Odd total length
Input
nums1 = [1, 3], nums2 = [2]
Output
2.0
Combined sorted array is [1,2,3]; median is 2.
Full lesson preview
Find median of two sorted arrays
Compute the median of two sorted arrays in logarithmic time by binary searching the smaller array.
Python practice30 minSearching & SortingAdvancedLast updated March 25, 2026
Problem statement
Given two sorted arrays nums1 and nums2 of sizes m and n respectively, return the median of the two sorted arrays. The overall run time complexity should be O(log(min(m, n))). If the combined length is odd, return the middle element as a float. If even, return the average of the two middle elements as a float. Do not merge the arrays into a single sorted array — use binary search on partitions instead.
Task
Implement an O(log(min(m, n))) time algorithm to find the median of two sorted arrays without fully merging them.
Examples
Even total length
Input
nums1 = [1, 2], nums2 = [3, 4]
Output
2.5
Combined sorted array is [1,2,3,4]; median is (2+3)/2 = 2.5.
Input format
Two Python lists of numbers: nums1 and nums2 (both sorted ascending).
Output format
A single number (float) — the median of the combined arrays.
Constraints
0 <= m, n <= 10^5. Elements are comparable. Aim for O(log(min(m, n))) time and O(1) extra space.
Samples
Sample 1
Input
nums1 = [0, 0], nums2 = [0, 0]
Output
0.0
All elements are zero; median is 0.0.