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Median of Two Sorted Arrays for Senior Backend Engineer — Interview Guide

How to approach Median of Two Sorted Arrays as a Senior Backend Engineer: the optimal approach, what Senior Backend Engineer interviewers evaluate, and role-specific tips.

Updated 2026-09HardBinary Search

The problem for a Senior Backend Engineer

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

As a Senior Backend Engineer, interviewers expect you to not only solve the problem but also demonstrate apis, data, and distributed systems. Be ready to discuss trade-offs and production concerns relevant to the role.

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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