Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jul 2026

Summary

Amazon SWE coding round with one algorithmic problem. Pretty clean problem once the key insight clicks, but I spent way too long trying to simulate operations before stepping back and thinking about it differently.

Questions Asked (1)

You have an integer array. In one operation, you can pick any contiguous subarray and add a positive integer to every element in it. The final array must be non-decreasing. Minimize the total sum of all values added across all operations.

Algorithms & Data Structures

Author's notes

Spent probably 10 minutes trying to think about greedy subarray coverage before I realized you don't need to simulate anything.

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AI HintsAI Generated

Suggested Approach

First, clarify that the goal is to make the array non-decreasing by only adding positive integers to contiguous subarrays, and that we want to minimize the total added sum. Then, derive the optimal strategy: for each position where the array decreases, add the difference to the suffix starting at that position, which is equivalent to setting each element to the running maximum of the original array. Finally, compute the total added sum as the sum of (running maximum - original value) for each element.

Pro tip: Mention that the optimal solution is to make each element equal to the maximum of all previous elements, and that the total added sum is simply the sum of differences between the running maximum and the original array. This shows you understand the greedy nature and can reduce the problem to a simple O(n) computation.

1. Understand the problem and constraints

Restate the problem: we can only add positive integers to contiguous subarrays, and the final array must be non-decreasing. We need to minimize the total sum of additions.

2. Identify the optimal strategy

Observe that to make the array non-decreasing, each element must be at least as large as the previous element. The minimal way is to set each element to the maximum of all elements up to that point (the running maximum).

3. Prove optimality

Argue that any valid final array must have each element >= the running maximum of the original array, so the minimal total addition is achieved by setting each element exactly to the running maximum.

4. Compute the total added sum

Iterate through the array, keep track of the running maximum, and sum the differences between the running maximum and the original element. This gives the minimal total sum of additions.

5. Analyze complexity and edge cases

The algorithm runs in O(n) time and O(1) extra space. Handle edge cases like already non-decreasing arrays (sum = 0) and arrays with negative numbers (running maximum may be negative, but additions are still positive).

Key Points to Mention

The operation allows adding to any contiguous subarray, but the optimal solution only requires adding to suffixes.
The final array must be non-decreasing, so each element must be at least the previous element.
The minimal final array is the running maximum of the original array.
The total added sum is the sum of (running maximum - original value) for each element.
Time complexity is O(n) and space complexity is O(1).
Edge cases: already non-decreasing array (sum = 0), negative numbers, and large integers (use 64-bit integers).

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