What is the time and space complexity of Median of Two Sorted Arrays?

Time complexity: O(log(min(m,n))). Space complexity: O(1).

Median of Two Sorted Arrays

Hard

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Solution Guide: Median of Two Sorted Arrays

Approach

Ensure nums1 is the shorter array. Binary search on the partition index i of nums1, compute j for nums2 so the left half has exactly half the total elements. Valid partition means max(left sides) <= min(right sides).

Complexity Analysis

Time: O(log(min(m,n)))
Space: O(1)

Pattern

Binary Search (Boundary Finding)

Why It Works

Binary search on where to partition the smaller array. The combined partition must have exactly half the total elements, and max of left side must be less than or equal to min of right side.

Updated Feb 2026