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Median of Two Sorted Arrays at Google — Interview Guide

How to approach Median of Two Sorted Arrays in a Google interview: the optimal approach, what Google interviewers look for, and company-specific tips.

Updated 2026-09HardBinary Search

The problem at Google

Given two sorted arrays, find the median of the combined sorted array in O(log(min(m,n))) time.

Google uses this problem to assess algorithmic rigor and generalist problem-solving. Expect Google-specific follow-ups that tie the solution back to production reasoning and the company's engineering bar.

Key concepts

Binary search a partition point in the smaller array so the left half of the merged array contains exactly half the elements.
A valid partition has maxLeftA ≤ minRightB and maxLeftB ≤ minRightA.
Adjust the partition by comparing maxLeftA with minRightB.

Approach

Ensure A is the smaller array; binary search a cut i in A, with j = (m+n+1)//2 - i in B.
If A[i-1] > B[j], move the cut left; if B[j-1] > A[i], move right.
When valid, compute the median from the edge elements (handle even/odd total length).

Complexity

Metric	Value
Time	O(log(min(m,n)))
Space	O(1)

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