Apple·Data Scientist·Technical Phone Screen·Senior

Senior

May 2026

Summary

Apple data scientist interview with a heavy algorithms focus. The main problem was a subarray removal question with a bunch of follow-ups tacked on, and the whole thing felt more like a systems/algorithms round than anything data science specific.

Questions Asked (4)

Given an integer array, find the shortest contiguous subarray you can remove so that the remaining elements are non-decreasing. Return [-1,-1] if the array is already sorted. Your solution must run in O(n) time with O(1) extra space.

Algorithms & Data Structures

Author's notes

The prefix/suffix approach clicked for me pretty fast but i fumbled the two-pointer bridging step.

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AI HintsAI Generated

Suggested Approach

First, identify the longest non-decreasing prefix and suffix. Then, use a two-pointer technique to find the minimal window to remove by checking if the middle part can be removed to connect the prefix and suffix, or if removing a subarray that includes part of the prefix or suffix yields a shorter removal. Return the shortest such subarray, or [-1,-1] if already sorted.

Pro tip: Emphasize that the solution must be O(n) time and O(1) space, so avoid extra arrays; instead, use indices and two pointers to track the boundaries. Also, consider edge cases like arrays of length 1 or 2, and arrays that are already sorted or reverse sorted.

1. Find longest non-decreasing prefix

Iterate from the start until the array is no longer non-decreasing, and record the end index of the prefix.

2. Find longest non-decreasing suffix

Iterate from the end backwards until the array is no longer non-decreasing, and record the start index of the suffix.

3. Check if array already sorted

If the prefix covers the entire array, return [-1,-1] as no removal is needed.

4. Initialize minimal removal window

Set the minimal window as removing either the entire suffix (i.e., from prefix_end+1 to n-1) or the entire prefix (i.e., from 0 to suffix_start-1), and update the minimum length accordingly.

5. Two-pointer to minimize window

Use two pointers: one starting at the end of the prefix and one at the start of the suffix. Move the pointer on the prefix side to find the smallest window such that the element at the prefix pointer is <= element at the suffix pointer, updating the minimal window length and boundaries.

Key Points to Mention

Time complexity O(n) and space complexity O(1) are required; avoid using extra arrays.
The removal window can be found by considering the longest non-decreasing prefix and suffix.
Two-pointer technique to efficiently find the minimal window that connects the prefix and suffix.
Edge cases: already sorted array returns [-1,-1], array of length 1 or 2, and arrays that are strictly decreasing.
The answer should return the indices of the shortest subarray to remove, not the length.
Explain why the two-pointer approach covers all possible minimal windows, including those that start before the prefix end or end after the suffix start.

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

How would you adapt this solution to handle streaming input where memory is limited? What data structures would you use and what are the trade-offs?

Algorithms & Data StructuresTechnical Trade-offsSystem Design

Author's notes

Wasn't expecting this pivot at all.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the constraints: what is the data volume, velocity, and available memory? Then propose a streaming architecture using appropriate data structures like sketches, sliding windows, or online algorithms, and discuss trade-offs in accuracy, latency, and complexity. Emphasize that the choice depends on the specific problem and metrics.

Pro tip: At Apple, interviewers value practical, production-ready solutions. Mention how you would monitor and validate the streaming solution in a real system, and be prepared to discuss how you would handle concept drift or data distribution changes.

1. Clarify Requirements and Constraints

Ask about data characteristics (volume, velocity, variety), memory limits, latency requirements, and accuracy expectations. This ensures your solution aligns with the actual problem.

2. Identify Core Operations

Determine what computations are needed (e.g., counting, aggregation, anomaly detection) and whether they can be approximated or must be exact.

3. Select Data Structures and Algorithms

Choose memory-efficient structures like Bloom filters, Count-Min Sketch, HyperLogLog, or sliding windows. Explain why they fit the operations and constraints.

4. Analyze Trade-offs

Discuss trade-offs between memory usage, accuracy, latency, and implementation complexity. Compare alternatives and justify your choices.

5. Consider Scalability and Robustness

Address how the solution handles increasing data rates, out-of-order data, and failures. Mention monitoring and adaptation strategies.

Key Points to Mention

Probabilistic data structures (e.g., Count-Min Sketch, HyperLogLog) for approximate counting with bounded memory.
Sliding window or exponential decay models for time-sensitive aggregations.
Online algorithms (e.g., stochastic gradient descent, reservoir sampling) that process data in one pass.
Trade-offs: memory vs. accuracy, latency vs. throughput, and simplicity vs. performance.
Handling out-of-order or late-arriving data with watermarks or allowed lateness.
Monitoring and validation: how to detect drift and ensure the streaming solution remains effective.

