Pinterest·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

Pinterest ML engineer round, one algorithmic problem that sounds deceptively simple but has a real O(n) trick buried in it. Left feeling like I probably over-explained the brute force before getting to the good part.

Questions Asked (1)

Given an array and an odd-sized sliding window, for each window position determine whether the values form a 'bitonic' shape centered on the middle element, meaning strictly decreasing in both directions away from the center. Return the positions where this holds. What is the time complexity of your solution, and can you achieve O(n)?

Algorithms & Data Structures

Author's notes

Spent way too long on the naive approach, checking each window independently which is obviously O(nk).

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AI HintsAI Generated

Suggested Approach

First, clarify the problem: for each window of size k (odd), check if the middle element is strictly greater than its immediate neighbors, and the sequence strictly decreases as you move away from the center in both directions. Then, propose an O(n) solution using precomputed arrays that track the length of decreasing runs to the left and right of each index, and for each window center, check if the required decreasing lengths are met. Finally, analyze the time and space complexity, emphasizing the O(n) time and O(n) space trade-off.

Pro tip: Mention that this is essentially a 'mountain array' check for each window, and that by precomputing the longest decreasing run ending at each index and the longest decreasing run starting at each index, you can answer each window in O(1) time, achieving overall O(n). Also, note that the problem can be solved in O(n) time with O(n) extra space, or O(n) time with O(1) extra space if you use a sliding window with two pointers, but the precomputation method is simpler to implement and explain.

1. Clarify the problem and edge cases

Confirm that the window size is odd, and that 'bitonic centered on the middle' means strictly decreasing from the center to both ends. Discuss edge cases: window size 1 (always true), array length less than window size, and handling of equal adjacent elements (should break the decreasing condition).

2. Propose a brute-force approach and its complexity

For each window, check the bitonic property by scanning from the center outwards. This takes O(n*k) time, which is O(n^2) if k is O(n). Acknowledge that this is not optimal.

3. Design an O(n) solution using precomputed decreasing runs

Create two arrays: left[i] = length of the longest strictly decreasing contiguous subarray ending at i (including i), and right[i] = length of the longest strictly decreasing contiguous subarray starting at i (including i). For a window centered at i with half-size h = (k-1)/2, the window is bitonic if left[i] >= h+1 and right[i] >= h+1. Iterate over all possible centers and collect positions where this holds.

4. Analyze time and space complexity

Precomputation takes O(n) time and O(n) space. Checking each center takes O(1) time, so total O(n) time. Space can be reduced to O(1) if we only need to check a fixed window size, but the precomputation method is straightforward.

5. Discuss potential optimizations and trade-offs

Mention that if the window size is fixed, we can use a sliding window with two pointers to check the bitonic property in O(n) time and O(1) space, but it requires careful handling of the decreasing conditions. Also, note that the precomputation method can be adapted to return all valid centers efficiently.

Key Points to Mention

Definition of bitonic centered on middle: strictly decreasing in both directions from the center.
Brute-force O(n*k) time complexity and why it's suboptimal.
Precomputation of left and right decreasing run lengths to achieve O(1) per window check.
Overall O(n) time complexity with O(n) space, or O(1) space with sliding window.
Handling of edge cases: window size 1, equal adjacent elements, array length < window size.
Connection to 'mountain array' or 'bitonic sequence' problems, common in interviews.

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