Atlassian·Data Scientist·Technical Phone Screen·Senior

SeniorPrefer not to say

Jul 2026Remote

Summary

Atlassian Data Scientist interview with a pretty brutal algorithmic question that felt more like a competitive programming contest than anything I'd call data science. One question, lots of depth required, and I'm still not sure I nailed the proof parts.

Questions Asked (1)

Given an array of n integers and an integer k, place k cluster centers on the real line to minimize the maximum L1 distance from any point to its nearest center. Design an algorithm faster than O(nk), prove correctness, handle large coordinates, and reconstruct the actual center positions.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

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AI HintsAI Generated

Suggested Approach

First, sort the array and recognize that the optimal clusters are contiguous segments. Then, binary search on the answer D (the maximum allowed distance) and check feasibility in O(n) using a greedy sweep, yielding O(n log n + n log range). Finally, reconstruct the centers by placing them at the midpoint of each segment's extreme points.

Pro tip: Mention that the greedy check is optimal because any valid clustering can be transformed into a contiguous one without increasing the maximum distance, and use integer arithmetic to avoid floating-point issues with large coordinates.

1. Sort and Define Decision Problem

Sort the array in O(n log n). Define the decision problem: given D, can we cover all points with k centers such that each point is within L1 distance D of some center?

2. Greedy Feasibility Check

For a fixed D, scan left to right: place a center at the midpoint of the current uncovered point and the farthest point within distance 2D, then skip all points within D of this center. Count centers; feasible if count ≤ k.

3. Binary Search for Optimal D

Binary search the minimal D in [0, max_coord - min_coord] using the feasibility check. Each check is O(n), so total O(n log n + n log range).

4. Reconstruct Centers

During the final feasibility check (or a separate pass with the optimal D), record the center positions placed by the greedy algorithm. These are the actual centers.

5. Prove Correctness

Argue that the greedy check is optimal: any valid solution can be shifted to align with the greedy choices without increasing the maximum distance, and binary search finds the minimal D.

Key Points to Mention

Sorting enables contiguous clusters and simplifies the greedy check.
Binary search on the answer D reduces the problem to a decision problem solvable in O(n).
Greedy placement: for each uncovered point, place a center at the midpoint of the interval covering as many points as possible within distance D.
Use integer arithmetic (e.g., compare 2*D) to handle large coordinates and avoid floating-point errors.
Reconstruction: store the centers chosen during the greedy pass with the optimal D.
Complexity: O(n log n + n log C) where C is the coordinate range, which is faster than O(nk) for large n and k.

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