Amazon·Software Engineer·Online Assessment (OA)·Intermediate

Intermediate

May 2026

Summary

Amazon SWE coding question, one problem about range increment operations on an array. Pretty clean problem once you see the pattern but I spent too long second-guessing my greedy approach.

Questions Asked (1)

Given an integer array, you can repeatedly pick any subarray and add a positive integer to every element in it. What is the minimum total sum of all added values needed to make the array non-decreasing?

Algorithms & Data Structures

Author's notes

Took me a while to realize this reduces to looking at the difference array.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Reframe the problem as finding the minimum total increments to make the array non-decreasing, where each increment operation adds a positive value to a contiguous subarray. Recognize that the optimal strategy is to increment each element just enough to match the previous element, and the total cost equals the sum of positive differences between consecutive elements. Present a greedy algorithm that scans the array once, accumulating the required increments.

Pro tip: Clarify that the increments must be positive integers, but the total sum is what matters; the greedy approach works because any increment to a later element can be shifted to earlier elements without increasing cost, and the minimum cost is exactly the sum of positive differences.

1. Understand the problem and constraints

Restate the problem: we can add a positive integer to any subarray, and we want the minimum total sum of added values to make the array non-decreasing. Note that the array elements are integers, and the added values are positive integers.

2. Identify the greedy strategy

Observe that to make the array non-decreasing, each element must be at least as large as the previous one. The minimal total increments can be achieved by only increasing elements that are smaller than their predecessor, and the amount needed is the difference.

3. Derive the formula

The minimum total sum of added values is the sum over all i from 1 to n-1 of max(0, a[i-1] - a[i]). This is because each such difference must be compensated by increments, and increments can be applied independently to each element without affecting others.

4. Validate with examples

Test the formula on simple cases: e.g., [3,2,1] requires increments of 1 and 1 (total 2) to become [3,3,3]; [1,2,3] requires 0; [5,1,1] requires 4 and 4 (total 8) to become [5,5,5]. Confirm that the sum of positive differences matches.

5. Analyze complexity and edge cases

The algorithm runs in O(n) time and O(1) space. Edge cases include already non-decreasing arrays (cost 0), strictly decreasing arrays, and arrays with negative numbers (the formula still holds).

Key Points to Mention

Greedy approach: only increase elements that are smaller than the previous element.
The minimum total sum is the sum of positive differences between consecutive elements.
Each increment operation can be applied to a subarray, but the optimal solution only requires incrementing individual elements (or contiguous segments) to match the previous maximum.
Proof of optimality: any valid solution must add at least the positive difference for each adjacent pair, and the greedy solution achieves exactly that bound.
Time complexity O(n) and space complexity O(1).
Handling of edge cases: already non-decreasing array, all equal elements, negative numbers.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.