Merged array = [1,2,3] and median is 2.

Input:nums1 = [1,2], nums2 = [3,4]
Output:2.5
Explanation:

Merged array = [1,2,3,4] and median is (2 + 3) / 2 = 2.5.

Input:nums1 = [5,6,7,8], nums2 = [1,2,3,4]
Output:4.5
Explanation:

Merged array = [1,2,3,4,5,6,7,8] and median is (4 + 5) / 2 = 4.5. This example demonstrates finding the median when arrays are completely non-overlapping in ranges.

Constraints

  • nums1.length == m
  • nums2.length == n
  • 0 ≤ m ≤ 1000
  • 0 ≤ n ≤ 1000
  • 1 ≤ m + n ≤ 2000
  • -10⁶ ≤ nums1[i], nums2[i] ≤ 10⁶

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