Amazon·Software Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Amazon Applied Scientist interview with a greedy algorithm problem around task scheduling under a time budget. Pretty standard stuff if you've seen this pattern before, but the setup takes a minute to parse.

Questions Asked (1)

Given two arrays of equal length where one represents total time required for each task and the other represents time already spent, and given a total additional time budget, how do you allocate the budget to maximize the number of tasks you can complete?

Algorithms & Data Structures

Author's notes

The key move is computing the remaining time per task and sorting ascending, then greedily finishing the cheapest tasks first until the budget runs out.

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AI HintsAI Generated

Suggested Approach

First, compute the remaining time needed for each task by subtracting time already spent from total time. Then, sort these remaining times in ascending order and greedily allocate the budget to the tasks with the smallest remaining times until the budget is exhausted. This greedy strategy maximizes the number of completed tasks.

Pro tip: Mention that this is a classic greedy problem where sorting by remaining time is optimal, and briefly discuss the time complexity (O(n log n)) and why a greedy approach works here (exchange argument).

1. Understand the problem

Clarify that you need to maximize the count of tasks completed by allocating additional time, where each task requires some remaining time to finish.

2. Compute remaining times

For each task, calculate the remaining time as total time minus time already spent. Ignore tasks that are already complete (remaining time <= 0).

3. Sort remaining times

Sort the remaining times in ascending order to prioritize tasks that require the least additional time.

4. Greedily allocate budget

Iterate through the sorted remaining times, subtracting each from the budget and incrementing the count until the budget is insufficient for the next task.

5. Return the count

The count of tasks successfully allocated within the budget is the maximum number of tasks that can be completed.

Key Points to Mention

Greedy algorithm: always pick the task with the smallest remaining time first.
Sorting the remaining times is crucial for optimality.
Time complexity: O(n log n) due to sorting, where n is the number of tasks.
Space complexity: O(n) if storing remaining times, or O(1) extra if modifying input.
Edge cases: tasks with zero or negative remaining time are already complete and should be counted without using budget.
Proof of optimality: exchange argument showing that swapping a chosen task with a smaller remaining time never decreases the count.

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