Amazon·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

Jun 2026

Summary

Amazon SWE coding round with a greedy string-building problem that looked approachable until the state-flip mechanic made it way more annoying than expected. The heap-with-lazy-admission pattern was the key insight I didn't fully have going in.

Questions Asked (1)

Given an array of positive integers and a binary state string of the same length, build a result sequence of length m by repeatedly picking the largest currently available element (available means state[i] == '1'). After each pick, any '0' in the state that sits directly to the right of a '1' flips to '1', unlocking more elements. Return the lexicographically largest result sequence.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I spent the first few minutes thinking this was just a straightforward greedy max problem and almost missed the flip mechanic entirely.

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AI HintsAI Generated

Suggested Approach

Model the problem as a greedy selection with dynamic availability: at each step, pick the maximum available element, then update the state by flipping any '0' immediately to the right of a '1'. Use a max-heap to efficiently retrieve the largest available element and a queue or set to track newly unlocked indices, ensuring O(n log n) time.

Pro tip: Clarify that the greedy choice is optimal because picking the largest available element never restricts future availability—unlocking only depends on the state, not on which element was picked. Also, mention that you can precompute the unlock propagation to avoid redundant scans.

1. Understand the mechanics

Restate the problem: you have an array of positive integers and a binary state string. At each step, pick the largest available element (state[i] == '1'), then flip any '0' directly to the right of a '1' to '1'. Repeat until you have m elements.

2. Identify the greedy strategy

Recognize that to get the lexicographically largest result, you should always pick the largest available element at each step. This greedy choice is safe because picking an element does not affect which elements become available later—only the state updates matter.

3. Design efficient data structures

Use a max-heap to store available elements (by value) for O(log n) extraction. Maintain the state string and a queue or list of indices to process for unlocking. When an element is picked, check its right neighbor: if state is '0', flip it to '1' and add that index to the heap.

4. Handle unlocking propagation

After flipping a '0' to '1', that new '1' may cause further flips to its right. Use a while loop or recursive function to propagate flips until no more '0's are directly right of a '1'. Add all newly available indices to the heap.

5. Analyze complexity and edge cases

Time complexity: O(n log n) due to heap operations, with each index added at most once. Space: O(n). Discuss edge cases: m=0, all states '0', all states '1', and large n. Confirm that the result length is exactly m.

Key Points to Mention

Greedy choice property: picking the largest available element is optimal for lexicographically largest sequence.
Use of a max-heap (priority queue) to efficiently retrieve the largest available element.
State update mechanism: flipping '0' to '1' only when directly right of a '1', and propagating flips.
Time and space complexity analysis: O(n log n) time, O(n) space.
Edge cases: m=0, no available elements initially, all elements available, and large input sizes.
Proof of correctness: exchange argument showing that any deviation from greedy yields a lexicographically smaller or equal sequence.

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