Amazon·Machine Learning Engineer·Technical Phone Screen·Senior

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Apr 2026

Summary

Amazon ML Engineer technical screen, basically a deep dive on binary search fundamentals. Not glamorous but they really wanted to see if you understood the mechanics, not just the pattern.

Questions Asked (1)

Implement lower_bound and upper_bound on a sorted integer array using binary search, handling edge cases like empty arrays, duplicates, and out-of-range targets. Also explain your loop invariants and argue correctness.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

More involved than I expected for a phone screen.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the definitions of lower_bound and upper_bound and the expected behavior for edge cases. Then present a unified binary search template with explicit loop invariants, and walk through correctness arguments and complexity for each function.

Pro tip: Emphasize that lower_bound and upper_bound are the building blocks for counting occurrences and range queries, which are common in ML feature engineering and data preprocessing at scale. Mention that using a single template reduces off-by-one errors and makes the code easier to verify.

1. Clarify definitions and edge cases

Define lower_bound as the first index where arr[i] >= target, and upper_bound as the first index where arr[i] > target. Explicitly state handling for empty arrays, duplicates, and targets outside the array range.

2. Present a unified binary search template

Use a half-open interval [lo, hi) with while lo < hi and mid = lo + (hi - lo) // 2. For lower_bound, if arr[mid] < target, lo = mid + 1; else hi = mid. For upper_bound, if arr[mid] <= target, lo = mid + 1; else hi = mid.

3. State loop invariants and prove correctness

Invariant: answer lies in [lo, hi). Show that each iteration preserves the invariant and that termination yields lo == hi, which is the correct insertion point. Argue that the returned index satisfies the definition and that all elements before it are < target (for lower_bound) or <= target (for upper_bound).

4. Analyze complexity and edge cases

Time complexity is O(log n) and space O(1). Walk through edge cases: empty array returns 0; target smaller than all elements returns 0; target larger than all elements returns n; duplicates are handled correctly because the search continues to the leftmost or rightmost boundary.

5. Connect to practical applications

Mention how these functions enable counting occurrences (upper_bound - lower_bound) and range queries, which are useful in ML for bucketing continuous features, handling imbalanced datasets, and efficient lookups in sorted arrays.

Key Points to Mention

Definition of lower_bound (first index with arr[i] >= target) and upper_bound (first index with arr[i] > target).
Use of half-open interval [lo, hi) and mid calculation to avoid overflow and infinite loops.
Loop invariant: the answer is always within [lo, hi), and termination when lo == hi.
Correctness argument: after loop, lo is the smallest index satisfying the condition, and all elements before lo do not satisfy it.
Edge cases: empty array, target out of range (smaller than min or larger than max), and duplicates.
Time complexity O(log n) and space O(1), with a note on practical applications in ML feature engineering.

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