Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Amazon coding round, one problem the whole time. The problem looked like a simple sliding window thing but the cost scheduling part tripped me up more than I expected.

Questions Asked (1)

You have a binary array of products (0s and 1s) and an integer k. Each operation lets you pick a contiguous subarray of exactly length k, pay a cost equal to its sum, then flip one 1 to a 0 within that window. Find the minimum total cost to eliminate all 1s.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

Took me a while to see why greedy even applies here.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem constraints and confirm that each operation flips exactly one 1 to 0 within the chosen window. Then, recognize that the optimal strategy is to always flip the leftmost remaining 1, choosing the window that minimizes the cost (i.e., the window with the fewest 1s) among those covering that 1. Use a greedy approach with a sliding window or priority queue to efficiently compute the minimum total cost.

Pro tip: Demonstrate awareness of trade-offs: a naive greedy that always picks the cheapest window containing any 1 may fail; instead, prove that fixing the leftmost 1 is optimal. Also, mention that if k is large, the cost can be computed in O(n) using a sliding window, but if k is small, a more complex data structure may be needed.

1. Clarify the problem

Ask clarifying questions: Is the array 0-indexed? Can we flip a 1 that is already 0? What if no 1 exists in the window? Confirm that each operation flips exactly one 1 to 0 and costs the sum of the window.

2. Identify the greedy choice

Argue that to minimize total cost, we should always eliminate the leftmost remaining 1 first, because any window covering it must include it, and delaying only increases future costs.

3. Design an efficient algorithm

For each leftmost 1, find the window of length k that covers it and has the minimum sum. This can be done by precomputing prefix sums and using a sliding window minimum over all valid windows, or by maintaining a data structure of window sums.

4. Analyze complexity and edge cases

Discuss time and space complexity. Consider edge cases: k > n, no 1s, all 1s, and windows that contain multiple 1s. Ensure the algorithm handles them correctly.

5. Test with examples

Walk through a small example (e.g., [1,0,1,0,1], k=3) to verify the greedy approach and compute the total cost. Compare with brute force for small n to validate.

Key Points to Mention

Greedy strategy: always eliminate the leftmost 1 to avoid higher future costs.
Window selection: among all windows of length k covering the leftmost 1, pick the one with the minimum sum (fewest 1s).
Efficiency: use prefix sums and a sliding window minimum (deque) to achieve O(n) time.
Edge cases: k > n (impossible if any 1s), no 1s (cost 0), all 1s (cost depends on k).
Proof of optimality: exchange argument showing that any optimal solution can be transformed to one that follows the greedy choice.
Trade-offs: if k is small, a priority queue of window sums might be simpler; if k is large, sliding window is better.

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