Minimize Sum of Absolute Differences
Reported by candidates from Amazon's online assessment. Pattern, common pitfall, and the honest play if you blank under the timer.
Amazon's March 2024 OA included this median-finding problem disguised as an optimization question. You're given an array and need to pick a single value that minimizes the sum of absolute differences to all elements. The trap is overthinking it. Most candidates try greedy or DP first. The answer is simpler: the optimal value is always the median of the array. Sort, pick the middle element, calculate the sum. That's it. StealthCoder can confirm your median logic in real time if you second-guess yourself during the OA.
Pattern and pitfall
The mathematical principle here is that the median minimizes L1 distance (sum of absolute deviations). If you pick any other value, the total distance grows. The algorithm: sort the array, grab the median (for even-length arrays, either middle element works), then iterate through once summing abs(element - median). Time is O(n log n) for sort, O(n) for the sum. The pitfall is candidates trying to binary search for the optimal value or use prefix sums unnecessarily. You don't need DP. You don't need optimization beyond the sort. Amazon likes this because it tests whether you know the statistical property, not just brute force. If you blank on why the median works, StealthCoder gives you the pattern instantly so you can code confidently.
Drill it cold or hedge it with StealthCoder. Either way, don't walk into the OA hoping you remember the trick.
You can drill Minimize Sum of Absolute Differences cold, or you can hedge it. StealthCoder runs invisibly during screen share and surfaces a working solution in under 2 seconds. The proctor sees the IDE. They don't see what's behind it. Made for the candidate who got the OA invite this morning and has 72 hours, not six months.
Get StealthCoderRelated leaked OAs
This OA pattern shows up on LeetCode as best meeting point. If you have time before the OA, drill that.
You've seen the question.
Make sure you actually pass Amazon's OA.
Amazon reuses patterns across OAs. Made for the candidate who got the OA invite this morning and has 72 hours, not six months. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Minimize Sum of Absolute Differences FAQ
Why is the median always the answer?+
The median minimizes sum of absolute deviations mathematically. For any value left of median, moving right decreases total distance. Right of median, moving left decreases it. The median is the equilibrium point. Amazon tests this property specifically, not your ability to derive it.
What if the array has even length?+
Pick either middle element (index n/2 or n/2 - 1). Both give the same sum of absolute differences. The median isn't unique for even-length arrays, but the result is. Pick one and move on.
Do I need to handle negative numbers or decimals?+
The problem likely uses integers. Negatives work fine with absolute value. Decimals don't matter for the median approach. Sort, pick median, sum abs differences. The logic is identical regardless.
Can I optimize space by not sorting?+
You need to sort to find the median efficiently. O(n log n) time, O(1) or O(n) space depending on sort implementation. Don't skip the sort trying to be clever. Amazon expects straightforward implementation here.
Is this really what Amazon asked in March 2024?+
Yes, reported by candidates in March 2024. It's a classic median-minimization problem. Amazon cycles this pattern regularly. If you see optimization + absolute differences, think median first.