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

Can you verify in a single pass whether a given (L, R) pair is actually the optimal solution?

Algorithms & Data Structures

Author's notes

Short answer: yes, but i fumbled explaining why.

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AI HintsAI Generated

Suggested Approach

First, clarify what 'optimal' means for the (L, R) pair—likely the maximum sum subarray or similar. Then, propose a single-pass algorithm that maintains the best solution seen so far and checks if the given (L, R) matches it, using O(1) extra space and O(n) time.

Pro tip: Mention that a single pass is possible only if the optimality condition can be checked incrementally; otherwise, you might need to precompute or use a two-pass approach. This shows you understand the trade-offs.

1. Clarify the problem and optimality criteria

Ask the interviewer to define what 'optimal' means for (L, R) in this context (e.g., maximum sum, longest subarray with property X). Confirm the input format and constraints.

2. Identify the single-pass algorithm

Choose an algorithm that computes the optimal (L, R) in one pass, such as Kadane's algorithm for maximum subarray sum. Explain how it maintains the current best and global best.

3. Adapt to verify a given (L, R)

Modify the algorithm to track whether the given (L, R) is encountered as the optimal solution during the pass. This may involve comparing the value of (L, R) with the current best at each step.

4. Handle edge cases and complexity

Discuss edge cases (e.g., all negative numbers, empty subarray) and confirm time and space complexity: O(n) time, O(1) space.

5. Validate with examples

Walk through a small example to demonstrate the single-pass verification, showing how the given (L, R) is checked against the running optimal.

Key Points to Mention

Kadane's algorithm or similar dynamic programming approach for single-pass optimal subarray
Maintaining current best and global best (and their indices) during the pass
Time complexity O(n) and space complexity O(1)
Edge cases: all negative numbers, multiple optimal subarrays, empty subarray
The importance of clarifying the definition of 'optimal' (e.g., maximum sum, minimum length)
Potential need for tie-breaking rules if multiple (L, R) pairs are optimal

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

How would you extend the solution if the target condition is strictly increasing instead of non-decreasing? What if you're allowed up to k deletions rather than a single contiguous removal?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The strictly increasing variant felt manageable, just tighten the comparison operator.

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AI HintsAI Generated

Suggested Approach

First, clarify the problem: the original likely asks for the longest non-decreasing subarray after removing one contiguous subarray. For strictly increasing, adjust the merge condition to require strictly greater. For up to k deletions, consider dynamic programming or sliding window with a deletion budget, but discuss trade-offs between time and space complexity.

Pro tip: Demonstrate awareness of edge cases (e.g., k >= n, all equal elements) and mention that for k deletions, a greedy approach may not work, so DP or binary search with prefix/suffix arrays is needed. Also, relate to real-world data cleaning where deletions represent removing outliers.

1. Clarify the original problem and assumptions

Restate the original problem: given an array, remove one contiguous subarray to maximize the length of a non-decreasing subarray. Confirm if the goal is to return the length or the subarray itself.

2. Adapt for strictly increasing condition

Change the merge condition from 'left <= right' to 'left < right'. Discuss how this affects the algorithm, especially when equal elements are present, and note that the maximum length may decrease.

3. Generalize to up to k deletions

Consider two approaches: (1) Dynamic programming with state (index, deletions used, last value) but optimize using coordinate compression or binary search; (2) Sliding window with a deletion counter, but note it only works for non-decreasing if we can skip elements, not for contiguous removal. Clarify that 'k deletions' likely means removing up to k individual elements, not a contiguous block.

4. Analyze time and space complexity

For strictly increasing with one contiguous removal, O(n) time and space. For k deletions, DP may be O(n*k) or O(n log n) with optimizations. Discuss trade-offs and potential for binary search on answer.

5. Discuss edge cases and testing

Mention edge cases: k=0, k>=n, array already strictly increasing, all elements equal, and negative numbers. Suggest testing with small arrays and comparing with brute force.

Key Points to Mention

Difference between non-decreasing and strictly increasing: equality condition changes.
For one contiguous removal, precompute prefix and suffix arrays of longest non-decreasing subarrays.
For k deletions, dynamic programming with state (index, deletions used) and transition using binary search for previous valid element.
Sliding window with deletion budget works for non-decreasing if we can skip elements, but not for contiguous removal.
Time complexity: O(n) for one removal, O(n*k) or O(n log n) for k deletions with optimization.
Edge cases: k=0, k>=n, all equal elements, and arrays with duplicates.

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