Amazon·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Amazon SWE coding round, one problem the whole time. Felt like a heap problem dressed up to look harder than it was, but the follow-up about duplicates is where things got interesting.

Questions Asked (1)

Given an integer array and a count n, perform n operations where each operation takes the current max and min, records their sum, then decrements the max by 1. Return all n sums. How do you implement this efficiently, and what do you do when the same value appears in both heaps?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Got the two-heap setup pretty quickly, max-heap for the top, min-heap for the bottom, pop and push each round.

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AI HintsAI Generated

Suggested Approach

Use two heaps (max-heap and min-heap) to efficiently track the current maximum and minimum, ensuring O(log n) per operation. Address the duplicate value issue by maintaining a shared count map or using lazy deletion to avoid incorrect removals. Clearly explain the algorithm, complexity, and edge cases.

Pro tip: Mention that you can avoid the duplicate problem entirely by using a balanced BST (like a multiset) if the language supports it, but if using heaps, always validate that the popped element is still present and update counts accordingly.

1. Clarify the problem and constraints

Confirm the operation: each step, find current max and min, record their sum, then decrement the max by 1. Ask about array size, value ranges, and whether n can exceed array length.

2. Choose the right data structures

Use a max-heap and a min-heap to track the maximum and minimum efficiently. To handle duplicates, maintain a frequency map or use a balanced BST (e.g., multiset) that supports duplicates.

3. Handle the duplicate value issue

If the same value appears in both heaps, ensure you don't remove the same element twice. Use lazy deletion: when popping, check if the value is still present in the frequency map; if not, discard and pop again.

4. Implement the operations

For each of the n operations: extract min and max (with lazy deletion), compute sum, decrement max by 1, and reinsert the updated max into both heaps (or update the multiset). Record the sum.

5. Analyze complexity and edge cases

Time complexity: O(n log m) where m is the number of elements. Space: O(m). Discuss edge cases: empty array, n larger than possible operations, all elements equal, etc.

Key Points to Mention

Use of two heaps (max-heap and min-heap) for O(log n) access to extremes.
Handling duplicates via frequency map or lazy deletion to avoid removing the same element twice.
Alternative: balanced BST (e.g., multiset) that naturally handles duplicates and provides O(log n) operations.
Time and space complexity analysis: O(n log m) time, O(m) space.
Edge cases: empty array, n > array length, all elements equal, negative numbers.
Correctness: ensure that after decrementing max, it is reinserted correctly and the heaps remain valid.

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